JP2013206201A - Detection method, detection device and detection program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce an arithmetic quantity required for the detection of a combination of output values which is better than the clarified combination of output values.SOLUTION: A detection device performs integration processing to each parameter of an initial parameter group reaching from the minimum parameter to the maximum parameter, and performs division processing to each parameter of a plurality of parameters after integration. The detection device gives each parameter of the plurality of parameters after division to first and second objective functions, and calculates a combination of output values of the first and second objective functions as for each parameter of the plurality of parameters after division. The detection device detects, from the calculated combination of the output values and the combination of the output values of the first and second objective functions as for each parameter of the initial parameter group, the combination as a candidate of a non-dominated solution. A graph 902 shows the state of update of the combination as the candidate of the non-dominated solution.

Description

  The present invention relates to a detection method, a detection device, and a detection program.

  Conventionally, there is a technique in which a plurality of descriptions of an execution target program are grouped, an output value related to one index is calculated for each grouping method, and a grouping method for specifying a group in which the output value satisfies a certain condition is specified. (For example, refer to Patent Document 1 below.) Further, for example, there is a technique for calculating output values of a plurality of indices when an optimal group candidate is specified from a plurality of group candidates (see, for example, Patent Document 2 below). Specifically, for example, when determining which production facility is used to process a lot grouping in which one or more lots are grouped, each of a plurality of group candidates that are a combination of lot grouping and production facility , The output value of each of the plurality of indices is calculated. Then, by specifying the non-inferior solution from the calculated output values of the plurality of indices, the optimum group candidate is identified from the plurality of group candidates. A non-inferior solution is a solution that is unclear as to whether it is an optimal solution but is not superior to any other solution. Whether the solution is superior to other solutions is determined based on the order of the solutions determined by the output values of each of the plurality of indices.

JP 2004-185271 A JP 2008-33518 A

  However, if there are multiple indicators for identifying non-inferior solutions, the output values of each of the multiple indicators must be calculated for all groupings when the number of elements that make up the group is large. The amount of computation increases.

  In one aspect, an object of the present invention is to reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that has been found.

  In order to solve the above-described problem and achieve the object, according to one aspect of the present invention, a parameter having a plurality of groups each obtained by grouping element groups each having an observation value is acquired, and the acquired parameter is obtained. Two groups of the plurality of groups included in the parameter are integrated into one, and one group including two or more elements in the group of elements among the one or more groups included in the parameters after integration is It is divided into groups, and one of the two parameters each having one or a plurality of groups in which the element group is grouped includes any group that one parameter has, and any group that the other parameter has Observed values of each of the element groups when the one parameter of the two parameters for which the ordered relationship is established is given The output value calculated based on the storage content of the storage unit to be stored is smaller than the output value calculated based on the storage content of the storage unit when the other parameter of the two parameters is given. When the first objective function and the one parameter are given, the output value calculated based on the storage content of the storage unit is calculated based on the storage content of the storage unit when the other parameter is given Each of the second objective function that is larger than the output value to be output is provided with a parameter after dividing the certain group into two groups, so that the first and second objective functions are based on the storage contents of the storage unit. When a combination of output values of two objective functions is calculated, and the combination of the calculated output values and the acquired parameter are given to each of the first and second objective functions The combination of the output values of the first and second objective function, among the detection method of detecting a combination of a non-dominated solution candidate, the detection device, and a detection program is proposed.

  According to another aspect of the present invention, a parameter having one or more groups each obtained by grouping element groups each having an observation value is acquired, and one or more groups of the acquired parameters are included. Among them, a group including two or more elements in the element group is divided into two groups, two groups among a plurality of groups included in the parameters after the division are integrated into one, and the element group is The above-described order 2 is established in which any one of the two parameters each having one or a plurality of grouped groups has one parameter and the other parameter has an included order relationship. Storage contents of a storage unit that stores observation values of each of the element groups when the one parameter of the two parameters is given A first objective function that decreases below an output value calculated based on the storage content of the storage unit when the output value calculated based on the other parameter of the two parameters is given; When one parameter is given, the output value calculated based on the storage content of the storage unit is larger than the output value calculated based on the storage content of the storage unit when the other parameter is given. Each of the second objective functions is provided with a parameter after the integration of the two groups into one, so that the output values of the first and second objective functions can be calculated based on the storage contents of the storage unit. A combination is calculated, and the output combination of the calculated output value and the output of the first and second objective functions when the acquired parameter is given to each of the first and second objective functions. Value Pair, from among the detection method for detecting a combination of a candidate for the non-dominated solutions, detecting device, and a detection program is proposed.

  According to one embodiment of the present invention, it is possible to reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found.

FIG. 1 is an explanatory diagram showing a comparison between a detection result example according to the present invention and a conventional detection result example. FIG. 2 is an explanatory diagram illustrating an example of a set of parameters. FIG. 3 is an explanatory diagram illustrating an example of the order relationship. FIG. 4 is an explanatory diagram showing integration processing in the first embodiment of the present invention. FIG. 5 is an explanatory diagram showing division processing in the first embodiment of the present invention. FIG. 6 is an explanatory diagram showing a detection example of a non-inferior solution candidate in the first embodiment according to the present invention. FIG. 7 is an explanatory diagram showing division processing in the second embodiment of the present invention. FIG. 8 is an explanatory diagram showing integration processing in the second embodiment of the present invention. FIG. 9 is an explanatory diagram illustrating Example 1 in which a combination that is a candidate for a non-inferior solution is updated. FIG. 10 is an explanatory diagram illustrating Example 2 in which a combination that is a non-inferior solution candidate is updated. FIG. 11 is a block diagram of a hardware configuration example of the detection apparatus 400 according to the embodiment. FIG. 12 is an explanatory diagram illustrating an example of a power table for each business office. FIG. 13 is an explanatory diagram illustrating an example of a reference value table. FIG. 14 is an explanatory diagram illustrating an example of calculating the output value of the first objective function. FIG. 15 is an explanatory diagram illustrating an example of calculating the output value of the second objective function. FIG. 16 is a block diagram illustrating an example of functions of the detection apparatus 400. FIG. 17 is a flowchart illustrating a detection processing procedure example 1 performed by the detection apparatus 400. FIG. 18 is a flowchart illustrating a detection processing procedure example 2 performed by the detection apparatus 400. FIG. 19 is a flowchart (part 1) illustrating a detection processing procedure example 3 performed by the detection apparatus 400. FIG. 20 is a flowchart (part 2) illustrating a detection processing procedure example 3 performed by the detection apparatus 400. FIG. 21 is a flowchart (part 1) illustrating a detection processing procedure example 4 performed by the detection apparatus 400. FIG. 22 is a flowchart (part 2) illustrating a detection processing procedure example 4 performed by the detection apparatus 400. FIG. 23 is a flowchart (part 1) illustrating a detection processing procedure example 5 performed by the detection apparatus 400. FIG. 24 is a flowchart (part 2) illustrating a detection processing procedure example 5 performed by the detection apparatus 400. FIG. 25 is a flowchart (part 1) illustrating a detection processing procedure example 6 performed by the detection apparatus 400. FIG. 26 is a flowchart (part 2) illustrating a detection processing procedure example 6 performed by the detection apparatus 400. FIG. 27 is a flowchart (part 1) illustrating a detection processing procedure example 7 performed by the detection apparatus 400. FIG. 28 is a flowchart (part 2) illustrating a detection processing procedure example 7 performed by the detection apparatus 400. FIG. 29 is a flowchart (part 1) illustrating a detection processing procedure example 8 performed by the detection apparatus 400. FIG. 30 is a flowchart (part 2) illustrating a detection processing procedure example 8 performed by the detection apparatus 400. FIG. 31 is a flowchart (part 1) illustrating a detection processing procedure example 9 performed by the detection apparatus 400. FIG. 32 is a flowchart (part 2) illustrating a detection processing procedure example 9 performed by the detection apparatus 400. FIG. 33 is a flowchart (part 1) illustrating a detection processing procedure example 10 performed by the detection apparatus 400. FIG. 34 is a flowchart (part 2) illustrating a detection processing procedure example 10 performed by the detection apparatus 400. FIG. 35 is a diagram illustrating an application example of the detection apparatus 400.

  Exemplary embodiments of a detection method, a detection apparatus, and a detection program according to the present invention will be described below in detail with reference to the accompanying drawings. When there are a plurality of grouping methods that satisfy a given condition, the problem of finding an optimal grouping method from a plurality of grouping methods is called a combinatorial optimization problem. If there is one index for specifying a non-inferior solution, the output value of the index that is the maximum value or the minimum value may be specified as a non-inferior solution, but an index for specifying a non-inferior solution If there are multiple, there is a high possibility that the non-inferior solution is not uniquely identified. In the present embodiment, in the combination optimization problem, when there are two indexes for identifying a non-inferior solution, the amount of calculation required for detecting a combination of output values that is better than the combination of output values of the already known indexes To reduce

  FIG. 1 is an explanatory diagram showing a comparison between a detection result example according to the present invention and a conventional detection result example. The graph 100 shows an example of a detection result example of a combination that is a non-inferior solution candidate according to the present invention, a combination example of output values of the first and second objective functions by a random search, and a Pareto solution. . The output value is a calculation result obtained by giving a parameter to the objective function. A Pareto solution is a set of optimal solutions. As described above, a non-inferior solution is a combination of output values that is unknown whether it is an optimal solution, but is not superior to any other combination of output values calculated with two objective functions. Therefore, the non-inferior solution may be one or plural.

  Here, the objective function is an index for determining the superiority or inferiority of the grouping method. The objective function is a function that changes the output value along a given parameter using the grouping method as a parameter. There is a trade-off relationship between the first objective function and the second objective function. For example, since there is a trade-off relationship between two conditions that the product is light and strong, the output value of the first objective function is the lightness of the product, and the output value of the second objective function is the robustness of the product.

  In FIG. 1, the horizontal axis of the graph 100 is the output value of the first objective function, and the vertical axis of the graph 100 is the output value of the second objective function. Hereinafter, the first objective function is indicated as f1 (x) and the second objective function is indicated as f2 (x) on the mathematical formulas and graphs. x represents a parameter. The points marked with ○ and ● are combinations of output values of the first and second objective functions. A combination of output values of the first and second objective functions indicated by a circle is a combination of output values of the first and second objective functions by random search. The combinations of the output values of the first and second objective functions indicated by ● are combinations that are candidates for non-inferior solutions detected by the present embodiment.

  The reason why grouping is performed on the same element group is that the output values of the first and second objective functions differ depending on how the groups are grouped. An element group is a plurality of data constituting a group. Each element group has an observed value. Here, the element group is assumed to be a plurality of business establishments of a company, and the average power consumption of each business establishment and the reduction rate of peak power are given as examples. For example, a plurality of establishments are element groups, and the observed value of each of the element groups is the average power used for each time zone at the establishment. For example, peak power is the maximum value of average power usage. The peak power reduction rate is the ratio between the reference power and the maximum value of the average power used. The power value serving as a reference for each office and the average power used for several months for each office are stored in advance in a storage device accessible by the detection apparatus. In this case, for example, the first objective function is a function for calculating the sum of the peak powers of the groups included in the parameters. The peak power of the group is the peak power of the entire offices included in the group. The objective function of 2 is a function for calculating the minimum value of the ratio between the reference power and the group peak power.

  Here, a case where there are two offices as elements is taken as an example. In the office 1, the average power consumption is “2500 [W]” in the time zone 1 and the average power usage is “1800 [W]” in the time zone 2. On the other hand, the office 2 has an average power consumption of “0 [W]” in time zone 1 and an average power usage of “900 [W]” in time zone 2.

  When the establishment 1 and the establishment 2 are different groups, the peak power of the establishment 1 is “2500 [W]” and the peak power of the establishment 2 is “900 [W]”. The output value of the first objective function, which is the sum total of “3400”, is “3400 [W]”. On the other hand, when the business office 1 and the business office 2 are the same group, the average power used by the business office 1 and the business office 2 is the peak in the time zone 2, and the peak power is “2700 [ W] ”, the output value of the first objective function is“ 2700 [W] ”. Therefore, the output value of the first objective function varies depending on how the groups are divided even in the same element group. Similarly, the output value of the second objective function differs depending on how the second objective function is divided into groups.

  In the present embodiment, the combination of the output values of the first and second objective functions is included within a dotted square. On the graph 100, the position where the output values of the first and second objective functions are both maximum is the upper right in the dotted square frame. Therefore, the combination of non-inferior solutions becomes a curve that goes from the upper left end of the dotted square frame to the upper right end in the dotted square frame as in the Pareto solution of FIG.

For example, when the number of business sites as elements is 21, there are approximately 4.7 × 10 ¹⁴ ways to divide groups. Therefore, if the number of elements is large, it takes time to calculate the output values of the first and second objective functions for all parameters as in the full search. In the random search, the number of parameters to be calculated is determined in advance, and combinations of output values of the first and second objective functions are calculated for parameters arbitrarily selected by that number. For example, when the number of business sites as elements is 21, in the random search, about 10,000 parameters are randomly selected. In the random search, as the number of parameters given to the first and second objective functions increases, the Pareto solution as shown in FIG. 1 can be detected, but the calculation amount increases.

  In the present embodiment, the detection apparatus repeats the detection processing of combinations that are candidates for non-inferior solutions as indicated by thick arrows in FIG. 1, so that combinations that are candidates for non-inferior solutions are approached so as to approach the Pareto solution. Update. Therefore, in the present embodiment, it is possible to reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found.

  Next, the reason why the peak power is reduced for each group in the above-described example of the power consumption at the office will be described. For example, it is assumed that a company has a goal of reducing the average power consumption peak power consumed by a plurality of offices that consume power by 15% from the reference value. Although it is desirable to reduce the peak power by 15 [%] from the reference value for each business location, for example, in a factory where a data center or a 24-hour device is operating, constant power is consumed at all times. It is difficult to reduce power consumption by 15 [%] at a single business site. On the other hand, if the office employs only a device such as a PC (Personal Computer) during the day, the power consumed varies depending on the time of the day, so peak power can be reduced.

  Therefore, for example, in a certain company, a plurality of business offices are divided into several groups, and the peak power is reduced by 15 [%] from the reference value for each group. As described above, the combinations of the output values of the first and second objective functions differ depending on the parameters. However, when the number of establishments is large, combinations of the output values of the first and second objective functions are set for all parameters. It takes time to calculate. Therefore, in the present embodiment, the detection apparatus determines parameters to be given to the first and second objective functions by paying attention to the relationship between parameters existing in a plurality of parameters. Next, with reference to FIG. 2 and FIG. 3, the order relationship between the parameter set and a pair of parameters belonging to the parameter set will be described.

<Parameter set and order relation>
FIG. 2 is an explanatory diagram illustrating an example of a set of parameters. FIG. 2 shows a set P of parameters obtained by grouping element groups into one or a plurality of groups. FIG. 2 shows a parameter set P when the number of elements is four (F1 to F4). As described above, an element is data constituting a group, and each element has an observed value. The elements and the observation values are stored in a storage device such as a ROM (Read-Only Memory), a RAM (Random Access Memory), an optical disc, and a magnetic disc that can be accessed by the detection device in association with each other. In the power example described above, the element is a business office, and the observed value is the average power used.

  In the example of FIG. 2, when the number of elements is four, the number of parameters belonging to the set P is fifteen parameters M1 to M15. In the set P, the order relation of parameters is defined. The parameter order relationship can be expressed by using, for example, a relational element “≦”. Specifically, for example, the order relationship is established in the set P when the following 1) to 3) are established for arbitrary parameters a, b, and c belonging to the set P. In the following, 1) shows the reflection rule, 2) shows the antisymmetric rule, and 3) shows the transition rule.

1) a ≦ a
2) If a ≦ b and b ≦ a, a = b
3) If a ≦ b and b ≦ c, a ≦ c

  In other words, with respect to the parameter H and the parameter L of the set P, the condition for establishing the order relationship “parameter H ≦ parameter L” is to satisfy the following. The condition is that any group of parameters H is included in any group of parameters L. Here, “inclusion” indicates equality or inclusion.

  When “parameter H ≦ parameter L” holds, the parameter H is equal to or less than the parameter L, or the parameter L is equal to or greater than the parameter H. When “parameter H <parameter L”, the parameter H is smaller than the parameter L or the parameter L is larger than the parameter H.

  When the integration process in which the two groups of the parameter M1, which is the parameter with the maximum number of groups, are integrated into one, is repeatedly performed, the parameter M15 with the minimum number of groups is created from the parameter with the maximum number of groups. . Since there is an upper limit and a lower limit of the subset {x, y} for the parameters x and y belonging to the set P for which the order relationship is defined, the set P is referred to as a “bundle”.

  The height of the bundle is the same as the number of parameter elements belonging to the set P. When the two parameters belonging to the set P have the same number of groups, the bundle height is the same. In the two parameters belonging to the set P, when the number of groups of one parameter is smaller than the number of groups of the other parameter, the height of one parameter bundle is higher than the height of the other parameter bundle.

  In FIG. 2, an order relationship is established between the parameter groups included in the path traced by a line from one of the lower stage to the upper stage and from the upper stage to the lower stage. Among parameters having an order relationship, the parameters in the upper stage in FIG. 2 are large in the bundle, and the parameters in the lower stage are small in the bundle. Accordingly, the parameter M1 is a minimum element (hereinafter referred to as “minimum parameter”), and the parameter M15 is a maximum element (hereinafter referred to as “maximum parameter”).

  There is no order relationship between parameters with the same bundle height. Even if the bundles have different heights, there is no order relationship between two parameters that cannot be traced in a line from either the lower stage to the upper stage or from the upper stage to the lower stage. The magnitude relationship between the output values of the first and second objective functions when two parameters having no order relation are given to the first and second objective functions is unknown unless calculation is performed. Thereafter, a combination of output values of the first and second objective functions when a certain parameter is given to each of the first and second objective functions is expressed as “the first and second objective functions for a certain parameter. This is referred to as “combination of output values”. Next, whether or not there is an order relationship will be described in detail with reference to FIG.

  FIG. 3 is an explanatory diagram illustrating an example of the order relationship. FIG. 3 shows an example in which an order relationship is established between two parameters and an example in which the order relationship is not established. {} Indicates a parameter, and () in {} indicates a group.

  First, an example is given of the parameter M10 and the parameter M6 belonging to the set P. The group (F1, F4) included in the parameter M6 is included in the group (F1, F2, F4) included in the parameter M10. The group (F2) included in the parameter M6 is included in the groups (F1, F2, F4) included in the parameter M10. The group (F3) included in the parameter M6 is included in the group (F3) included in the parameter M10. Accordingly, since any group included in the parameter M6 is included in any group included in the parameter M10, “parameter M6 ≦ parameter M10” is established for the parameter M6 and the parameter M10.

  Next, an example is given of the parameters M9 and M4 belonging to the set P. The group (F2) of the parameter M4 is included in the group (F1, F2) of the parameter M9. The group (F4) of the parameter M4 is included in the group (F3, F4) of the parameter M9. The group (F1, F3) of the parameter M4 is not included in any group of the parameter M9. Therefore, “parameter M4 ≦ parameter M9” does not hold for parameter M4 and parameter M9.

<First objective function and second objective function>
Next, the relationship between the first objective function and the second objective function will be described in detail. In the present embodiment, the detection device gives parameters belonging to the set P to the first and second objective functions as shown in the following formula (1), and outputs the output values of the first and second objective functions. Calculate the combination.

Here, R indicates the entire real number. R ² represents a Cartesian product set of R and R. And in this Embodiment, the relationship as shown to a following formula (2) and Formula (3) is realized between the parameter which belongs to the set P, and the 1st and 2nd objective function.

a, bεP, a ≦ b => f1 (a) ≧ f1 (b) (2)
a, bεP, a ≦ b => f2 (a) ≦ f2 (b) (3)

  The parameters a and b belong to the set P. Expression (2) indicates that when the parameter a is equal to or less than the parameter b, the output value of the first objective function for the parameter a is greater than or equal to the output value of the first objective function for the parameter b. . Expression (3) indicates that when the parameter a is equal to or smaller than the parameter b, the output value of the second objective function for the parameter a is equal to or smaller than the output value of the second objective function for the parameter b. .

  In other words, the first objective function has two parameters that have an order relationship, and the smaller one of the two parameters is given than the larger one of the two parameters. The output value decreases. The second objective function outputs an output value in the case of giving the smaller parameter of the two parameters when the smaller one of the two parameters is given in the two parameters having the order relation. Will increase. Therefore, as described above, the first objective function decreases as the parameter in the set P increases, and the second objective function increases as the parameter in the set P increases.

<First Example and Second Example>
Next, two examples according to the present embodiment will be described. In the present embodiment, a new process is performed by executing an integration process that integrates two groups of groups of parameters into one and a division process that divides one group of parameters into two groups. Create parameters. In the first embodiment, the detection apparatus executes the dividing process on the integrated parameter obtained by executing the integrating process on a certain parameter. In the second embodiment, the detection apparatus executes the integration process on the divided parameters obtained by executing the division process on a certain parameter. As a result, in the first and second embodiments, it is possible to reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have already been found.

  In the first embodiment and the second embodiment, the order of the integration processing and the division processing is reversed. The parameters obtained by performing the division process after the integration process shown in the first embodiment include the parameters obtained by performing the integration process after the division process shown in the second embodiment. That is, the number of parameters obtained by performing the division process after the integration process shown in the first embodiment is larger than the number of parameters obtained by performing the integration process after the division process shown in the second embodiment. There is. In the first embodiment, the number of detection targets of combinations that are candidates for non-inferior solutions is increased compared to the second embodiment. Therefore, the detection apparatus according to the first embodiment is a candidate for non-inferior solutions. Therefore, it is possible to improve the accuracy of detecting a combination as a non-inferior solution. On the other hand, in the second embodiment, since the number of detection targets of combinations that are candidates for non-inferior solutions is reduced as compared to the first embodiment, the detection apparatus according to the second embodiment is not inferior. It is possible to increase the detection speed for detecting a combination that is a candidate for the above.

  Here, the division process and the integration process will be briefly described using mathematical expressions. For example, the integration process for the parameter a and the parameter or the set of parameters obtained by the integration process are described as join (a). In (), an integration source parameter or a set of integration source parameters is described. For example, the split process for the parameter a and the parameter or the set of parameters obtained by the split process are described as split (a). In (), a division source parameter or a set of division source parameters is described.

  For example, the parameter obtained by the integration process performed on the set S of parameters belonging to the set P and the parameter obtained by the division process performed on the set S are respectively expressed by the following expressions (4) and (5). It is expressed as

  Here, “<•” will be described. For example, “parameter H <• parameter L” indicates that the parameter H on the left side is smaller than the parameter L on the right side, and the height of the bundle of the parameter H on the left side is different from the height of the bundle of the parameter L on the right side. Show. According to the equation (4), the parameters obtained by performing the integration process on each parameter s of the parameter set S are more bundled than the parameter s among the parameters having an order relationship with the parameter s belonging to the set S. All parameters t whose height is one higher. According to Equation (5), the parameters obtained by performing the division process on each parameter s of the parameter set S are more bundled than the parameter s among the parameters having an order relationship with the parameter s belonging to the set S. All parameters t whose height is one lower. The relationship between the integration process and the division process will be described later. Next, detailed description of the division processing and integration processing using parameters will be described in the first embodiment and the second embodiment.

<First embodiment>
As described above, in the first embodiment, the detection apparatus executes the division process on the integrated parameter obtained by executing the integration process on a certain parameter. As a result, the detection apparatus can reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found. Furthermore, in the first embodiment, the number of detection targets of combinations that are candidates for non-inferior solutions increases compared to performing the integration processing after the division processing, and thus the detection apparatus according to the first embodiment. Can improve the accuracy of detecting a combination as a non-inferior solution candidate as a non-inferior solution.

  FIG. 4 is an explanatory diagram showing integration processing in the first embodiment of the present invention. First, the detection apparatus 400 acquires the parameter M2. The detection device 400 may acquire the parameter M2 stored in a storage device such as a RAM, ROM, optical disk, or hard disk accessible by the detection device 400, or may acquire the parameter M2 input by the input unit. Good. Examples of the input means include a keyboard and a mouse. Details of the detection device 400 will be described later.

  The detection apparatus 400 acquires a set of output values of the first and second objective functions when the parameter M2 is given to each of the first objective function and the second objective function. The detection apparatus 400 may calculate a combination of output values of the first and second objective functions when the parameter M2 is given to each of the first and second objective functions.

  The detection apparatus 400 integrates two groups in the group group that the acquired parameter M2 has into one. The groups that the parameter M2 has are the group (F1, F2), the group (F3), and the group (F4). Specifically, for example, the detection apparatus 400 creates the parameter M8 by integrating the group (F1, F2) and the group (F3) included in the parameter M2. Similarly, the parameter M10 and the parameter M9 are created by integrating two groups of the parameter M2 into one group.

  Here, the detection apparatus 400 creates all the parameters obtained by integrating the two groups of the parameter M2 into one. However, only a predetermined number of parameters may be created. For example, the predetermined number may be designated in advance by the user. For example, if the predetermined number is small, the number of parameters to be integrated is reduced, so that the detection apparatus 400 can increase the detection speed for detecting a combination that is a non-poor candidate. Alternatively, for example, as shown in FIG. 4, if the predetermined number is the maximum number that can be integrated, the number of parameters that are targets of integration processing increases, and thus the detection apparatus 400 becomes a non-poor candidate. The accuracy of detecting a combination as a non-inferior solution can be improved.

  Here, the lower graph 401 in FIG. 4 shows combinations of output values of the first and second objective functions for the parameters before integration and the parameters after integration. The horizontal axis of the graph 401 is the output value of the first objective function, and the vertical axis of the graph 401 is the output value of the second objective function. Actually, the combination of the output values of the first and second objective functions for each of the integrated parameters is not calculated by the detection device 400, but is illustrated for ease of understanding.

  In the graph 401, the combination of the output values of the first and second objective functions for the parameter M2 is (f1 (M2), f2 (M2)), and the first and second objective functions for the parameter M8 are The combination of output values is (f1 (M8), f2 (M8)). In the graph 401, the combination of the output values of the first and second objective functions for the parameter M9 is (f1 (M9), f2 (M9)), and the first and second objective functions for the parameter M10 The combination of output values is (f1 (M10), f2 (M10)).

  According to the above equations (2) and (3), the output value of the first objective function for the parameter M1, which is the smallest parameter among the parameters belonging to the set P, is the largest, and the second objective function The output value is the smallest. In the graph 401, the combination of the output values of the first and second objective functions for the parameter M1 is (f1 (M1), f2 (M1)). According to the equations (2) and (3), the output value of the first objective function for the parameter M15 that is the largest parameter among the parameters belonging to the set P is the smallest, and the output value of the second objective function Is the largest. In the graph 401, the combination of the output values of the first and second objective functions for the parameter M15 is (f1 (M15), f2 (M15)). Therefore, the combination of the output values of the first and second objective functions for the parameters belonging to the set P falls within the dotted square frame.

  Here, the parameter before integration is smaller than the parameter after integration. Therefore, the relationship between the combination of the output values of the first and second objective functions for the parameter M2 and the combination of the output values of the first and second objective functions for the parameters after the group of the parameters M2 is integrated is Hereinafter, it is expressed as Equation (6) and Equation (7).

f1 (M2) ≧ max {f1 (X) | X∈join (M2)} (6)
f2 (M2) ≦ min {f2 (X) | X∈join (M2)} (7)

  As shown in Expression (6), even if the output value f1 (X) obtained by giving each of the parameters X included in the set of join (M2) to the first objective function is the maximum output value. , The output value f1 (M2) or less obtained by giving the parameter M2 to the first objective function. As shown in Expression (7), even if the output value f2 (X) obtained by giving each of the parameters X included in the set of join (Y) to the second objective function is the minimum output value. , The output value f2 (M2) or more obtained by giving the parameter M2 to the second objective function.

  Therefore, on the graph 401, the combination of the output values of the first and second objective functions for each of the integrated parameters is the upper left of the combination of the output values of the first and second objective functions for the parameter M2. Included in the area. This area is a shaded portion on the graph 401.

  FIG. 5 is an explanatory diagram showing division processing in the first embodiment of the present invention. The detection apparatus 400 divides a certain group including two or more elements into two groups for each of the integrated parameters M8, M9, and M10.

  Taking parameter M8 as an example, a group including two or more elements of parameter M8 is a group (F1, F2, F3). First, the detection apparatus 400 divides the group (F1, F2, F3) included in the parameter M8 into two groups of a group (F2, F3) and a group (F1). Next, the detection apparatus 400 divides the group (F1, F2, F3) included in the parameter M8 into two groups, a group (F1, F3) and a group (F2). Then, the detection apparatus 400 divides the group (F1, F2, F3) included in the parameter M8 into two groups, a group (F1, F2) and a group (F3). That is, the detection apparatus 400 creates a parameter M7, a parameter M4, and a parameter M2 by dividing a group including two or more elements included in the parameter M8 into two groups.

  Taking parameter M9 as an example, groups including two or more elements of parameter M9 are group (F1, F2) and group (F3, F4). First, the detection apparatus 400 divides the group (F1, F2) included in the parameter M9 into two groups, a group (F1) and a group (F2). And the detection apparatus 400 divides | segments the group (F3, F4) which the parameter M9 has into two groups, a group (F3) and a group (F4). That is, the detection apparatus 400 creates a parameter M2 and a parameter M3 by dividing a group including two or more elements included in the parameter M9 into two groups.

  Taking parameter M10 as an example, a group including two or more elements included in parameter M10 is a group (F1, F2, F4). First, the detection apparatus 400 divides the group (F1, F2, F4) included in the parameter M10 into two groups of a group (F1, F2) and a group (F4). Next, the detection apparatus 400 divides the group (F1, F2, F4) included in the parameter M10 into two groups of a group (F1, F4) and a group (F2). And the detection apparatus 400 divides | segments the group (F1, F2, F4) which the parameter M10 has into two groups, a group (F2, F4) and a group (F1). That is, the detection apparatus 400 creates a parameter M2, a parameter M6, and a parameter M5 by dividing a group including two or more elements included in the parameter M10 into two groups.

  Here, the detection apparatus 400 creates all the parameters obtained by integrating the two groups into one for each of the parameters M8, M9, and M10. Not limited to this, the detection apparatus 400 may create a predetermined number of parameters, such as creating one parameter. The predetermined number may be stored in a storage device such as a RAM, ROM, optical disk, or hard disk accessible by the detection device 400 accessible by the detection device 400, or may be input by an input unit. Examples of the input means include a keyboard and a mouse. For example, when the number of parameters to be created decreases, the number of parameters to be integrated is reduced, so that the detection apparatus 400 can shorten the non-poor detection time. On the other hand, as shown in FIG. 5, by setting the predetermined number to the maximum number that can be integrated, the number of parameters to be integrated is increased, so that the detection apparatus 400 selects combinations that are candidates for non-poor solutions. The accuracy of detection as a non-inferior solution can be improved.

  Then, the detection apparatus 400 gives each parameter of the divided parameters to each of the first and second objective functions, so that the first and second objectives for each parameter of the divided parameters are obtained. Calculate the combination of function output values. For example, for the first objective function and the second objective function, predetermined mathematical expressions and processes are stored in the storage device. Specifically, when each parameter of the divided parameters is given to the first objective function and the second objective function, the detection apparatus 400 stores the parameters associated with the group and the elements of each group. Formulas and processes determined along the observed values are executed.

  Here, the parameter before division is larger than the parameter after division. Therefore, combinations of output values of the first and second objective functions for the parameters included in the set of join (M2), and outputs of the first and second objective functions for the parameters after dividing the group of parameters The relationship between the combination of values is represented by the following formulas (8) and (9).

f1 (Y) ≦ min {f1 (X) | X∈split (Y)} (8)
f2 (Y) ≧ max {f2 (X) | X∈split (Y)} (9)
Yεjoin (M2)

  A set of parameters obtained by dividing the parameter Y included in the set of join (M2) is split (Y). As shown in Expression (8), even if the output value f1 (X) obtained by giving each of the parameters X included in the set of split (Y) to the first objective function is the minimum output value, , The output value f1 (Y) or more obtained by giving the parameter Y to the first objective function. As shown in Expression (9), even if the output value f2 (X) obtained by giving the parameter X included in the set of split (Y) to the second objective function is the maximum output value, the parameter It is less than or equal to the output value f2 (Y) obtained by giving Y to the second objective function.

  Therefore, in the three graphs 501 to 503 shown in the center of FIG. 5, the combination of the output values of the first and second objective functions for the parameters after division is the first and second objective functions for the parameters before division. It is included in the lower right area of the output value combination. This area is a shaded portion of each of the graphs 501 to 503. The combinations of output values indicated by crosses on the graphs 501 to 503 and 510 are described for easy understanding, but are not actually calculated. The horizontal axis of the graphs 501 to 503 and 510 is the output value of the first objective function, and the vertical axis of the graphs 501 to 503 and 510 is the output value of the second objective function.

  In the graph 501 shown on the left side of the central stage in FIG. 5, the parameter M8 and the parameters M2, M4, and M7 obtained by dividing the parameter M8 are given to the first and second objective functions, respectively. The combination of the output values of the first and second objective functions is shown. The combination of the output values of the first and second objective functions for the parameter M8 on the graph 501 is (f1 (M8), f2 (M8)). The output values of the first and second objective functions for each of the parameters M2, M4, M7 after being divided into the shaded area 511 at the lower right of the point represented by (f1 (M8), f2 (M8)) There are combinations.

  In the graph 502 shown in the center of the center stage of FIG. 5, the parameter M10 and the parameters M2, M5, and M6 obtained by dividing the parameter M10 are given to the first and second objective functions, respectively. The combination of the output values of the first and second objective functions is shown. The combination of the output values of the first and second objective functions for the parameter M10 on the graph 502 is (f1 (M10), f2 (M10)). A combination of output values of the first and second objective functions for each of the parameters M2, M5, and M6 is shown in the shaded area 512 at the lower right of the point represented by (f1 (M10), f2 (M10)). .

  In the graph 503 shown on the right side of the center stage of FIG. 5, when the parameter M9 and the parameters M2 and M3 obtained by dividing the parameter M9 are given to the first and second objective functions, respectively. , Shows combinations of output values of the first and second objective functions. The combination of the output values of the first and second objective functions for the parameter M9 on the graph 503 is (f1 (M9), f2 (M9)). In the shaded area 513 at the lower right of the point represented by (f1 (M9), f2 (M9)), there are combinations of output values of the first and second objective functions for each of the parameters M2 and M3.

  The lower part of FIG. 5 shows a graph 510 that is a combination of the three graphs 501 to 503 in the central stage. Area 521 is a logical sum of area 511, area 512, and area 513. A combination of output values indicated by ● on the graph 510 is a combination of output values to be detected as candidates for non-inferior solutions. As shown in the equations (8) and (9), the combination of output values obtained by giving the parameters included in the set of split (Y) to the first and second objective functions is a shaded graph 510. It is included in the area 521. Next, an example in which a combination that is a candidate for a non-inferior solution is detected from a combination of output values indicated by ● in the graph 510 will be described with reference to FIG.

  FIG. 6 is an explanatory diagram showing a detection example of a non-inferior solution candidate in the first embodiment according to the present invention. The detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from among the combination of the calculated output values and the combination of the output values of the first and second objective functions for the acquired parameter M2. To do. As described above, the combinations of the output values of the first and second objective functions for the parameters belonging to the set P fall within the dotted square frame.

  First, the graph 510 on the left side of the upper stage shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M3 is a combination that is a candidate for a non-inferior solution. A combination of output values better than the combination of the output values of the first and second objective functions for the parameter M3 is that the output values of both the first and second objective functions are the first and second objectives for the parameter M3. It becomes larger than the output value of the function. Therefore, a combination of output values better than a combination of output values of the first and second objective functions for the parameter M3 is included in the shaded area 601 on the graph 510. In the graph 510, the area 601 includes a combination of a plurality of output values. Therefore, the detection apparatus 400 does not detect the combination of the output values of the first and second objective function candidates for the parameter M3 as a non-poor combination.

  Next, the upper middle graph 510 shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M4 is a combination that is a non-inferiority candidate. A combination of output values better than a combination of output values of the first and second objective functions for the parameter M4 is included in the shaded area 602 on the graph 510. In the graph 510, the area 602 does not include a combination of a plurality of output values. Therefore, the detection apparatus 400 detects the combination of the output values of the first and second objective functions for the parameter M4 as a combination that is a non-inferiority candidate.

  The upper right graph 510 shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M7 is a non-poor candidate. A combination of output values better than the combination of the output values of the first and second objective functions for the parameter M7 is included in the shaded area 603 on the graph 510. In the graph 510, the area 603 does not include a combination of a plurality of output values. Therefore, the detection apparatus 400 detects the combination of the output values of the first and second objective functions for the parameter M7 as a combination that is a non-inferiority candidate.

  A graph 510 on the left side of the lower stage shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M6 is a combination that is a non-inferiority candidate. A combination of output values better than a combination of output values of the first and second objective functions for parameter M6 is included in shaded area 604 on graph 510. In the graph 510, a shaded area 604 includes a plurality of combinations of output values. Therefore, the detection apparatus 400 does not detect the combination of the output values of the first and second objective functions for the parameter M6 as a combination that is a non-inferior solution candidate.

  The lower middle graph 510 shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M5 is a non-poor candidate. A combination of output values better than the combination of the output values of the first and second objective functions for the parameter M5 is included in the shaded area 605 on the graph 510. In the graph 510, a shaded area 605 includes a plurality of combinations of output values. Therefore, the detection apparatus 400 does not detect the combination of the output values of the first and second objective functions for the parameter M5 as a combination that is a non-inferior solution candidate.

  Finally, the graph 510 on the right side of the lower stage shows an example of determining whether or not the combination of the output values of the first and second objective functions for the parameter M2 is a combination that is a non-inferior solution candidate. A combination of output values better than the combination of the output values of the first and second objective functions for parameter M2 is included in shaded area 606 on graph 510. In the graph 510, a shaded area 606 includes a plurality of combinations of output values. Therefore, the detection apparatus 400 does not detect the combination of the output values of the first and second objective functions for the parameter M2 as a combination that is a non-inferiority candidate.

  Therefore, the detection apparatus 400 detects a combination of output values of the first and second objective functions for each of the parameters M7 and M4 as a combination that is a candidate for a non-inferior solution.

  And the detection apparatus 400 outputs the combination used as the candidate of the detected non-inferior solution. Further, the detection apparatus 400 outputs the combination of the detected non-inferior solution candidate and the parameters given to the first and second objective functions in association with obtaining the combination of the non-inferior solution candidate. May be. The output format may be stored in a storage device such as a RAM, ROM, optical disk, or magnetic disk accessible by the detection apparatus 400. Or as an output format, you may make it output on the display which the detection apparatus 400 can access the graph by which the combination used as the candidate of the detected non-inferiority was plotted.

  Here, as described above, the parameter after integration is larger than the parameter before integration. Therefore, the output value of the first objective function for any of the parameters after integration is less than or equal to the output value of the first objective function for the parameter before division. And even if it is the output value of the 2nd objective function about any parameter of the parameters after integration, it becomes more than the output value of the 2nd objective function about the parameter before integration.

  Furthermore, as described above, the parameter before the division is larger than the parameter after the division. Therefore, even if the output value of the first objective function for any of the parameters after division is greater than the output value of the first objective function for the parameter before division. And even if it is the output value of the 2nd objective function about any parameter of the parameters after division, it becomes below the output value of the 2nd objective function about the parameter before division.

  Therefore, the combination of the output values of the first and second objective functions for each of the parameters after the integration processing performed on the parameter M2 is performed on the graph 510 on the first and second objectives for the parameter M2. It is included in the upper left area than the combination of function output values. The combination of the output values of the first and second objective functions for each of the divided parameters obtained by performing the dividing process on the parameters after integration is shown on the graph 510 on the first and second values for the parameters after integration. It is included in the lower right area from the combination of output values of the objective function.

  Accordingly, the combination of the output values of the first and second objective functions for the parameters that are divided after being integrated is represented on the graph 510 by the output values of the first and second objective functions for the acquired parameter M2. It may be a better solution than the combination. Thereby, the detection apparatus 400 detects the combination of the output values of the first and second objective functions, which is better than the combination of the output values of the first and second objective functions, for the acquired parameters. It is possible to reduce the amount of calculation required to detect poor candidates.

  In the first embodiment described above, the integration process and the division process are each performed once. However, the detection apparatus 400 recursively sets the number of integration processes and the number of division processes as the same number. Multiple times may be performed. If the number of integration processes and the number of division processes increase, the detection apparatus 400 sets combinations of output values in a wider range that can be taken by combinations of output values of the first and second objective functions as non-inferiority candidates. It can be set as a detection target of a combination. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  In addition, when the integration process and the division process are each performed once, and the combination that is a non-inferior solution candidate is not updated, the detection apparatus 400 sets the number of integration processes and the number of division processes as the same number of times. You may perform it recursively several times. Furthermore, even if the integration process and the division process are recursively performed a plurality of times, when the combination that is a non-inferior solution candidate is not updated, the detection apparatus 400 calculates the number of integration processes and the number of division processes. It may be increased the same number of times. If the number of integration processes and the number of division processes increase, the detection apparatus 400 sets combinations of output values in a wider range that can be taken by combinations of output values of the first and second objective functions as non-inferiority candidates. It can be set as a detection target of a combination. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Further, the detection apparatus 400 may newly acquire parameters given to the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution. Thereby, the detection apparatus 400 can repeatedly perform the detection process of the combination which becomes a non-inferiority candidate. When obtaining a combination that is a candidate for a non-inferior solution, a combination of output values for parameters obtained by performing integration processing and division processing on the parameters given to the first and second objective functions, There is a possibility that the output value combination is better than the combination. Therefore, as compared with the case where parameters are selected at random as in the conventional random search, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior candidate as a non-inferior solution.

<Second embodiment>
Next, a second embodiment will be described. In the first embodiment, the detection apparatus 400 executes the division process for the parameters after integration obtained by the integration process. In the second embodiment, the detection apparatus 400 performs the integration process for the parameters after division obtained by the division process. Run. That is, in the second embodiment, the execution order of the dividing process and the integrating process is reversed from that of the first embodiment. Thereby, the detection apparatus 400 can achieve a reduction in the amount of calculation required to detect a combination of output values that is better than a combination of output values that have already been determined. Further, as described above, the number of parameters after integration obtained in the second embodiment may be smaller than the number of parameters after division obtained in the first embodiment. In the second embodiment, the number of detection targets of combinations that are candidates for non-inferior solutions is reduced as compared to the first embodiment. Therefore, the detection apparatus 400 according to the second embodiment has a non-poor solution. It is possible to increase the detection speed required to detect candidate combinations.

  FIG. 7 is an explanatory diagram showing division processing in the second embodiment of the present invention. The detection apparatus 400 acquires the parameter M11 and a set of output values of the first and second objective functions when the parameter M11 is given to each of the first and second objective functions. The detection device 400 may calculate a combination of output values of the first and second objective functions when the parameter M11 is given to each of the first and second objective functions.

  Then, the detection apparatus 400 divides a certain group including two or more elements out of the group group included in the acquired parameter M11 into two groups. Groups including two or more elements included in the parameter M11 are a group (F1, F3) and a group (F2, F4). Therefore, the detection apparatus 400 creates the parameter M5 by dividing the group (F1, F3) included in the parameter M11 into a group (F1) and a group (F3). Furthermore, the detection apparatus 400 creates the parameter M4 by dividing the group (F2, F4) included in the parameter M11 into a group (F2) and a group (F4). Here, the detection apparatus 400 performs processing for dividing each group including two or more elements included in the parameter M11 into two groups. However, for any one group among the groups including two or more elements. You may go only.

  Here, a lower graph 700 in FIG. 7 shows combinations of output values of the first and second objective functions for the parameter M11 before division and the parameters M4 and M5 after division. Actually, the combination of the output values of the first and second objective functions for each of the divided parameters is not calculated by the detection device 400, but is illustrated for ease of understanding. The horizontal axis of the graph 700 is the output value of the first objective function, and the vertical axis of the graph 700 is the output value of the second objective function. In the graph 700, the combination of the output values of the first and second objective functions for the parameter M11 is (f1 (M11), f2 (M11)). In the graph 700, the combination of the output values of the first and second objective functions for the parameter M4 is (f1 (M4), f2 (M4)), and the first and second objective functions for the parameter M5 are The combination of output values is (f1 (M5), f2 (M5)).

  Here, the parameter before division is larger than the parameter after division. Therefore, the relationship between the combination of the output values of the first and second objective functions for the parameter M11 and the combination of the output values of the first and second objective functions for the parameters after dividing the group of the parameter M11 is Hereinafter, it is expressed as Expression (10) and Expression (11).

f1 (M11) ≦ min {f1 (X) | X∈split (M11)} (10)
f2 (M11) ≧ max {f2 (X) | X∈split (M11)} (11)

  As shown in Expression (10), even if the output value obtained by giving each parameter of the parameters included in the set of split (M11) to the first objective function is the minimum output value, the parameter M Is greater than or equal to the output value obtained by giving to the first objective function. As shown in Expression (11), even if the output value obtained by giving each of the parameters included in the set of splits (M11) to the second objective function is the maximum output value, the parameter M is It becomes below the output value obtained by giving to the objective function of 2. In the graph 700, the first and second values for the parameters M4 and M5 are displayed in the shaded area 701 at the lower right of the point represented by the combination of the output values of the first and second objective functions for the parameter M11. Contains a combination of objective function output values.

  FIG. 8 is an explanatory diagram showing integration processing in the second embodiment of the present invention. The detection apparatus 400 integrates two groups into one for each of the parameter M5 and the parameter M4. Taking parameter M5 as an example, the group that parameter M5 has is group (F1), group (F3), and group (F2, F4). Therefore, the detection apparatus 400 creates the parameter M14, the parameter M10, and the parameter M11 by integrating two of the groups included in the parameter M5 into one.

  Taking parameter M4 as an example, the groups that parameter M4 has are group (F1, F3), group (F2), and group (F4). Therefore, the detection apparatus 400 creates the parameter M11, the parameter M8, and the parameter M12 by integrating two of the groups included in the parameter M4 into one.

  Next, the detection apparatus 400 gives each parameter of the plurality of parameters after integration to each of the first and second objective functions, whereby the first and second parameters for each of the plurality of parameters after integration are provided. A combination of output values of the objective function is calculated. Specifically, when each parameter of the plurality of parameters after the integration is given to the first and second objective functions, the detection apparatus 400 stores the observations associated with the groups of the parameters and the elements of each group. Execute mathematical formulas and processing determined according to the value.

  Here, the parameter before integration is smaller than the parameter after integration. Therefore, combinations of output values of the first and second objective functions for the parameters included in the set of split (M11), and outputs of the first and second objective functions for the parameters after integrating the group of parameters. The relationship between the combination of values is represented by the following formulas (12) and (13).

f1 (Y) ≧ max {f1 (X) | X∈join (Y)} (12)
f2 (Y) ≦ min {f2 (X) | X∈join (Y)} (13)
Yεsplit (M11)

  A set of parameters obtained by performing integration processing on any one of the parameters Y included in the set of split (M11) is join (Y). As shown in Expression (12), even if the output value f1 (X) obtained by giving each of the parameters X included in the set of join (Y) to the first objective function is the maximum output value , The output value f1 (Y) or less obtained by giving the parameter Y to the first objective function. As shown in Expression (13), even if the output value f2 (X) obtained by giving each of the parameters X included in the set of split (Y) to the second objective function is the minimum output value. , The output value f2 (Y) or more obtained by giving the parameter Y to the second objective function.

  A graph 801 on the left side of the center stage shows a combination of output values of the first and second objective functions for the parameter M5. The horizontal axis of the graph 801 is the output value of the first objective function, and the vertical axis of the graph 801 is the output value of the second objective function. Further, a graph 801 shows combinations of output values of the first and second objective functions for the parameters M10, M11, and M14 obtained by integrating two groups of the parameter M5 into one group. . In the graph 801, the combination of the output values of the first and second objective functions for the parameter M5 is (f1 (M5), f2 (M5)). The combination of the output values of the first and second objective functions for the parameter M10 is (f1 (M10), f2 (M10)). The combination of the output values of the first and second objective functions for the parameter M11 is (f1 (M11), f2 (M11)), and the combination of the output values of the first and second objective functions for the parameter M14 Is (f1 (M14), f2 (M14)).

  The parameter M5 is smaller than the parameters M10, M11, and M14. Therefore, even if the output value obtained by giving each of the parameters included in the set of join (M5) to the first objective function is the maximum output value, the parameter M5 is given to the first objective function. The obtained output value is f1 (M5) or less. Among the output values obtained by giving each of the parameters X included in the set of join (M5) to the second objective function, even if it is the smallest output value, it is obtained by giving the parameter M5 to the first objective function. Output value f2 (M5) or less. Therefore, on the graph 801, the combination of the output values of the first and second objective functions for each of the parameters M10, M11, and M14 is the combination of the output values of the first and second objective functions for the parameter M5. It is included in the shaded area 811 in the upper left.

  A graph 802 on the right side of the center stage shows a combination of output values of the first and second objective functions for the parameter M4. The horizontal axis of the graph 802 is the output value of the first objective function, and the vertical axis of the graph 802 is the output value of the second objective function. Further, a graph 802 shows a combination of output values of the first and second objective functions for the parameters M8, M11, and M12 obtained by integrating the two groups of the parameter M4 into one group. . In the graph 802, the combination of the output values of the first and second objective functions for the parameter M4 is (f1 (M4), f2 (M4)). The combination of the output values of the first and second objective functions for the parameter M8 is (f1 (M8), f2 (M8)). The combination of the output values of the first and second objective functions for the parameter M11 is (f1 (M11), f2 (M11)), and the combination of the output values of the first and second objective functions for the parameter M12. Is (f1 (M12), f2 (M12)).

  The parameter M4 is smaller than the parameters M8, M11, and M12. Therefore, even if the output value obtained by giving each parameter included in the set of join (M4) to the first objective function is the maximum output value, the parameter M4 is given to the first objective function. The obtained output value is f1 (M4) or less. Even if the output value obtained by giving each of the parameters X included in the set of join (M4) to the second objective function is the smallest output value, it is obtained by giving the parameter M4 to the first objective function. Output value f2 (M4) or less. Therefore, on the graph 802, the combination of the output values of the first and second objective functions for each of the parameters M8, M11, and M12 is the combination of the output values of the first and second objective functions for the parameter M4. It is included in the shaded area 812 in the upper left.

  The lower part of FIG. 8 shows a graph 820 in which a graph 801 and a graph 802 are superimposed. The horizontal axis of the graph 820 is the output value of the first objective function, and the vertical axis of the graph 820 is the output value of the second objective function. A combination of output values indicated by ● on the graph is a detection target of a non-inferior solution candidate. Area 821 is a logical sum of area 811 and area 812. As shown in the equations (12) and (13), the combination of output values obtained by giving the parameters included in the set of split (Y) to the first and second objective functions is the shaded graph 820. It is included in area 821.

  Then, the detection apparatus 400 calculates the non-poor solution from among the calculated combination of output values and the combination of output values when the acquired parameter M11 is given to each of the first and second objective functions. A candidate combination of is detected. Here, the detection apparatus 400 detects the combination of the output values of the first and second objective functions for each of the parameter M8 and the parameter M12 as a combination that is a non-inferior solution candidate.

  And the detection apparatus 400 outputs the combination used as the candidate of the detected non-inferior solution. As an output format, the detection device 400 may be stored in a storage device such as a RAM, a ROM, an optical disk, or a magnetic disk, or a graph in which a combination of detected non-poor candidate is plotted is used as the detection device. You may make it output on the display which 400 has.

  Here, as described above, the parameter before the division is larger than the parameter after the division. Therefore, even if the output value of the first objective function for any of the parameters after division is greater than the output value of the first objective function for the parameter before division. And even if it is the output value of the 2nd objective function about any parameter of the parameters after division, it becomes below the output value of the 2nd objective function about the parameter before division.

  Furthermore, as described above, the parameter after integration is larger than the parameter before integration. Therefore, the output value of the first objective function for any of the parameters after integration is less than or equal to the output value of the first objective function for the parameter before division. And even if it is the output value of the 2nd objective function about any parameter of the parameters after integration, it becomes more than the output value of the 2nd objective function about the parameter before integration.

  That is, the combination of the output values of the first and second objective functions for the parameters after the division processing performed on the parameter M11 is the first and second objective function combinations for the parameter M11 on the graph 700. It is included in the lower right of the output value combination. The combination of the output values of the first and second objective functions for the post-integration parameters obtained by performing the integration process on the post-partition parameters on the graph 820 is the first and second combinations of the first and second output parameters. It is included in the upper left of the combination of output values of the objective function.

  Therefore, the combination of the output values of the first and second objective functions for the integrated parameters that have undergone the integration processing after the division are shown in the graph 820 as the first and second objective functions for the acquired parameter M11. May be included in the upper right of the output value combination. As a result, the detection apparatus 400 has a calculation amount required for detecting a combination of output values of the first and second objective functions that is better than a combination of output values of the first and second objective functions for the acquired parameter. Reduction can be achieved.

  In the second embodiment described above, the dividing process and the integrating process are each performed once, but the integrating process and the dividing process may be performed a predetermined number of times. Accordingly, it is possible to increase the number of detection targets for combinations that are candidates for non-inferior solutions. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Further, the detection apparatus 400 may newly acquire parameters given to the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution. Thereby, the detection apparatus 400 can repeatedly perform the detection process of the combination which becomes a non-inferiority candidate. When obtaining a combination that is a candidate for a non-inferior solution, a combination of output values for parameters obtained by performing integration processing and division processing on the parameters given to the first and second objective functions, There is a possibility that the output value combination is better than the combination. Therefore, as compared with the case where parameters are selected at random as in the conventional random search, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior candidate as a non-inferior solution.

<Relationship between integration processing and division processing>
Between a parameter group obtained by performing division processing after integration processing as in the first embodiment and a parameter group obtained by performing integration processing after division processing as in the second embodiment. In addition, the relationship of Expression (14) is established. The left side of Expression (14) indicates a parameter group obtained when the division process is performed on the parameter group obtained by performing the integration process on a certain parameter a belonging to the parameter set P. On the other hand, the right side of Expression (14) indicates a parameter group obtained when the integration process is performed on the parameter group after the division obtained by performing the division process on the parameter a.

  split (join (a)) ⊇join (split (a)) (14)

  Taking the parameter M11 as an example for the relationship represented by the equation (14), split (join (M11)) and join (split (M11)) are as follows.

join (split (M11)) = {M8, M10, M11, M12, M14}
split (join (M11)) = {M8, M9, M10, M11, M12, M13, M14}

  That is, in the case of the parameter M11, M13 included in the split (join (M11)) is not included in the join (split (M11)). Therefore, the relationship between split (join (M11)) and join (split (M11)) is expressed as follows.

  split (join (M11)) ⊃join (split (M11))

  Taking parameter M12 as an example of the relationship represented by equation (14), split (join (M12)) and join (split (M12)) are as follows.

join (split (M12)) = {M8, M9, M10, M11, M12, M13, M14}
split (join (M12)) = {M8, M9, M10, M11, M12, M13, M14}

  That is, in the case of the parameter M12, since split (join (M12)) and join (split (M12)) match, the relationship between split (join (M12)) and join (split (M12)) is as follows: It is expressed in

  split (join (M12)) = join (split (M12))

  Next, when a certain parameter p belonging to the parameter set P and a certain parameter q belonging to the set P satisfy the relationship of p <· q, the following equations (15) and (16) are established.

split (join (q)) ⊇join (p) (15)
split (join (p)) ⊇split (q) (16)

  As shown in Expression (14) to Expression (16), the number of parameters obtained when the division process is executed after the integration process shown in the first embodiment is the number of parameters obtained in the second embodiment. It is more than the number of parameters obtained when the integration process is executed after the process. Therefore, in the first embodiment, the number of detection targets of parameters that are candidates for non-inferior solutions increases compared to the second embodiment, and thus the detection apparatus 400 according to the first embodiment has a non-poor solution. It is possible to improve the accuracy of detecting candidate combinations as non-inferior solutions. On the other hand, in the second embodiment, since the number of detection targets of combinations that are candidates for non-inferior solutions is reduced compared to the first embodiment, the detection apparatus 400 according to the second embodiment is not inferior. It is possible to increase the detection speed for detecting combinations that are solution candidates.

<Renewal of non-inferior combinations>
Next, an example in which the detection apparatus 400 repeats the processing shown in the first embodiment or the second embodiment will be described. FIG. 9 illustrates an example in which a combination that is a non-inferior solution is obtained by updating a combination that is a candidate for a non-inferior solution obtained from a parameter group that is acquired first. Accordingly, the detection apparatus 400 can obtain a combination that is a candidate for a non-inferior solution estimated as a Pareto solution. Therefore, the detection apparatus 400 can detect a combination that is a candidate for a non-inferior solution from a wide range of combinations that can be taken by a combination of output values of the first and second objective functions.

  FIG. 9 is an explanatory diagram illustrating Example 1 in which a combination that is a candidate for a non-inferior solution is updated. FIG. 9 shows a state where a combination that is a non-inferior solution candidate is updated. In the example of FIG. 9, first, the detection apparatus 400 acquires a parameter group that extends from the first parameter to the second parameter that is larger than the first parameter according to the order relationship. The parameter group may be designated by the user using the input means, or the detection apparatus 400 may be arbitrarily selected from the set P. Examples of the input means include a keyboard and a mouse.

Initial Parameter Group A graph 901 shows combinations of output values of the first and second objective functions when each parameter of the parameter group is given to each of the first and second objective functions. In the graph 901, for easy understanding, the output values of the first and second objective functions for the second parameter from the combination of the output values of the first and second objective functions for the first parameter. The combination of output values up to the combination is connected with a line. Here, this line is referred to as an initial non-inferiority line, and a combination of output values of the first and second objective functions for each parameter of the parameter group is a combination that is an initial non-inferiority candidate.

  Although the first and second parameters are not particularly limited, in FIG. 9, the first parameter is the parameter having the largest number of groups among the parameters belonging to the set P, and the second parameter is the parameter belonging to the set P. Of these, the number of groups is one parameter. That is, the first parameter is the minimum parameter, and the second parameter is the maximum parameter. The detection apparatus 400 can obtain a combination of non-inferior solutions such as a Pareto solution by repeatedly updating combinations that are candidates for non-inferior solutions obtained from the initial parameter group ranging from the minimum parameter to the maximum parameter. .

First Update Next, the detection apparatus 400 performs integration processing on each parameter of the acquired parameter group as shown in the first embodiment, and divides each parameter of the plurality of parameters after integration. Execute the process. Alternatively, the detection apparatus 400 executes the integration process for each parameter of the plurality of divided parameters obtained by executing the division process for each parameter of the acquired parameter group as shown in the second embodiment. Then, for example, the detection apparatus 400 gives each parameter of the plurality of parameters after division to each of the first and second objective functions, and the first and second objectives for each parameter of the plurality of parameters after division. Calculate the combination of function output values.

  And the detection apparatus 400 is a candidate for a non-inferior solution from the combination of the calculated plurality of output values and the combination of the output values of the first and second objective functions for each parameter of the acquired parameter group. The combination that becomes is detected. The detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution. For example, when the detection device 400 obtains a combination that is a candidate for a detected non-inferior solution and a combination that is a candidate for a detected non-inferior solution, the parameters given to the first objective function and the second objective function May be stored in the storage device in association with each other. Furthermore, as illustrated in FIG. 9, the detection apparatus 400 may graph the combinations that are candidates for non-inferior solutions and output them on a display. A graph 902 shows a combination that is an initial non-inferiority candidate and a combination that is a detected non-inferiority candidate.

Second Update Next, the detection apparatus 400 newly acquires the parameters given to the first objective function and the second objective function when obtaining a combination that is a candidate for the detected non-inferior solution. Since there are a plurality of combinations that are detected non-inferiority candidates, there are a plurality of acquired parameters. And the detection apparatus 400 performs the process similar to the process which detects the candidate of the 1st non-inferior solution about each parameter of the several parameter newly acquired.

  A graph 903 shows a combination that is a candidate for non-inferiority detected at the first time and a combination that is a candidate for non-inferiority detected at the second time. In this way, combinations that are candidates for non-inferior solutions are updated.

-Combination of non-inferior solutions In the example of FIG. 9, an example in which a combination that is a candidate for non-inferior solution is updated twice is shown. For example, the detection apparatus 400 matches a combination that is a non-inferiority candidate detected at the nth (n ≧ 0) time and a combination that is a non-inferiority candidate detected at the (n + 1) th time. It may be determined whether or not. When it is determined that the combination that is a non-inferiority candidate detected at the nth time matches the combination that is a non-inferiority candidate detected at the (n + 1) th time, the detection apparatus 400 has detected A combination that is a candidate for a non-inferior solution is set to a combination of non-inferior solutions. The detection device 400 outputs the set combination of non-inferior solutions. That is, if the detected combination that is a non-inferior solution candidate is not updated, the detected combination that is a candidate for non-inferior solution is output as a combination of non-inferior solutions obtained from the first acquired parameter group. . Therefore, the detection apparatus 400 can obtain a combination of non-inferior solutions by repeatedly updating combinations that are candidates for non-inferior solutions.

  Next, in FIG. 10, the detection apparatus 400 includes a combination of non-poor solutions obtained by updating a combination that is a non-poor candidate obtained from one parameter of the parameter group acquired in the initial stage. An example of ending when the number reaches a predetermined number is shown. That is, here, the detection speed for detecting a combination that is a non-inferiority candidate is more important than the accuracy with which a combination that is a non-inferior solution candidate is detected as a non-inferior solution combination. Therefore, the detection apparatus 400 can increase the detection speed for detecting a combination that is a non-poor candidate.

  FIG. 10 is an explanatory diagram illustrating Example 2 in which a combination that is a non-inferior solution candidate is updated. A graph 1001 in the upper left indicates a combination of output values of the first and second objective functions for each parameter of the parameter group acquired in the initial stage. In the example of FIG. 10, the detection apparatus 400 obtains parameters by performing division processing and integration processing from one parameter selected from the initially acquired parameter group.

First Update The detection apparatus 400 calculates a combination of output values of the first and second objective functions for the parameters obtained by the division process and the integration process. The detection apparatus 400 includes a combination of the calculated output values of the first objective function and output values of the first and second objective functions when the selected parameter is given to the first and second objective functions. And combinations that are candidates for non-inferior solutions are detected. In the graph 1002, in addition to the combinations of output values shown in the graph 1001, combinations that are newly detected candidates for non-inferior solutions are shown.

Second Update The detection apparatus 400 uses the parameters given to the first and second objective functions when obtaining one selected combination among the newly detected combinations of non-inferiority candidates. The update is repeated by performing the dividing process and the integrating process for. And the detection apparatus 400 calculates the combination of the output value of the 1st and 2nd objective function about the obtained parameter. The detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from the selected combination and the combination of the calculated output values.

  Furthermore, for example, the detection apparatus 400 determines whether or not a combination that is a candidate for a non-inferior solution detected matches one selected combination. If the newly detected combination that is a candidate for non-inferiority matches the selected combination, the detection apparatus 400 can determine whether the selected combination is a non-inferior solution that cannot be updated any more. You may judge that it is a candidate combination. The graph 1003 is a non-inferior solution candidate that is estimated not to be updated to a combination of output values that is better than the combination of the output values indicated by ◯. A combination of output values of the first and second objective functions for the maximum parameter and the minimum parameter in the parameter group acquired in the initial stage is indicated by a circle because it is an optimal solution.

  Furthermore, the detection apparatus 400 measures the number of times that the newly detected combination that is a non-inferiority candidate matches one selected combination. And the detection apparatus 400 may judge whether the measured frequency | count is more than predetermined number. The predetermined number may be stored in a storage device such as a RAM, ROM, optical disk, or hard disk accessible by the detection device 400 accessible by the detection device 400, or may be input by an input unit. Examples of the input means include a keyboard and a mouse. Thereby, the detection apparatus 400 determines whether or not the number of combinations that are candidates for non-inferior solutions that are assumed not to be updated is a predetermined number or more. When the number of times measured is a predetermined number or more, the detection apparatus 400 may set a combination that is a non-inferior candidate determined to match the selected combination as a non-inferior combination. Then, the detection device 400 outputs the set combination of non-inferior solutions. A graph 1004 shows an example in which a presumed fifth non-inferior candidate that is not updated is detected.

<Hardware Configuration Example of Detection Device 400>
FIG. 11 is a block diagram of a hardware configuration example of the detection apparatus 400 according to the embodiment. In FIG. 11, the detection device 400 includes a CPU (Central Processing Unit) 1101, a ROM 1102, a RAM 1103, a magnetic disk drive 1104, a magnetic disk 1105, an optical disk drive 1106, and an optical disk 1107. Further, the detection apparatus 400 includes a display 1108, an I / F (Interface) 1109, a keyboard 1110, and a mouse 1111. Each unit is connected by a bus 1112.

  Here, the CPU 1101 governs overall control of the detection device 400. The ROM 1102 stores a program such as a boot program. The RAM 1103 is used as a work area for the CPU 1101. The magnetic disk drive 1104 controls reading / writing of data with respect to the magnetic disk 1105 according to the control of the CPU 1101. The magnetic disk 1105 stores data written under the control of the magnetic disk drive 1104.

  The optical disk drive 1106 controls reading / writing of data with respect to the optical disk 1107 according to the control of the CPU 1101. The optical disc 1107 stores data written under the control of the optical disc drive 1106, and causes the computer to read data stored on the optical disc 1107.

  The display 1108 displays data such as a document, an image, and function information as well as a cursor, an icon, or a tool box. As the display 1108, for example, a CRT, a TFT liquid crystal display, a plasma display, or the like can be adopted.

  The I / F 1109 is connected to a network NW such as a LAN (Local Area Network), a WAN (Wide Area Network), and the Internet through a communication line, and is connected to another device via the network NW. The I / F 1109 controls an internal interface with the network NW, and controls data input / output from an external device. For example, a modem or a LAN adapter may be employed as the I / F 1109.

  The keyboard 1110 has keys for inputting characters, numbers, various instructions, and the like, and inputs data. Moreover, a touch panel type input pad or a numeric keypad may be used. The mouse 1111 performs cursor movement, range selection, window movement, size change, and the like. A trackball or a joystick may be used as long as they have the same function as a pointing device.

<An example of the observed value of each element>
In the present embodiment, detection apparatus 400 detects combinations that are candidates for non-inferior solutions in the above-described combination optimization problem regarding power consumption and peak power reduction rate.
Problem “Group A offices in TEPCO so that the total peak power of the group and the minimum peak power reduction rate of the group are large.”

  In the above problem, the first objective function is a function for calculating the sum of the peak powers of the groups of the parameters, and the second objective function is a function for specifying the minimum value of the peak power reduction rate of the groups of the parameters. It is. Here, information used for calculating the output value of the first objective function and the output value of the second objective function is shown in FIG. 12 and FIG. An example of calculating the output value of the objective function 2 is shown in FIG.

  FIG. 12 is an explanatory diagram illustrating an example of a power table for each business office. The power table group 1200 includes power tables 1201-1 to 1200-A for each office. In the example of FIG. 12, A = 4. In the power tables 1201-1 to 1201-4, average power used per hour is registered for several months. The power tables 1201-1 to 1201-4 include an establishment ID item, a date item, and an average power consumption item for each time zone. The establishment ID for identifying the establishment is registered in the establishment ID item. In the example of FIG. 12, the establishment ID and the element number of the element group of the set P shown in FIG. In the date item, dates for several months are registered. In the item of average power consumption for each time zone, the average power usage in each time zone of the date registered in the date item is registered. In the power tables 1201-1 to 1201-4, one day is divided every 30 minutes into time zones. The power table group 1200 is stored in a storage device such as the RAM 1103, the ROM 1102, the magnetic disk 1105, and the optical disk 1107.

  FIG. 13 is an explanatory diagram illustrating an example of a reference value table. In the reference value table 1300, electric power serving as a reference is registered for each office. The reference value table 1300 has an establishment ID item and a reference value item. The establishment ID for identifying the establishment is registered in the establishment ID item. In the item of reference value, electric power that serves as a reduction standard for each office is registered.

  By setting information in each field, reference data 1301-1 to 1301-4 are stored as records. The reference value table 1300 is stored in a storage device such as the RAM 1103, the ROM 1102, the magnetic disk 1105, and the optical disk 1107. It is assumed that the reference value table 1300 and the power tables 1201-1 to 1201-4 are associated with each other by the establishment ID.

  Next, a calculation example of the output value of the first objective function will be described with reference to FIG. 14, and a calculation example of the output value of the second objective function will be described with reference to FIG. Here, as a parameter belonging to the set P, a parameter M15 that is the maximum parameter and a parameter M1 that is the minimum parameter will be described as an example.

  FIG. 14 is an explanatory diagram illustrating an example of calculating the output value of the first objective function. First, the output value of the first objective function when the parameter M15 is given to the first objective function will be described. For example, the detection device 400 can calculate the peak power of the group (F1, F2, F3, F4) included in the parameter M15 by referring to the power table group 1200. The peak power of the group (F1, F2, F3, F4) is the average use of each office included in the group when the date is “September 10” and the time zone is “0: 30-” Since it is the sum of electric power, it is as follows.

Peak power of group (F1, F2, F3, F4) = 1800 + 1800 + 800 + 820
= 5220

  PW in FIG. 14 is the peak power of the group. Since the parameter M15 has only one group, f1 (M15) is 5220 [W].

  Next, the output value of the first objective function when the parameter M1 is given to the first objective function will be described. For example, the detection apparatus 400 refers to the power table group 1200 to calculate the peak power of each of the group (F1), the group (F2), the group (F3), and the group (F4) included in the parameter M1.

  The peak power of the group (F1) is the average power used “2500” in the case of the date “August 30” and the time zone “14:00”. The peak power of the group (F2) is the average power consumption “1800” in the case of the date “September 10” and the time zone “0: 30-”. The peak power of the group (F3) is the average used power “900” when the date is “September 10” and the time zone is “1:00”. The peak power of the group (F4) is the average power used “910” when the date is “August 1” and the time zone is “1:00”. Therefore, f1 (M1) is as follows.

f1 (M1) = 2500 + 1800 + 900 + 910
= 6110 [W]

  The relationship “f1 (M1) ≧ f1 (M15)” is established. Next, an example of calculating the output value of the second objective function will be described with reference to FIG.

  FIG. 15 is an explanatory diagram illustrating an example of calculating the output value of the second objective function. The second objective function is a function for calculating the minimum value of the peak power reduction rate of the group included in each parameter. The peak power reduction rate is an index indicating how much the peak power of a group included in a certain parameter is reduced with respect to the power when the reference value table 1300 is used.

  The upper left side of FIG. 15 shows the peak power of the group included in the parameter M15 based on the power table group 1200 and the peak power of each group of the group group included in the parameter M1. The upper right side of FIG. 15 shows the peak power of the group included in the parameter M15 based on the reference value table 1300 and the peak power of each group of the group group included in the parameter M1.

  The peak power of the group included in the parameter M15 based on the power table group 1200 and the peak power of each group of the group group included in the parameter M1 are the same as the example illustrated in FIG. The peak power of the group (F1, F2, F3, F4) included in the parameter M15 based on the reference value table 1300 is 7000. The peak power of the group (F1) included in the parameter M1 based on the reference value table 1300 is 3000, the peak power of the group (F2) is 2000, the peak power of the group (F3) is 1000, and the group (F4) The peak power is 1000.

  Since the parameter M15 has one group, the detection apparatus 400 calculates f2 (M15) by calculating the peak reduction rate of one group. f2 (M15) is 0.254 (25.4 [%]). Since the parameter M1 has four groups, the detection apparatus 400 calculates the peak reduction rate of each of the four groups. Then, the detection apparatus 400 identifies the minimum value from the calculated four peak reduction rates. f2 (M1) is 0.09 (9 [%]). Therefore, the relationship “f2 (M1) ≦ f2 (M15)” is established.

  Hereinafter, calculation of the output values of the first and second objective functions has been described with reference to FIGS. 14 and 15, respectively, and a detailed example will be omitted.

<Functional Example of Detection Device 400>
FIG. 16 is a block diagram illustrating an example of functions of the detection apparatus 400. The detection apparatus 400 includes an acquisition unit 1601, an integration unit 1602, a division unit 1603, a calculation unit 1604, a detection unit 1605, a determination unit 1606, a determination unit 1607, a setting unit 1608, an output unit 1609, Have The detection apparatus 400 includes a power table group 1200 and a reference value table 1300.

  Specifically, the processing from the acquisition unit 1601 to the output unit 1609 is coded in a detection program stored in a storage device such as the ROM 1102, the RAM 1103, the magnetic disk 1105, and the optical disk 1107 shown in FIG. For example, the CPU 1101 reads the detection program stored in the storage device and executes the processing coded in the detection program. Thereby, the functions of the acquisition unit 1601 to the output unit 1609 are realized.

  Further, the processing results of the respective functional units are stored in a storage device such as the RAM 1103, the magnetic disk 1105, and the optical disk 1107, for example.

  First, the acquisition unit 1601 acquires parameters obtained by grouping element groups each having an observed value into one or a plurality of groups. Specifically, for example, the acquisition unit 1601 may acquire parameters from a storage device such as the RAM 1103, the magnetic disk 1105, and the optical disk 1107. As described above, the element groups are the establishments F1 to F4 which are establishment IDs, and the power values are stored in association with the establishments F1 to F4 in the power tables 1201-1 to 1201-4. is there. The acquisition result is stored in a storage device such as the RAM 1103, the magnetic disk 1105, and the optical disk 1107.

  Then, the integration unit 1602 integrates two groups in the group group included in the acquired parameter into one, and the division unit 1603 includes two or more elements in the group group included in the parameter after integration. Divide the group into two groups. The integration result and the division result are stored in storage devices such as the RAM 1103, the magnetic disk 1105, and the optical disk 1107, respectively.

  Further, when there are a plurality of parameters after integration, the dividing unit 1603 performs a dividing process on each parameter of the plurality of parameters after integration. As a result, a combination of output values of the first and second objective functions, which are detection targets of non-inferiority candidates, is obtained for each parameter after division.

  Here, a case where the parameter M2 is acquired by the acquisition unit 1601 will be described as an example. The integration unit 1602 integrates the two groups in the parameter M2 into one, thereby creating parameters M8, M9, and M10 as parameters after integration. Then, the dividing unit 1603 generates parameters M1, M2, M3, M5, M6, and M7 by dividing a group including two or more elements for each of the integrated parameters M8, M9, and M10 into two groups. Is done. Here, the acquired parameter M2 is included in the parameters after division by the division unit 1603 with respect to the parameters after integration by the integration unit 1602.

  Next, the calculation unit 1604 calculates a combination of output values of the first and second objective functions by giving the divided parameters to each of the first objective function and the second objective function. The calculation result is stored in a storage device such as the RAM 1103, the magnetic disk 1105, and the optical disk 1107.

  In the case described above, the integration process by the integration unit 1602 and the division process by the division unit 1603 are each performed once. However, the present invention is not limited to this. For example, the integration process by the integration unit 1602 and the division process by the division unit 1603 are respectively performed. Multiple times may be performed. For example, when the integration is performed for the acquired parameters, the integration unit 1602 recursively executes the integrated parameters a predetermined number of times. When the division unit 1603 executes division for a parameter after integration obtained by executing a predetermined number of times, the division unit 1603 recursively executes the predetermined number of times for the parameter after division. Then, the calculation unit 1604 gives a combination of output values of the first and second objective functions by giving the divided parameters obtained by executing the predetermined number of times to each of the first and second objective functions. calculate.

  The detection apparatus 400 increases the number of division processing and integration processing to increase a wider range of output value combinations that can be taken by the combination of the output values of the first and second objective functions as a non-inferior solution candidate. It can be set as a detection target of a combination. Accordingly, since the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared with the case where the number of division processing and integration processing is one each, the detection apparatus 400 becomes a candidate for non-inferior solutions. The accuracy of detecting a combination as a non-inferior solution can be improved. In addition, even when the number of detection targets of combinations that are non-poor candidates is increased, the detection apparatus 400 is smaller than the number of combinations of output values by a conventional random search or full search, so Reduction can be achieved.

  Then, the detection unit 1605 generates a non-inferior solution from among the calculated combination of output values and the combination of output values when the acquired parameters are given to each of the first and second objective functions. Detect candidate combinations.

  Next, the output unit 1609 outputs combinations that are candidates for non-inferior solutions detected by the detection unit 1605. For example, the output format may be stored in a storage device such as the RAM 1103, the ROM 1102, the magnetic disk 1105, and the optical disk 1107, or the detected combinations of non-poor candidates are graphed and displayed on the display 1108. May be. For example, the output unit 1609 may output a combination that is a candidate for a non-inferior solution and a parameter that is given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution. .

  The acquisition unit 1601 newly acquires parameters to be given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution detected by the detection unit 1605. Thereby, the detection apparatus 400 can repeatedly perform the detection process of the combination which becomes a non-inferiority candidate. Therefore, the detection apparatus 400 can reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found.

  Then, for example, the determination unit 1607 determines whether or not the combination that is a candidate for non-inferiority detected by the detection unit 1605 matches the acquired parameter. Then, when the determination unit 1607 determines that the combination that is a candidate for the non-inferior solution detected matches the acquired parameter, the setting unit 1608 selects a combination that is a candidate for the non-inferior solution detected. Set to a non-poor combination. The output unit 1609 outputs a non-poor combination set by the setting unit 1608.

  In addition, when the determination unit 1607 determines that the combination that is a detected candidate for non-inferiority matches the acquired parameter, the number of combinations that are detected candidates for non-inferior solution is predetermined. It is determined whether or not the number is more than the number. If the setting unit 1608 determines that the number is equal to or greater than the predetermined number, the setting unit 1608 sets the detected combination that is a non-inferior solution candidate to a combination that is a non-inferior solution.

  In addition, the acquisition unit 1601 acquires a parameter group from the first parameter to the second parameter in which the number of groups is smaller than the first parameter according to the order relationship. Then, the integration unit 1602 integrates two groups into one for each parameter of the acquired parameter group. That is, for each acquired parameter, a combination of output values of the first and second objective functions that are detection targets of non-inferiority candidates is obtained. Thereby, compared with the case where one parameter is acquired, the number of parameters that are targets of integration processing increases, and thus the number of detection targets of combinations that are candidates for non-inferiority increases. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Further, the first parameter may be a minimum parameter and the second parameter may be a maximum parameter. When the minimum parameter is given to the output values of the first and second objective functions, the output value of the first objective function is the maximum, and the output value of the second objective function is the minimum. When the maximum parameter is given to the output values of the first and second objective functions, the output value of the first objective function is the minimum and the output value of the second objective function is the maximum. Therefore, the detection apparatus 400 can obtain a combination that is a candidate for a non-inferior solution such as the Pareto solution shown in FIG.

  In addition, the determination unit 1606 determines whether or not the integration processing by the integration unit 1602 and the division processing by the division unit 1603 have been performed for a threshold value or more. For example, when the process of detecting combinations that are candidates for non-inferior solutions is repeatedly performed, the determination unit 1606 determines whether or not a predetermined time has elapsed since the time when the parameter was first acquired by the acquisition unit 1601. Also good. Alternatively, for example, the determination unit 1606 may count the number of integration processes and the number of division processes to determine whether the count value is equal to or greater than a threshold value.

  When the determination unit 1606 determines that the integration process and the division process have been performed by a threshold or more, the dividing unit 1603 includes two or more elements for the acquired parameter before the integration process by the integration unit 1602. Divide the group into two groups. Next, the integration unit 1602 integrates two groups into one for the parameters after division by the division unit 1603. Then, the calculation unit 1604 gives the parameters after integration obtained by the integration unit 1602 to each of the first objective function and the second objective function, thereby outputting the first and second objective functions. Calculate a combination of values.

  As described above, a parameter group obtained when the division process is executed after the integration process is executed for a certain parameter, and a parameter group obtained when the integration process is executed after the division process is executed. And the relationship of Expression (14) is established. Therefore, when the number of parameters obtained when the division processing is executed after the integration processing is executed is larger than the number of parameters obtained when the integration processing is executed after the division processing is executed. There is.

  Therefore, even if the acquired parameters are in the execution order in which the division process is performed after the integration process, if it is determined that the time taken to detect a combination that is a non-inferior solution candidate is long, the detection device 400 integrates Swap the execution order of processing and split processing. As a result, the detection apparatus 400 can reduce the combination of output values to be detected as non-poor candidate candidates, and the amount of calculation required for detecting a combination of output values that is better than a combination of output values that have already been determined. Can be reduced. Therefore, the detection apparatus 400 can increase the detection speed for detecting a combination that is a non-poor candidate.

  The example in which the dividing process by the dividing unit 1603 is executed next to the integrating process by the integrating unit 1602 as in the first embodiment has been described. Next, an example in which the dividing process by the dividing unit 1603 is executed next to the integrating process by the integrating unit 1602 as in the second embodiment will be described.

  First, the acquisition unit 1601 acquires parameters obtained by grouping element groups each having an observed value into one or a plurality of groups. Then, the dividing unit 1603 divides a certain group including two or more elements out of the group group included in the acquired parameter into two groups. The integration unit 1602 integrates two groups in the group group included in the divided parameters into one.

  Further, when there are a plurality of parameters after division, the integration unit 1602 performs integration processing for each parameter of the plurality of parameters after division. Thereby, compared with the case where the number of parameters after division is one, the number of detection targets of combinations that are candidates for non-inferior solutions increases. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Here, a case where the parameter M11 is acquired by the acquisition unit 1601 will be described as an example. The dividing unit 1603 generates parameters M4 and M5 by dividing a group including two or more elements included in the parameter M11 into two groups. The integration unit 1602 creates parameters M8, M10, M11, M12, and M14 by integrating two groups into one for each of the divided parameters M4 and M5.

  Next, the calculation unit 1604 calculates a combination of output values of the first and second objective functions by giving the integrated parameters to each of the first objective function and the second objective function. Further, when there are a plurality of parameters after integration, the calculation unit 1604 gives each parameter of the plurality of parameters after integration to each of the first objective function and the second objective function. A combination of output values of the first and second objective functions is calculated.

  In the above-described case, the dividing process by the dividing unit 1603 and the integrating process by the integrating unit 1602 are each performed once, but the present invention is not limited to this. For example, the dividing process by the dividing unit 1603 and the integrating process by the integrating unit 1602 are respectively Multiple times may be performed. For example, when the division is executed for the acquired parameter, the division unit 1603 recursively executes the predetermined number of times for the parameter after the division. Then, when the integration is executed for the divided parameters obtained by executing the predetermined number of times, the integration unit 1602 recursively executes the predetermined number of times for the parameters after the integration. Then, the calculation unit 1604 gives the first and second objective functions by giving the integrated parameters obtained by executing the predetermined number of times to the first objective function and the second objective function, respectively. The combination of output values is calculated.

  As a result, the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared to the case where the division process and the integration process are each performed once. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution. Accordingly, even when the number of detection targets of combinations that are non-inferior solution candidates is increased, the detection apparatus 400 is less than the number of combinations of output values obtained by a random search or a full search as in the related art. Can be reduced.

  Then, the detection unit 1605 generates a non-inferior solution from among the calculated combination of output values and the combination of output values when the acquired parameters are given to each of the first and second objective functions. Detect candidate combinations.

  Then, the output unit 1609 outputs a combination that is a non-inferior solution candidate detected by the detection unit 1605. For example, the output unit 1609 outputs a combination that is a non-poor candidate to a storage device such as the RAM 1103, the ROM 1102, the magnetic disk 1105, and the optical disk 1107. Alternatively, for example, the output unit 1609 associates a combination that is a candidate for a non-inferior solution with a parameter that is given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution in the storage device. It may be memorized.

  The acquisition unit 1601 newly acquires parameters to be given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution detected by the detection unit 1605. As a result, the integration process, the division process, and the detection process are repeatedly executed.

  Then, for example, the determination unit 1607 determines whether or not the combination that is a candidate for non-inferiority detected by the detection unit 1605 matches the acquired parameter. Then, when the determination unit 1607 determines that the combination that is a candidate for the non-inferior solution detected matches the acquired parameter, the setting unit 1608 selects a combination that is a candidate for the non-inferior solution detected. Set to a non-poor combination. The output unit 1609 outputs a non-poor combination set by the setting unit 1608.

  In addition, when the determination unit 1607 determines that the detected combination that is a non-inferiority candidate matches the acquired parameter, the number of combinations that are non-inferiority candidates is equal to or greater than a predetermined number. Judge whether there is. If the setting unit 1608 determines that the number is equal to or greater than the predetermined number, the setting unit 1608 sets the detected combination that is a non-inferior solution candidate to a combination that is a non-inferior solution.

  In addition, the acquisition unit 1601 acquires a parameter group from the first parameter to the second parameter in which the number of groups is smaller than the first parameter according to the order relationship. Then, the integration unit 1602 integrates two groups into one for each parameter of the acquired parameter group. Thereby, compared with the case where the acquired parameter is one, the number of parameters that are targets of integration processing increases, and thus the number of detection targets of combinations that are candidates for non-inferior solutions increases. Therefore, the detection apparatus 400 can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution. In addition, even when the number of detection targets of combinations that are non-poor candidates is increased, the detection apparatus 400 is smaller than the number of combinations of output values obtained by a random search or a full search as in the related art, so that the amount of calculation is reduced. Can be achieved.

  Further, the first parameter may be a minimum parameter and the second parameter may be a maximum parameter. When the minimum parameter is given to the output values of the first and second objective functions, the output value of the first objective function is the maximum, and the output value of the second objective function is the minimum. When the maximum parameter is given to the output values of the first and second objective functions, the output value of the first objective function is the minimum and the output value of the second objective function is the maximum. Thereby, it is possible to obtain a Pareto output value that connects from the combination of the output values of the first and second objective functions for the minimum parameter to the combination of the output values of the first and second objective functions for the maximum parameter. .

  Further, the integration unit 1602 acquires the combination before the division processing by the division unit 1603 when the determination unit 1607 determines that the detected combination that is a non-inferiority candidate matches the acquired parameter. The two groups possessed by the parameters are integrated into one. Then, the dividing unit 1603 divides a group including two or more elements out of the group group included in the post-integration parameters obtained by the integration unit 1602 into two groups. The calculation unit 1604 gives a combination of output values of the first and second objective functions by giving the parameters after division by the division unit 1603 to each of the first objective function and the second objective function. calculate.

  As described above, a parameter group obtained when division processing is performed after integration processing has been performed for a certain parameter, and obtained when integration processing is executed when division processing has been performed for a certain parameter. The relationship of the formula (14) is established with the parameter group. Therefore, when the number of parameters obtained when the division processing is executed after the integration processing is executed is larger than the number of parameters obtained when the integration processing is executed after the division processing is executed. There is.

  Therefore, if the detected combination that is a candidate for non-inferiority is not updated, the detection apparatus 400 executes the division process and the integration process so that the division unit 1603 performs the division process after the integration process by the integration unit 1602. May be switched. As a result, the number of detection targets of combinations that are candidates for non-inferior solutions after switching increases, so that the detection apparatus 400 can improve the accuracy of detecting combinations that are candidates for non-inferior solutions as non-inferior solutions. it can.

(Example of detection processing procedure performed by the detection apparatus 400)
FIG. 17 is a flowchart illustrating a detection processing procedure example 1 performed by the detection apparatus 400. First, the detection apparatus 400 acquires a parameter (step S1701). Here, the acquired parameter is referred to as an acquisition parameter. The detection apparatus 400 acquires a combination of output values of the first and second objective functions for the acquisition parameters (step S1702). Here, the detection apparatus 400 acquires the combination of the output values of the first and second objective functions when the acquisition parameters are given to the first and second objective functions, but may calculate them. .

  The detection apparatus 400 sets the set Q ← split (join (acquisition parameter)) (step S1703). In step S1703, the detection apparatus 400 performs integration processing on the acquired parameters. And the detection apparatus 400 divides | segments the parameter after integration by a division | segmentation process. The detection apparatus 400 puts the divided parameters into the set Q.

  Then, the detection apparatus 400 specifies a parameter group obtained by removing the acquired parameter from the set Q (step S1704), and calculates a combination of the output values of the first and second objective functions for each parameter of the remaining parameters ( Step S1705). The parameters obtained by executing the post-division process after the integration process is executed for the acquisition parameters include the acquisition parameters. Since the combination of the output values of the first and second objective functions for the acquired parameters has already been acquired in step S1702, in step S1704, the combination of the output values of the first and second objective functions is excluded from the calculation target. ing.

  Next, the detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from among a combination of output values for the acquired parameter and a combination of calculated output values (step S1706). Then, the detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S1707), and ends the series of processes. In step S <b> 1707, the detection apparatus 400 includes a combination that is a candidate for a detected non-inferior solution and a parameter that is given to the first and second objective functions when obtaining a combination that is a candidate for a detected non-inferior solution. May be output in association with each other.

  FIG. 18 is a flowchart illustrating a detection processing procedure example 2 performed by the detection apparatus 400. Step S1801, step S1802, and step S1804 to step S1807 shown in FIG. 18 are the same as S1701, step S1702, and step S1704 to step S1707 shown in FIG.

  Here, step S1803 which is processing different from the detection processing procedure example 1 shown in FIG. 17 will be described. After step S1802, the detection apparatus 400 sets the set Q ← join (split (acquisition parameter)) (step S1803), and proceeds to step S1804. In step S1803, the detection apparatus 400 performs a dividing process on the acquired parameter. In step S1803, the detection apparatus 400 performs integration processing on the divided parameters. In step S1803, the detection apparatus 400 puts the integrated parameters into the set Q.

  FIGS. 19 and 20 are flowcharts illustrating a detection processing procedure example 3 performed by the detection apparatus 400. The detection processing procedure example 3 shows a procedure example in which the integration processing and the division processing are recursively repeated when the division processing is executed next to the integration processing.

  First, the detection apparatus 400 acquires a parameter (step S1901). Here, the acquired parameter is referred to as an acquisition parameter. Next, the detection apparatus 400 acquires a combination of output values of the first and second objective functions for the acquisition parameter (step S1902).

  The detection apparatus 400 sets “set Q ← acquired parameter” (step S1903) and “j = 0” (step S1904). “Set Q ← acquired parameter” indicates that an acquired parameter is to be included in set Q. The detection apparatus 400 determines whether or not “the number of times T ≧ j” is satisfied (step S1905). When “the number of times T ≧ j” (step S1905: Yes), the detection apparatus 400 sets “set Q = join (Q)” (step S1906). In step S1906, the detection apparatus 400 newly sets the parameters obtained by performing the integration process on the parameters belonging to the set Q to the set Q.

  The detection apparatus 400 sets “j = j + 1” (step S1907), and returns to step S1905. Returning to step S1905, the processes of steps S1906 and S1907 are repeated until j becomes larger than T. That is, when the integration is executed for the acquired parameters, the detection apparatus 400 recursively executes the integration parameters a predetermined number of times. Here, the predetermined number of times is the number of times T, and the integration process is performed the number of times T + 1 times.

  On the other hand, when “number of times T ≧ j” is not satisfied (step S1905: No), the detection apparatus 400 sets j = 0 (step S1908), and determines whether “number of times T ≧ j” is satisfied (step S1909). If “the number of times T ≧ j” (step S1909: Yes), the detection apparatus 400 sets “set Q = split (Q)” (step S1910). In step S1910, the detection apparatus 400 performs division processing on each parameter belonging to the set Q, and sets the divided parameters as a new set Q.

  Next, the detection apparatus 400 sets “j = j + 1” (step S1911), and returns to step S1909. Returning to step S1909, the processes of step S1910 and step S1911 are repeated until j becomes larger than T. That is, when the division is performed on the parameters after integration, the detection apparatus 400 recursively executes the predetermined number of times on the parameters after the division. Here, the predetermined number of times is the number of times T, and the division process is performed the number of times T + 1 times.

  On the other hand, when “the number of times T ≧ j” is not satisfied (step S1909: NO), the detection apparatus 400 specifies a parameter group obtained by removing the acquired parameter from the set Q (step S1912). Then, the detection apparatus 400 calculates a combination of output values of the first and second objective functions for each of the remaining parameters (step S1913). Next, the detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from among a combination of output values for the acquired parameter and a combination of calculated output values (step S1914). Then, the detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S1915), and ends the series of processes. The detection apparatus 400 associates a combination that is a candidate for a detected non-inferior solution with a parameter given to the first and second objective functions when obtaining a combination that is a candidate for a detected non-inferior solution. It may be output.

  21 and 22 are flowcharts illustrating a detection processing procedure example 4 performed by the detection apparatus 400. The detection processing procedure example 4 shows a procedure example in which the division processing and the integration processing are recursively repeated when the integration processing is executed next to the division processing.

  First, the detection apparatus 400 acquires a parameter (step S2101). Here, the acquired parameter is referred to as an acquisition parameter. Next, the detection apparatus 400 acquires a combination of output values of the first and second objective functions for the acquisition parameter (step S2102).

  The detection apparatus 400 sets “set Q ← acquired parameter” (step S2103) and j = 0 (step S2104). The detection apparatus 400 determines whether or not “the number of times T ≧ j” (step S2105). When “the number of times T ≧ j” (step S2105: Yes), the detection apparatus 400 sets “set Q = split (Q)” (step S2106). In step S <b> 2106, the detection apparatus 400 newly sets a parameter obtained by performing a division process on parameters belonging to the set Q as a set Q.

  Then, the detection apparatus 400 sets “j = j + 1” (step S2107), and returns to step S2105. Returning to step S2105, the processes of step S2106 and step S2107 are repeated until j becomes larger than T. That is, when the obtained parameter is divided, the detection apparatus 400 recursively executes the divided parameter a predetermined number of times. Here, the predetermined number of times is the number of times T, and the division process is performed the number of times T + 1 times.

  On the other hand, when “number of times T ≧ j” is not satisfied (step S2105: No), the detection apparatus 400 sets “j = 0” (step S2108), and determines whether or not “number of times T ≧ j” (step S2109). ). If “the number of times T ≧ j” (step S2109: Yes), the detection apparatus 400 sets “set Q = join (Q)” (step S2110). In step S2110, the detection apparatus 400 newly sets the parameter after integration obtained by performing the integration process on the parameters belonging to the set Q as the set Q.

  Next, the detection apparatus 400 sets “j = j + 1” (step S2111), and returns to step S2109. Returning to step S2109, the processes of step S2110 and step S2111 are repeated until j becomes larger than T. That is, when the integration is executed for the divided parameters, the detection device 400 recursively executes the integration parameters a predetermined number of times. Here, the predetermined number of times is the number of times T, and the integration process is performed the number of times T + 1 times.

  On the other hand, when “number of times T ≧ j” is not satisfied (step S2109: NO), the detection apparatus 400 specifies a parameter group obtained by removing the acquired parameter from the set Q (step S2112). Then, the detection apparatus 400 calculates a combination of output values of the first and second objective functions for each of the remaining parameters (step S2113). Next, the detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from among a combination of output values for the acquired parameter and a combination of calculated output values (step S2114). Then, the detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S2115), and ends the series of processes. The detection apparatus 400 associates a combination that is a candidate for a detected non-inferior solution with a parameter given to the first and second objective functions when obtaining a combination that is a candidate for a detected non-inferior solution. It may be output.

  23 and 24 are flowcharts illustrating a detection processing procedure example 5 performed by the detection apparatus 400. In detection processing procedure example 5, a description will be given of a procedure in which, when division processing is executed next to integration processing, a combination that is a candidate for a non-inferior solution is repeatedly detected and a combination of non-poor solutions is set.

  First, the detection apparatus 400 acquires a parameter group from the first parameter to the second parameter (step S2301). Next, the detection apparatus 400 gives each parameter of the parameter group to each of the first and second objective functions, so that the output values of the first and second objective functions are obtained for each parameter of the acquired parameter group. A combination is calculated (step S2302). In step S2302, the detection apparatus 400 calculates a combination of output values of the first and second objective functions for each parameter of the acquired parameter group. Not only this but the combination of the calculated output value about each parameter of the acquired parameter group may be acquired. Then, the detection apparatus 400 sets the calculated combination of output values as a combination that is a non-inferior solution candidate (step S2303). That is, for each parameter in the acquired parameter group, the combination of the output values of the first and second objective functions is a combination that is an initial non-inferiority candidate.

  Then, the detection apparatus 400 outputs a combination that is a candidate for a non-inferior solution (step S2304). The detection apparatus 400 may associate and store a combination that is a candidate for a non-inferior solution and a parameter that is given to the first and second objective functions when a combination that is a candidate for a non-inferior solution is obtained.

  Next, the detection apparatus 400 sets the set S = the acquired parameter group (step S2305), sets the set Q to be empty (step S2306), and sets “set Q = split (join (S))” (step). S2307). In step S2307, integration processing is performed for each parameter of the acquired parameter group. Then, division processing is performed on the parameters after integration.

  Then, the detection apparatus 400 specifies a remaining parameter group obtained by removing the parameters included in the set S from the set Q (step S2308). Next, the detection apparatus 400 gives each parameter of the residual parameter to the first and second objective functions, thereby combining the output values of the first and second objective functions for each parameter of the residual parameter. Calculate (step S2309).

  The detection apparatus 400 newly sets a combination of output values of the first and second objective functions for each parameter of the set S and a combination of calculated output values as candidates for non-inferior solutions. Is detected (step S2310). Thereafter, the detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S2311). The detection apparatus 400 outputs the combination of the detected non-inferiority candidate and the parameters given to the first and second objective functions in association with each other when obtaining the non-inferiority candidate combination. Also good.

  Then, the detection apparatus 400 determines whether or not the end condition is satisfied (step S2312). For example, in step S2312, the detection apparatus 400 determines that all combinations of the output values of the first and second objective functions for each parameter of the set S and combinations that are newly detected non-inferiority candidates are all. It may be determined whether or not they match. If all match, there is no change in the combination that is a non-inferior solution candidate, and the detection apparatus 400 determines that the termination condition is satisfied.

  Further, for example, in step S2312, the detection apparatus 400 may determine whether or not the division process and the integration process have been performed for a threshold value or more. When the division process and the integration process are executed for the threshold value or more, the detection apparatus 400 determines that the end condition is satisfied. Thereby, if the time taken to determine the combination of non-inferior solutions is longer than the time desired by the user, the detection apparatus 400 can be forcibly terminated. Further, for example, the user may instruct the end using the input unit, and the detection apparatus 400 may accept the end instruction and determine that the end condition is satisfied. Examples of the input means include a mouse 1111 and a keyboard 1110.

  If the termination condition is not satisfied (step S2312: NO), the detection apparatus 400 determines that “the set S = the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution”. It is assumed that “the parameter is given” (step S2313). In step S <b> 2313, the detection apparatus 400 newly acquires the parameters given to the first and second objective functions as the parameters of the integration process when obtaining a combination that is a candidate for the detected non-inferior solution. By returning to step S2307 after step S2313, the detection apparatus 400 repeats the process of detecting combinations that are candidates for non-inferior solutions until the end condition is satisfied.

  On the other hand, when the end condition is satisfied (step S2312: YES), the detection apparatus 400 sets the combination that is a candidate for the detected non-inferiority to a combination that is a non-inferior solution (step S2314). And the detection apparatus 400 outputs the set which becomes the set non-poor solution (step S2315), and complete | finishes a series of processes. The detection apparatus 400 may associate and output the set combination that is not inferior and the parameters given to the first and second objective functions when the combination that is not inferior is obtained.

  25 and 26 are flowcharts illustrating a detection processing procedure example 6 performed by the detection apparatus 400. In the detection processing procedure example 6, in the case where the integration processing is executed next to the division processing for the acquired parameters, the combination that is a candidate for the non-poor solution is repeatedly detected, and the combination of the non-poor solution is determined. This is the procedure for setting.

  The processes other than step S2507 in steps S2501 to S2515 shown in FIGS. 25 and 26 are the same as the processes other than step S2307 in steps S2301 to S2315 shown in FIGS. Therefore, detailed description of the same processing is omitted.

  Here, step S2507, which is processing different from the detection processing procedure 5 shown in FIGS. 23 and 24, will be described. After step S2506 or step S2513, the detection apparatus 400 sets “set Q = join (split (S))” (step S2507). In step S2507, division processing is performed for each parameter of the acquired parameter group. Then, an integration process is performed on the divided parameters.

  27 and 28 are flowcharts illustrating a detection processing procedure example 7 performed by the detection device 400. The detection processing procedure example 7 describes a procedure that is switched to be executed in the order from the division processing to the integration processing when the processing is executed in the order from the integration processing to the division processing.

  First, the detection apparatus 400 acquires a parameter group from the first parameter to the second parameter (step S2701). Next, the detection apparatus 400 gives each parameter of the parameter group to each of the first and second objective functions, so that the output values of the first and second objective functions are obtained for each parameter of the acquired parameter group. A combination is calculated (step S2702). In step S2702, the detection apparatus 400 calculates a combination of output values of the first and second objective functions for each parameter of the acquired parameter group. However, the present invention is not limited to this, and a combination of calculated output values for each parameter of the acquired parameter group may be acquired from the storage device. Then, the detection apparatus 400 sets the calculated combination of output values as a combination that is a non-inferior solution candidate (step S2703). That is, for each parameter in the acquired parameter group, the combination of the output values of the first and second objective functions is a combination that is an initial non-inferiority candidate.

  Then, the detection apparatus 400 outputs a combination that is a candidate for a non-inferior solution (step S2704). Here, the detection apparatus 400 may associate and store a combination that is a candidate for a non-inferior solution and a parameter that is given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution. Good.

  Next, the detection apparatus 400 sets “set S = acquired parameter group” (step S2705), sets the set Q to be empty (step S2706), and determines whether or not the integration process and the division process have been executed above the threshold. Judgment is made (step S2707). If it is determined that the integration process and the division process are not executed above the threshold (step S2707: No), the detection apparatus 400 sets “set Q = split (join (S))” (step S2708). In step S2708, integration processing is performed for each parameter of the acquired parameter group. Then, division processing is performed on the parameters after integration.

  On the other hand, if it is determined that the integration process and the division process have been executed for the threshold value or more (step S2707: Yes), the detection apparatus 400 sets “set Q = join (split (S))” (step S2709). As described above, the relationship of “split (join (S)) ⊇join (split (S))” is established. That is, there are cases in which “join (split (S))” is fewer than “split (join (S))” as the detection targets of combinations that are candidates for non-inferior solutions.

  Therefore, if the time taken for determining a combination of non-inferior solutions in step S2707 is longer than the time desired by the user, the detection apparatus 400 switches the order of the integration process and the division process. Since the number of parameters given to the first and second objective functions decreases, the calculation time for the detection apparatus 400 to calculate a combination of output values of the first and second objective functions can be reduced. Furthermore, it is possible to reduce the detection targets of combinations that are candidates for non-inferior solutions. Therefore, the detection apparatus 400 can reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found.

  Subsequently to step S2708 or step S2709, the detection apparatus 400 specifies a remaining parameter group obtained by removing the parameters included in the set S from the set Q (step S2710). Next, the detection apparatus 400 gives each parameter of the residual parameter to the first and second objective functions, thereby combining the output values of the first and second objective functions for each parameter of the residual parameter. Calculate (step S2711).

  The detection apparatus 400 newly sets a combination of output values of the first and second objective functions for each parameter of the set S and a combination of calculated output values as candidates for non-inferior solutions. Is detected (step S2712). The detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S2713). In step S2713, the detection apparatus 400 associates the detected combination that is a non-inferior solution candidate with the parameters given to the first and second objective functions when obtaining the combination that is a non-inferior solution candidate. May be output.

  Then, the detection apparatus 400 determines whether or not the end condition is satisfied (step S2714). For example, in step S2714, the detection apparatus 400 may determine whether or not a combination that has been detected as a non-inferiority candidate matches a combination that has been newly detected as a non-inferiority candidate. Good. If all match, there is no change in the combination that is a non-inferior solution candidate, so the detection apparatus 400 determines that the termination condition is satisfied. Alternatively, for example, the user may instruct termination using the input unit, and the detection apparatus 400 may accept the termination instruction and determine that the termination condition has been satisfied. Examples of the input means include a mouse 1111 and a keyboard 1110.

  If the termination condition is not satisfied (step S2714: NO), the detection apparatus 400 gives the first and second objective functions when the set S = a combination that is a detected non-inferior solution candidate is obtained. (Step S2715). In step S2715, the detection apparatus 400 newly acquires the parameters given to the first and second objective functions as the parameters of the integration process when obtaining a combination that is a candidate for the detected non-inferior solution. By returning to step S2706 after step S2715, the detection apparatus 400 repeats the process of detecting combinations that are candidates for non-inferior solutions until the end condition is satisfied.

  On the other hand, when the end condition is satisfied (step S2714: YES), the detection apparatus 400 sets the detected combination that is a non-inferior solution candidate to a combination that is a non-inferior solution (step S2716). And the detection apparatus 400 outputs the set which becomes the set non-poor solution (step S2717), and complete | finishes a series of processes.

  FIG. 29 and FIG. 30 are flowcharts illustrating a detection processing procedure example 8 performed by the detection apparatus 400. In detection processing procedure example 8, a description will be given of a procedure that is switched to be executed in the order of integration processing to division processing when executed in the order of division processing to integration processing.

  First, the detection apparatus 400 acquires a parameter group from the first parameter to the second parameter (step S2901). Next, the detection apparatus 400 gives each parameter of the parameter group to each of the first and second objective functions, so that the output values of the first and second objective functions are obtained for each parameter of the acquired parameter group. A combination is calculated (step S2902). In step S2902, the detection apparatus 400 calculates the combination of the output values of the first and second objective functions for each parameter in the acquired parameter group. The combination may be obtained from the storage device. Then, the detection apparatus 400 sets the combination of the calculated output values as a combination that is a non-inferior solution candidate (step S2903). That is, for each parameter in the acquired parameter group, the combination of the output values of the first and second objective functions is a combination that is an initial non-inferiority candidate.

  Then, the detection apparatus 400 outputs a combination that is a candidate for a non-inferior solution (step S2904). Here, the detection apparatus 400 may associate and store a combination that is a candidate for a non-inferior solution and a parameter that is given to the first and second objective functions when obtaining a combination that is a candidate for a non-inferior solution. Good.

  Next, the detection apparatus 400 sets the set S = the acquired parameter group (step S2905), sets the set Q to be empty (step S2906), and sets “set Q = join (split (S))” (step). S2907). In step S2907, division processing is performed for each parameter of the acquired parameter group. Then, division processing is performed on the parameters after integration.

  Then, the detection apparatus 400 specifies a remaining parameter group obtained by removing the parameters included in the set S from the set Q (step S2908). Next, the detection apparatus 400 gives each parameter of the residual parameter to the first and second objective functions, thereby combining the output values of the first and second objective functions for each parameter of the residual parameter. Calculate (step S2909).

  The detection apparatus 400 newly sets a combination of output values of the first and second objective functions for each parameter of the set S and a combination of calculated output values as candidates for non-inferior solutions. Is detected (step S2910). The detection apparatus 400 outputs a combination that is a candidate for the detected non-inferior solution (step S2911). In step S2911, the detection apparatus 400 associates the detected combination that is a non-inferior solution candidate with the parameters that are given to the first and second objective functions when obtaining a combination that is a non-inferior solution candidate. May be output.

  The detection apparatus 400 determines whether or not the combination of the output values of the first and second objective functions for each parameter of the set S matches the detected candidate combination of non-inferior solution ( Step S2912). If they do not match in step S2912 (step S2912: No), the detection apparatus 400 “set S = parameters given to the first and second objective functions when obtaining a combination that is a non-poor candidate” (Step S2913). In step S2913, the detection apparatus 400 newly acquires parameters to be given to the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution. After returning to step S2907 after step S2913, the detection apparatus 400 repeats the process of detecting combinations that are candidates for non-inferior solutions.

  On the other hand, if they match in step S2912 (step S2912: Yes), the detection apparatus 400 switches from executing the processing from the division processing to the integration processing to executing from the integration processing to the division processing. It is determined whether or not it has been completed (step S2914). If not switched (step S2914: No), the detection apparatus 400 sets the set Q to be empty (step S2917), sets “set Q = split (join (S))” (step S2918), and returns to step S2908. .

  On the other hand, when the switching has been completed in step S2914 (step S2914: Yes), the detection apparatus 400 sets the detected combination that is a non-inferior solution candidate to a combination that is a non-inferior solution (step S2915). And the detection apparatus 400 outputs the set which becomes the set non-poor solution (step S2916), and complete | finishes a series of processes.

  FIGS. 31 and 32 are flowcharts showing a detection processing procedure example 9 performed by the detection apparatus 400. FIG. Detection processing procedure example 9 shows a procedure for counting the number of combinations that are candidates for non-inferior solutions that are presumed to have been updated, and ending the detection processing when the count value is equal to or greater than a predetermined number. Thereby, the detection apparatus 400 can detect the combination which becomes non-poor solution as many as desired by the user.

  First, the detection apparatus 400 acquires a parameter group from the first parameter to the second parameter (step S3101). The detection apparatus 400 calculates a combination of output values of the first and second objective functions for each parameter of the acquired parameter group (step S3102).

  Then, the detection apparatus 400 sets “set S = acquired parameter group” (step S3103), and determines whether there is an unselected parameter in the set S (step S3104). When there is an unselected parameter (step S3104: Yes), the detection apparatus 400 selects one parameter from the unselected parameters (step S3105). Here, the selected parameter is referred to as a selection parameter.

  Next, the detection apparatus 400 sets “set Q = split (join (selection parameter))” (step S3106). In step S3106, the integration process is executed for the selected parameter. Then, a division process is executed for the parameters after integration, and the parameters after the division are substituted into the set Q. Next, the detection apparatus 400 specifies a residual parameter group obtained by removing the parameters of the set S from the set Q (step S3107), and the output values of the first and second objective functions for each parameter of the residual parameter group. Is calculated (step S3108). The detection apparatus 400 detects a combination that is a candidate for a non-inferior solution from the combination of the output values of the first and second objective functions for the parameters of the set S and the combination of the calculated output values. (Step S3109).

  And the detection apparatus 400 outputs the combination used as the candidate of the detected non-inferior solution (step S3110). The detection apparatus 400 determines whether or not there is a combination of the output values of the first and second objective functions for the selected parameter in the detected candidate combinations of non-inferior solutions (step S3111). In the case where the detected candidate combination of non-inferior solutions includes a combination of output values of the first and second objective functions for the selection parameter (step S3111: Yes), the detection apparatus 400 determines that “set W ← selection parameter (Step S3112). Then, the detection apparatus 400 determines whether or not “the number of parameters of the set W ≧ a predetermined number” (step S3113).

  In the case of “number of parameters in set W ≧ predetermined number” (step S3113: Yes), the detection apparatus 400 sets a combination that is a non-inferior solution candidate included in the set W as a combination of non-inferior solutions (step S3114). Then, the set combination of non-inferior solutions is output (step S3115), and the series of processing ends. On the other hand, if “the number of parameters of the set W ≧ predetermined number” is not satisfied (step S3113: No), the process returns to step S3104.

  On the other hand, when there is no combination of the output values of the first and second objective functions for the selected parameter in the detected candidate combination of non-inferior solutions (step S3111: No), the process proceeds to step S3116. In step S3116, the detection apparatus 400 determines whether or not the combination of the output values of the first and second objective functions for the parameters of the set W is a combination that is a detected candidate for non-inferiority ( Step S3116).

  When the combination of the output values of the first and second objective functions with respect to the parameters of the set W is not among the detected combinations that are candidates for non-inferior solutions (step S3116: No), the detection apparatus 400 has detected Parameters that are not in combinations that are candidates for non-inferior solutions are removed from the set W (step S3117). After step S3117, the process proceeds to step S3118. On the other hand, when the combination of the output values of the first and second objective functions for the parameters of the set W is a combination that is a candidate for the detected non-inferior solution (step S3116: Yes), the process proceeds to step S3118.

  Next to step S3117 or Yes in step S3116, the detection apparatus 400 determines that “the set S = parameters given to the first and second objective functions when obtaining a combination that is a detected non-inferior solution candidate”. (Step S3118). Then, the detection apparatus 400 selects one parameter from the detection parameters (step S3119), and returns to step S3106. The parameter selected in step S3119 is referred to as a selection parameter.

  In step S3104, when there is no unselected parameter in the set S (step S3104: No), a series of processing is ended. Alternatively, when there is no unselected parameter in the set S, the detection apparatus 400 sets a combination that is a candidate for a non-inferior solution detected to a combination that is a non-inferior solution, and a combination that is a non-inferior solution May be output. Alternatively, when there is no unselected parameter in the set S, the detection apparatus 400 may newly acquire a parameter and repeat the processes in steps S3101 to S3119.

  In the procedure shown in FIG. 31 and FIG. 32, the detection apparatus 400 detects a predetermined number of combinations that are non-inferiority rather than the accuracy of whether or not the update is completed for combinations that are candidates for non-inferior solutions. Has priority. Thereby, the detection apparatus 400 can detect the combination which becomes non-poor solution as many as desired by the user.

  33 and 34 are flowcharts illustrating a detection processing procedure example 10 performed by the detection apparatus 400. In the detection processing procedure example 10, for the non-inferiority candidates obtained by performing the division process and the integration process on the parameters, the number of combinations that are non-inferiority candidates that are estimated to have been updated is counted. If the count value is equal to or greater than the predetermined number, a procedure for ending the detection process is shown. Thereby, the detection apparatus 400 can detect the combination which becomes non-poor solution as many as desired by the user.

  The processes other than step S3306 in steps S3301 to S3319 shown in FIGS. 33 and 34 are the same as the processes other than step S3106 in steps S3101 to S3119 shown in FIGS. Therefore, detailed description of the same processing is omitted.

  After step S3305, the detection apparatus 400 sets “set Q = join (split (selection parameter))” (step S3306), and proceeds to step S3307. In step S3306, the division process is executed for the selected parameter. Then, an integration process is performed on the divided parameters, and the integrated parameters are substituted into the set Q.

<Application Example of Detection Device 400>
FIG. 35 is a diagram illustrating an application example of the detection apparatus 400. In FIG. 35, a network NW is a network NW in which servers 3501 and 3502 and clients 3531 to 3534 can communicate with each other. For example, in a local area network (LAN), a wide area network (WAN), the Internet, a mobile phone network, and the like. Composed.

  The server 3502 is a management server for a group of servers (servers 3521 to 3525) constituting the cloud 3520. Among the clients 3531 to 3534, the client 3531 is a notebook personal computer, the client 3532 is a desktop personal computer, the client 3533 is a mobile phone (may be a smartphone or a PHS (Personal Handyphone System)), and the client 3534 is a tablet terminal. Servers 3501, 3502, 3521 to 3525 and clients 3531 to 534 in FIG. 35 are realized by, for example, the computer shown in FIG.

  Further, in this embodiment, each CPU 1101 shown in FIG. 11 and a computer with different shared resources (for example, a mobile phone or a server shown in FIG. 35) are installed, and a plurality of computers are distributed via a network NW. It can also be applied to a configuration that performs parallel processing.

<Other problems>
In the present embodiment, as an example of the problem, an example in which a plurality of business establishments are divided into one or a plurality of groups has been described. Here is another example.
There is a problem “a set of workers E = {e1,..., Em (m ≧ 2)}, and each worker ei can perform work of quality q_ei at work time t_ei. Work time and work quality In order to improve both, the workers are divided into one or more groups. "

  Here, the set E is an element group. A parameter G = {G1,..., Gs} in which the set E is divided into one or a plurality of groups. For example, the work time taken for a certain work for each worker ID and data obtained by quantifying the work quality may be stored in the storage device.

  In another problem, the first objective function is a function that calculates the maximum work time among the group work times that the parameter has, and the second objective function calculates the total value of the work quality of the group that the parameter has. Function. As the quality of work increases when working in a group, the quality of work of the group is greater than the sum of the quality of work of each worker. For example, when the number of people in a group is one, the data obtained by quantifying the quality of work is used as it is, and when the number of people in a group is two, the data obtained by quantifying the quality of work of each worker. Is multiplied by 1.1 to calculate the work quality of the group. Therefore, the first objective function and the second objective function are in a trade-off relationship. Then, the present embodiment described above is used to solve other problems, so that the detection apparatus 400 can reduce the amount of computation required to detect a combination of output values that is better than a combination of output values that have already been determined. Can be achieved.

  As described above, the output values of the first and second objective functions change in a contradictory manner along the order relationship established by the group inclusion relationship between the two parameters. Therefore, the detection apparatus performs a group integration of a parameter that is presumed to obtain a better combination of output values than a combination of output values of the first and second objective functions for a certain parameter. Created by dividing groups. As a result, the detection apparatus can reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found. Therefore, the detection apparatus can increase the detection speed for detecting a combination that is a non-poor candidate.

  Further, the detection device acquires a parameter group from the first parameter to the second parameter larger than the first parameter according to the order relation. Accordingly, a combination of output values in a wider range that can be taken by the combination of output values of the first and second objective functions for the parameters included in the parameter set is set as a detection target of a combination that is a non-inferior solution candidate. Can do. Therefore, even when the number of detection targets of combinations that are non-poor candidates is increased, the detection device is smaller than the number of combinations of output values by the conventional random search or full search, so that the amount of calculation is reduced. Can be achieved. In addition, since the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared to the case of division after integration, the detection device has an accuracy of detecting combinations that are candidates for non-inferior solutions as non-inferior solutions. Improvements can be made.

  In addition, when the acquired parameters are integrated, the detection device recursively integrates the integrated parameters. Then, when division is performed on the integrated parameters obtained by recursively integrating, the detection apparatus performs recursive division on the divided parameters. Thereby, combinations of output values for a wider range of parameters along the parameters having an order relationship with the acquired parameters can be set as detection targets for combinations that are candidates for non-inferior solutions. Therefore, even when the number of detection targets of combinations that are non-poor candidates is increased, the detection device is smaller than the number of combinations of output values by the conventional random search or full search, so that the amount of calculation is reduced. Can be achieved. In addition, since the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared to the case of division after integration, the detection device has an accuracy of detecting combinations that are candidates for non-inferior solutions as non-inferior solutions. Improvements can be made.

  In addition, when there are a plurality of parameters after integration, the parameters after integration become targets for division, and the number of parameters to be divided increases. For this reason, the number of detection targets for combinations that are candidates for non-inferior solutions increases as compared to the case where there is one parameter after integration, so the detection apparatus detects combinations that are candidates for non-inferior solutions as non-inferior solutions. It is possible to improve accuracy.

  In addition, when there are a plurality of parameters after division, the number of parameters given to the first and second objective functions increases. For this reason, since the number of detection targets for combinations that are candidates for non-inferior solutions increases as compared to the case of one parameter after division, the detection apparatus detects combinations that are candidates for non-inferior solutions as non-inferior solutions. It is possible to improve accuracy.

  The detection apparatus newly obtains the parameters given to the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution. Thereby, the detection apparatus can repeat the detection of a combination that is a non-poor candidate. When obtaining a combination that is a candidate for a non-inferior solution, a combination of output values for parameters obtained by performing integration processing and division processing on the parameters given to the first and second objective functions, There is a possibility that the output value combination is better than the combination. Therefore, the detection device can improve the accuracy of detecting a combination that is a candidate for a non-inferior solution as a non-inferior solution compared to a case where parameters are randomly selected as in a conventional random search or a full search. it can.

  In addition, the number of parameters obtained by executing the division process after executing the integration process for the acquired parameters is the number of parameters obtained by executing the integration process after executing the division process for the acquired parameters. There may be more. Therefore, in the case where division processing is performed next to the integration processing for the acquired parameters, if it is determined that the time for detecting a combination that is a non-inferior solution candidate is long, the detection apparatus performs the integration processing and the division processing. Switch the execution order of processes. As a result, the number of detection targets of combinations that are candidates for non-inferior solutions is reduced, and the detection apparatus can increase the detection speed for detecting combinations that are candidates for non-inferior solutions.

  In addition, the detection apparatus sets the parameter group acquired first to the parameter group from the minimum parameter to the maximum parameter. Then, the detection device detects combinations that are candidates for non-inferior solutions based on the acquired parameter group. Furthermore, the detection apparatus can obtain a combination that becomes a non-inferiority candidate such as a Pareto solution by repeatedly detecting a combination that becomes a non-inferiority candidate. As a result, the detection apparatus can detect combinations that are candidates for non-inferior solutions from a wide range that can be taken by combinations of output values of the first and second objective functions. Therefore, the detection apparatus can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  In addition, when there is no change in a combination that is a non-inferior candidate, the detection apparatus determines that the combination that is a non-inferior candidate is not updated and determines that the combination that is a non-inferior candidate is not inferior. Set to a combination of solutions. Thereby, the detection apparatus can detect the non-inferior solution which can be taken along the order relationship of a certain acquired parameter. Therefore, the detection apparatus can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Further, when a predetermined number of combinations that are candidates for non-inferior solutions are obtained, the detection apparatus outputs combinations that have already been detected as candidates for non-inferior solutions as combinations of non-inferior solutions. Thereby, the detection apparatus can detect the combination which becomes a non-poor solution as many as desired by the user.

  Further, when the detection apparatus determines that the integration process and the division process have been executed for a threshold or more, the detection apparatus sets a combination that is a non-inferior solution candidate at the determination time to a non-inferior combination. Thereby, the detection apparatus can detect the combination which becomes a non-poor solution at high speed. For example, the detection device performs an update while displaying a combination that is a non-poor candidate on the display, so that when the user finds a desired combination of output values, an instruction to end the detection process by the detection device is detected. May be input using an input means. Examples of the input means include a mouse and a keyboard. Alternatively, for example, the detection apparatus may forcibly end the detection process when a predetermined time has elapsed in detecting a combination that is a non-inferior candidate.

  As described above, the detection apparatus divides a parameter that is estimated to obtain a better combination of output values than a combination of the output values of the first and second objective functions for a certain parameter. It is created by performing the integration process after performing. As a result, the detection apparatus can reduce the amount of calculation required to detect a combination of output values that is better than a combination of output values that have been found.

  In addition, the number of all parameters obtained by performing integration processing after division processing for a certain parameter may be less than the number of all parameters obtained by performing division processing after integration processing for a certain parameter. In other words, when the integration process is performed after the division process, the number of detection targets of combinations that are candidates for non-inferior solutions is reduced as compared to the case where the division process is performed after the integration process. Therefore, when the integration process is performed after the division process, the detection apparatus can increase the detection speed for detecting a combination that is a non-poor candidate. Conversely, when the division process is performed after the integration process, the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared to the case where the integration process is performed after the division process. When the integration process is performed after the division process, the detection device can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution.

  Further, the detection device acquires a parameter group from the first parameter to the second parameter larger than the first parameter according to the order relation. Thus, combinations of output values in a wider range that can be taken by the combinations of the output values of the first and second objective functions for the parameters included in the parameter set become detection targets for combinations that are candidates for non-inferior solutions. Accordingly, since the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared with the case where one parameter is acquired, the detection apparatus detects combinations that are candidates for non-inferior solutions as non-inferior solutions. It is possible to improve accuracy. In addition, even when the number of detection targets of combinations that are candidates for non-inferior solutions increases, the detection device is smaller than the number of combinations of output values by conventional random search or full search, so the amount of calculation is reduced. Can be achieved.

  In addition, when the obtained parameter is divided, the detection apparatus performs recursive division on the divided parameters and performs integration on the divided parameters obtained by recursive division. In the case of integration, the integration is recursively executed for the parameters after integration. Thereby, combinations of output values for a wider range of parameters along the parameters having an order relationship with the acquired parameters can be set as detection targets for combinations that are candidates for non-inferior solutions. Therefore, since the number of detection targets of combinations that are candidates for non-inferior solutions increases, the detection device can improve the accuracy of detecting combinations that are candidates for non-inferior solutions as non-inferior solutions. it can. In addition, even when the number of detection targets of combinations that are candidates for non-inferior solutions increases, the detection device is smaller than the number of combinations of output values by conventional random search or full search, so the amount of calculation is reduced. Can be achieved.

  Further, when there are a plurality of parameters after division, the parameters to be integrated increase. As a result, the number of detection targets for combinations that are candidates for non-inferior solutions increases as compared to the case where the number of parameters after division is one. Therefore, the detection apparatus can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution. In addition, even when the number of detection targets of combinations that are candidates for non-inferior solutions increases, the detection device is smaller than the number of combinations of output values by conventional random search or full search, so the amount of calculation is reduced. Can be achieved.

  In addition, when there are a plurality of parameters after integration, the parameters that are the calculation target of the output values of the first and second objective functions increase. Thereby, the number of detection targets of combinations that are candidates for non-inferior solutions increases as compared to the case of one parameter after integration. Therefore, the detection apparatus can improve the accuracy of detecting a combination that is a non-inferior solution candidate as a non-inferior solution. In addition, even when the number of detection targets of combinations that are candidates for non-inferior solutions increases, the detection device is smaller than the number of combinations of output values by conventional random search or full search, so the amount of calculation is reduced. Can be achieved.

  The detection apparatus newly obtains the parameters given to the first and second objective functions when obtaining a combination that is a candidate for the detected non-inferior solution. Thereby, the detection apparatus can repeat the update of the combination which becomes a non-inferiority candidate. When obtaining a combination that is a candidate for a non-inferior solution, a combination of output values for parameters obtained by performing integration processing and division processing on the parameters given to the first and second objective functions, There is a possibility that the output value combination is better than the combination. Therefore, the detection apparatus can improve the accuracy of detecting a combination that is a non-inferior candidate as a non-inferior solution compared to a case where parameters are randomly selected as in a conventional random search.

  In addition, the number of parameters obtained by executing the division process after executing the integration process for the acquired parameters is the number of parameters obtained by executing the integration process after executing the division process for the acquired parameters. There may be more. Therefore, even if the detection apparatus determines that the detection time for detecting a combination that is a candidate for non-inferiority is long even in the execution order in which the division processing is performed after the integration processing for the acquired parameters, Change the execution order of the split processing. As a result, the number of output value combinations to be detected as candidates for non-inferior solutions is reduced, so that the detection apparatus can reduce the amount of calculation required for detecting a combination of output values that is better than a combination of output values that have already been determined. Can be achieved.

  In addition, the detection apparatus sets the parameter group acquired first to the parameter group from the minimum parameter to the maximum parameter. The detection device can obtain a combination that is a non-inferior solution candidate, such as a Pareto solution, by repeatedly detecting a combination that is a non-inferior solution candidate. Thereby, the detection apparatus can detect a combination that is a candidate for a non-inferior solution from a wide range that a combination of output values of the first and second objective functions can take.

  In addition, when there is no change in a combination that is a non-inferior candidate, the detection device determines that the combination that is a non-inferior candidate is not updated, and the detected combination that is a non-inferior candidate is determined to be a non-inferior solution. Set to a combination of Thereby, the detection apparatus can detect the non-inferior solution which can be taken along the order relationship of a certain acquired parameter.

  In addition, when a combination that is a desired number of non-inferiority candidates is obtained by the user, the detection apparatus outputs a combination that has already been detected as a non-inferiority candidate as a non-inferiority combination. Thereby, the detection apparatus can detect the combination which becomes a non-poor solution as many as desired by the user.

  Further, when the detection apparatus determines that the integration process and the division process have been executed for a threshold or more, the detection apparatus sets a combination that is a non-inferior solution candidate at the determination time to a non-inferior combination. Thereby, the detection apparatus can detect the combination which becomes a non-poor solution at high speed.

  Note that the detection method described in the present embodiment can be realized by executing a detection program prepared in advance by a computer as shown in FIG. The detection program is recorded on a computer-readable recording medium such as a hard disk, a flexible disk, a CD-ROM, an MO, and a DVD, and is executed by being read from the recording medium by the computer. The detection program may be distributed through a network such as the Internet.

  The following additional notes are disclosed with respect to the embodiment described above.

(Supplementary note 1)
Obtaining a parameter having a plurality of groups each grouped with an element group each having an observation value;
Merging two of the plurality of groups of the acquired parameters into one,
Dividing one group including two or more elements in the group of elements among one or more groups of the parameters after integration into two groups;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output of the first and second objective functions based on the storage contents of the storage unit by giving a parameter after dividing the certain group into two groups for each of the second objective function numbers Calculate a combination of values,
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect non-poor candidate combinations,
A detection method characterized by executing processing.

(Supplementary Note 2) The process of acquiring the parameter is as follows:
From the first parameter having a plurality of groups in which the element group that is the same as or different from the acquired parameter is grouped to the second parameter having a number of groups smaller than the first parameter according to the order relation Parameter group of
The process of integrating the two groups into one is as follows:
The detection method according to appendix 1, wherein the two groups are integrated into one for each parameter of the acquired parameter group.

(Supplementary Note 3) The process of integrating the two groups into one is as follows:
When integration is executed for the acquired parameters, recursively executed a predetermined number of times for the parameters after the integration,
The process of dividing the certain group into two groups is as follows:
When the division is executed for the parameter after integration obtained by executing the predetermined number of times, the predetermined number of times is executed recursively for the parameter after the division,
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving a parameter after division obtained by executing the predetermined number of times to each of the first objective function and the second objective function, the first objective function is based on the storage contents of the storage unit. And the combination of the output values of the second objective function is calculated.

(Supplementary Note 4) The process of dividing the certain group into two groups is as follows:
Dividing a certain group including the two or more elements into two groups for each parameter of the plurality of parameters after integration;
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving each parameter of the plurality of parameters after the division to each of the first objective function and the second objective function, the plurality of parameters after the division based on the storage contents of the storage unit A combination of output values of the first and second objective functions for each parameter of
The process of detecting a combination that is a candidate for the non-inferior solution,
A combination of a plurality of calculated output values and a combination of output values of the first and second objective functions when the acquired parameter is given to each of the first and second objective functions; The detection method according to any one of appendices 1 to 3, wherein a combination that is a candidate for the non-inferior solution is detected.

(Additional remark 5) The process which calculates the combination of the output value of the said 1st and 2nd objective function is as follows.
By giving each parameter of the plurality of parameters after the division to each of the first objective function and the second objective function, the first and second parameters for each of the plurality of parameters after the division are provided. Calculate the output value combination of the objective function of 2
The process of detecting a combination that is a candidate for the non-inferior solution,
A combination of a plurality of calculated output values and a combination of output values of the first and second objective functions when the acquired parameter is given to each of the first and second objective functions; The detection method according to any one of appendices 1 to 3, wherein a combination that is a candidate for the non-inferior solution is detected.

(Additional remark 6) The process which acquires the said parameter is
The parameter given to the first and second objective functions is acquired when obtaining a combination that is a candidate for the detected non-inferior solution, according to any one of supplementary notes 1 to 5, Detection method.

(Supplementary note 7)
A process of determining whether or not the process of integrating the two groups into one and the process of dividing the certain group into two groups have been executed above a threshold;
The process of dividing the certain group into two groups is as follows:
If it is determined that the execution is performed over the threshold, two groups including two or more elements of the plurality of groups included in the acquired parameter are included in two groups before the process of integrating the two groups into one. Divided into groups,
The process of integrating the two groups into one is as follows:
Merge two groups of multiple groups in the parameter after division into one,
The process of calculating the combination of output values of the first and second objective functions is as follows:
A combination of output values of the first and second objective functions is calculated by giving an integrated parameter to each of the first objective function and the second objective function. The detection method according to appendix 6.

(Appendix 8) The computer
Obtaining a parameter having one or more groups each grouped with elements having observations;
Dividing one group including two or more elements in the group of elements among one or more groups of the acquired parameter into two groups;
Merge two groups of multiple groups in the parameter after division into one,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage section by giving the parameters after the integration of the two groups to each of the second objective functions. The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect a combination that is a candidate for the non-inferior solution,
A detection method characterized by executing processing.

(Supplementary Note 9) The process of acquiring the parameter is as follows:
From the first parameter having a plurality of groups in which the element group that is the same as or different from the acquired parameter is grouped to the second parameter having a number of groups smaller than the first parameter according to the order relation Parameter group of
The process of dividing the certain group into two groups is as follows:
The detection method according to appendix 8, wherein a group including the two or more elements is divided into two groups for each parameter of the acquired parameter group.

(Supplementary Note 10) The process of dividing the certain group into two groups is as follows:
When the obtained parameter is divided, the parameter after the division is recursively executed a predetermined number of times,
The process of integrating the two groups into one is as follows:
When integration is performed for the divided parameters obtained by executing the predetermined number of times, the predetermined number of times is executed recursively for the parameters after the integration,
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving the integrated parameters obtained by executing the predetermined number of times to each of the first objective function and the second objective function, outputs of the first and second objective functions The detection method according to appendix 5 or 6, wherein a combination of values is calculated.

(Supplementary Note 11) The process of integrating the two groups into one is as follows:
Combining the two groups into one for each of the plurality of parameters after the division;
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving each parameter of the plurality of parameters after the integration to each of the first objective function and the second objective function, the first and second parameters for each parameter of the plurality of parameters after the division are given. Calculate the output value combination of the objective function of 2
The process of detecting a combination that is a candidate for the non-inferior solution,
A combination of the plurality of calculated output values, and a combination of output values of the first and second objective functions when the acquired parameter is given to each of the first and second objective functions; The detection method according to any one of appendices 8 to 10, wherein a combination that is a candidate for the non-inferior solution is detected.

(Additional remark 12) The process which calculates the combination of the output value of the said 1st and 2nd objective function is as follows.
By giving each parameter of the plurality of parameters after the division to each of the first objective function and the second objective function, the first and second parameters for each of the plurality of parameters after the integration are provided. Calculate the output value combination of the objective function of 2
The process of detecting a combination that is a candidate for the non-inferior solution,
The combination of the plurality of output values calculated for each parameter of the plurality of parameters after the division, and the first and second when the acquired parameter is given to each of the first and second objective functions The detection method according to any one of appendices 8 to 10, wherein a combination that is a candidate for the non-inferior solution is detected from among combinations of output values of the objective function of 2.

(Supplementary Note 13) The process of acquiring the parameter is as follows:
The parameter given to the first and second objective functions is acquired when obtaining the detected combination that is a candidate for the non-inferior solution, according to any one of appendices 8 to 12, Detection method.

(Supplementary note 14)
A combination of the detected candidate for non-inferior solution and a combination of output values of the first and second objective functions when the acquired parameters are given to each of the first and second objective functions And a process for determining whether or not are the same,
The process of integrating the two groups into one is as follows:
When it is determined that they are the same, before the process of dividing the certain group into two groups, two groups among the plurality of groups of the acquired parameters are integrated into one,
The process of dividing the certain group into two groups is as follows:
Dividing one group including two or more elements out of one or more groups included in the merged parameter into two groups;
The process of calculating the combination of output values of the first and second objective functions is as follows:
A combination of output values of the first and second objective functions is calculated by giving the integrated parameter to each of the first objective function and the second objective function. The detection method according to appendix 13.

(Supplementary note 15) The supplementary note 2 or 9, wherein the first parameter is a parameter whose number of groups is the number of elements of the element group, and the second parameter is a parameter whose number of groups is one. The detection method according to.

(Supplementary Note 16) The computer
A combination of the detected candidate for non-inferior solution and a combination of output values of the first and second objective functions when the acquired parameters are given to each of the first and second objective functions And are the same,
When it is determined that they are the same, the combination that is a candidate for the detected non-inferior solution is set to a combination that is a non-inferior solution,
The detection method according to any one of appendices 1 to 15, wherein the process is executed.

(Supplementary Note 17) The computer
If it is determined that they are the same, execute a process of determining whether or not the number of detected combinations that are candidates for non-inferiority is a predetermined number or more,
The process to set the combination that is not inferior is
The detection according to appendix 16, wherein when it is determined that the number is not less than the predetermined number, the combination that is the candidate for the non-inferior solution detected is set to the combination that is the non-inferior solution. Method.

(Supplementary note 18)
It is determined whether or not the process of integrating the two groups into one and the process of dividing the certain group into two groups have been executed above a threshold,
When it is determined that the above-mentioned threshold value has been executed, the combination that is the candidate for the non-inferior solution detected is set to a combination that is a non-inferior solution,
The detection method according to any one of appendices 1 to 15, wherein the process is executed.

(Supplementary Note 19) A storage unit that stores observation values of each of the element groups;
An acquisition unit for acquiring a parameter having a plurality of groups in which the element group is grouped;
An integration unit that integrates two of the plurality of groups of the acquired parameter into one;
A dividing unit that divides a group including two or more elements in the element group into two groups out of one or more groups included in a parameter after integrating the two groups into one group by the integrating unit; ,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. When the output parameter calculated based on the storage content of the storage unit gives the other parameter of the two parameters when the one parameter of the two parameters to be satisfied is given The first objective function that is smaller than the output value calculated based on the storage content of the storage unit and the output value calculated based on the storage content of the storage unit when the one parameter is given Each of the second objective function that increases more than the output value calculated based on the storage contents of the storage unit when the parameters of By giving the parameters of the divided groups in the two groups by the dividing unit, and a calculation unit for calculating a combination of the output values of the first and second objective function based on the stored contents of the storage unit,
A combination of the output values calculated by the calculation unit and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. And a detection unit that detects combinations that are candidates for non-inferior solutions,
An output unit that outputs a combination that is a candidate for a non-inferior solution detected by the detection unit;
A detection apparatus comprising:

(Supplementary Note 20) A storage unit that stores observation values of each of the element groups;
An acquisition unit for acquiring a parameter having one or a plurality of groups into which the element group is grouped;
A dividing unit that divides a group including two or more elements in the element group into two groups among one or a plurality of groups of the parameter acquired by the acquiring unit;
An integration unit that integrates two groups among a plurality of groups included in a parameter after dividing the certain group into two groups by the division unit;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. When the output parameter calculated based on the storage content of the storage unit gives the other parameter of the two parameters when the one parameter of the two parameters to be satisfied is given The first objective function that is smaller than the output value calculated based on the storage content of the storage unit and the output value calculated based on the storage content of the storage unit when the one parameter is given Each of the second objective function that increases more than the output value calculated based on the storage contents of the storage unit when the parameters of By giving the parameter after integrating the two groups into one integration unit, and a calculation unit for calculating a combination of the output values of the first and second objective function based on the stored contents of the storage unit,
A combination of the output values calculated by the calculation unit and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. And a detection unit that detects a combination that is a candidate for the non-inferior solution,
An output unit that outputs a combination that is a candidate for a non-inferior solution detected by the detection unit;
A detection apparatus comprising:

(Supplementary note 21)
Obtaining a parameter having a plurality of groups each grouped with an element group each having an observation value;
Merging two of the plurality of groups of the acquired parameters into one,
Dividing one group including two or more elements in the group of elements among one or more groups of the parameters after integration into two groups;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving a parameter after dividing the certain group into two groups. The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect non-poor candidate combinations,
A detection program characterized by causing a process to be executed.

(Supplementary note 22)
Obtaining a parameter having one or more groups each grouped with elements having observations;
Merging two groups among a plurality of groups included in the parameters after dividing the certain group into two groups,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving the parameters after the integration of the two groups to each of the second objective functions The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect a combination that is a candidate for the non-inferior solution,
A detection program characterized by causing a process to be executed.

400 detection device 1601 acquisition unit 1602 integration unit 1603 division unit 1604 calculation unit 1605 detection unit 1609 output unit 1200 power table F1 to F4 elements, offices M1 to M15, a, b, c, p, q parameter f1 (x) Objective function 1 f2 (x) Second objective function

Claims (15)

Computer
Obtaining a parameter having a plurality of groups each grouped with an element group each having an observation value;
Merging two of the plurality of groups of the acquired parameters into one,
Dividing one group including two or more elements in the group of elements among one or more groups of the parameters after integration into two groups;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving a parameter after dividing the certain group into two groups. The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect non-poor candidate combinations,
A detection method characterized by executing processing. The process of acquiring the parameter is as follows:
The first parameter having one or a plurality of groups in which the same or different element group as the acquired parameter is grouped is changed to a second parameter in which the number of groups is smaller than the first parameter according to the order relation. To get a group of parameters
The process of integrating the two groups into one is as follows:
The detection method according to claim 1, wherein the two groups are integrated into one for each parameter of the acquired parameter group. The process of integrating the two groups into one is as follows:
When integration is executed for the acquired parameters, recursively executed a predetermined number of times for the parameters after the integration,
The process of dividing the certain group into two groups is as follows:
When the division is executed for the parameter after integration obtained by executing the predetermined number of times, the predetermined number of times is executed recursively for the parameter after the division,
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving a parameter after division obtained by executing the predetermined number of times to each of the first objective function and the second objective function, the first objective function is based on the storage contents of the storage unit. The detection method according to claim 1, wherein a combination of output values of the second objective function is calculated. The process of acquiring the parameter is as follows:
The parameter given to said 1st and 2nd objective function is acquired when obtaining the combination used as said detected candidate of the non-inferiority, The Claim 1 characterized by the above-mentioned. Detection method. Computer
Obtaining a parameter having one or more groups each grouped with elements having observations;
Dividing one group including two or more elements in the group of elements among one or more groups of the acquired parameter into two groups;
Merge two groups of multiple groups in the parameter after division into one,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving the parameters after the integration of the two groups to each of the second objective functions The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect a combination that is a candidate for the non-inferior solution,
A detection method characterized by executing processing. The process of acquiring the parameter is as follows:
From the first parameter having a plurality of groups in which the element group that is the same as or different from the acquired parameter is grouped to the second parameter having a number of groups smaller than the first parameter according to the order relation Parameter group of
The process of dividing the certain group into two groups is as follows:
The detection method according to claim 5, wherein a group including the two or more elements is divided into two groups for each parameter of the acquired parameter group. The process of dividing the certain group into two groups is as follows:
When the obtained parameter is divided, the parameter after the division is recursively executed a predetermined number of times,
The process of integrating the two groups into one is as follows:
When integration is performed for the divided parameters obtained by executing the predetermined number of times, the predetermined number of times is executed recursively for the parameters after the integration,
The process of calculating the combination of output values of the first and second objective functions is as follows:
By giving the integrated parameters obtained by executing the predetermined number of times to each of the first objective function and the second objective function, outputs of the first and second objective functions The detection method according to claim 5 or 6, wherein a combination of values is calculated. The process of acquiring the parameter is as follows:
8. The parameter given to the first and second objective functions is acquired when obtaining a combination that is a candidate for the detected non-inferior solution. Detection method.   The first parameter is a parameter whose number of groups is the number of elements of the element group, and the second parameter is a parameter whose number of groups is one. Detection method. The computer is
A combination of the detected candidate for non-inferior solution and a combination of output values of the first and second objective functions when the acquired parameters are given to each of the first and second objective functions And are the same,
When it is determined that they are the same, the combination that is a candidate for the detected non-inferior solution is set to a combination that is a non-inferior solution,
The detection method according to claim 1, wherein processing is executed. The computer is
If it is determined that they are the same, execute a process of determining whether or not the number of detected combinations that are candidates for non-inferiority is a predetermined number or more,
The process to set the combination that is not inferior is
11. The method according to claim 10, wherein when it is determined that the number is equal to or greater than the predetermined number, the combination that is the candidate for the non-inferior solution detected is set to the combination that is the non-inferior solution. Detection method. A storage unit for storing observation values of each element group;
An acquisition unit for acquiring a parameter having a plurality of groups in which the element group is grouped;
An integration unit that integrates two of the plurality of groups of the acquired parameter into one;
A dividing unit that divides a group including two or more elements in the element group into two groups out of one or more groups included in a parameter after integrating the two groups into one group by the integrating unit; ,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. When the output parameter calculated based on the storage content of the storage unit gives the other parameter of the two parameters when the one parameter of the two parameters to be satisfied is given The first objective function that is smaller than the output value calculated based on the storage content of the storage unit and the output value calculated based on the storage content of the storage unit when the one parameter is given Each of the second objective function that increases more than the output value calculated based on the storage contents of the storage unit when the parameters of By giving the parameters of the divided groups in the two groups by the dividing unit, and a calculation unit for calculating a combination of the output values of the first and second objective function based on the stored contents of the storage unit,
A combination of the output values calculated by the calculation unit and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. And a detection unit that detects combinations that are candidates for non-inferior solutions,
An output unit that outputs a combination that is a candidate for a non-inferior solution detected by the detection unit;
A detection apparatus comprising: A storage unit for storing observation values of each element group;
An acquisition unit for acquiring a parameter having one or a plurality of groups into which the element group is grouped;
A dividing unit that divides a group including two or more elements in the element group into two groups among one or a plurality of groups of the parameter acquired by the acquiring unit;
An integration unit that integrates two groups among a plurality of groups included in a parameter after dividing the certain group into two groups by the division unit;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. When the output parameter calculated based on the storage content of the storage unit gives the other parameter of the two parameters when the one parameter of the two parameters to be satisfied is given The first objective function that is smaller than the output value calculated based on the storage content of the storage unit and the output value calculated based on the storage content of the storage unit when the one parameter is given Each of the second objective function that increases more than the output value calculated based on the storage contents of the storage unit when the parameters of By giving the parameter after integrating the two groups into one integration unit, and a calculation unit for calculating a combination of the output values of the first and second objective function based on the stored contents of the storage unit,
A combination of the output values calculated by the calculation unit and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. And a detection unit that detects a combination that is a candidate for the non-inferior solution,
An output unit that outputs a combination that is a candidate for a non-inferior solution detected by the detection unit;
A detection apparatus comprising: On the computer,
Obtaining a parameter having a plurality of groups each grouped with an element group each having an observation value;
Merging two of the plurality of groups of the acquired parameters into one,
Dividing one group including two or more elements in the group of elements among one or more groups of the parameters after integration into two groups;
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving a parameter after dividing the certain group into two groups. The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect non-poor candidate combinations,
A detection program characterized by causing a process to be executed. On the computer,
Obtaining a parameter having one or more groups each grouped with elements having observations;
Dividing one group including two or more elements among one or more groups of the acquired parameter into two groups;
Merging two groups among a plurality of groups included in the parameters after dividing the certain group into two groups,
There is an order relationship that is included in any group that one parameter has among two parameters each having one or a plurality of groups in which the element group is grouped, even if the other parameter has any other group. The output value calculated based on the storage content of the storage unit that stores the observed value of each of the element groups when the one parameter of the two parameters that are established is given is the value of the two parameters. The first objective function that is smaller than the output value calculated based on the storage content of the storage unit when the other parameter is given, and the storage content of the storage unit when the one parameter is given When the output value calculated based on the value given by the other parameter is greater than the output value calculated based on the storage content of the storage unit Output values of the first and second objective functions based on the storage contents of the storage unit by giving the parameters after the integration of the two groups to each of the second objective functions The combination of
A combination of the calculated output values and a combination of output values of the first and second objective functions when the acquired parameters are given to the first and second objective functions, respectively. To detect a combination that is a candidate for the non-inferior solution,
A detection program characterized by causing a process to be executed.

Images