JPH11212948A - Quantity setting device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a quantity setting device which can quickly search for a quasi-optimal solution to a problem where a value set to a variable takes a discrete value and a candidate set of the value is provided and also can incorporate the condition that approximates the number of variables having value '0' to a predetermined number. SOLUTION: This quantity setting device 1 sets an initial value to each variable by an initial solution generation part 3, repetitively increases and decreases each variable value to decide a first local optimum solution by a local optimization part 4, stores the local optimum solution in a storage part 5 and also deteriorates the solution by an escape part 6. Further, the device 1 decides the next local optimum solution by the part 4, compares the solution with the first one by a comparison/evaluation part 7 to select the better solution and to store in the part 5 and further, repeats this procedure to obtain the optimum solution.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a quantity setting device for searching for a solution to a combination optimization problem.

[0002]

2. Description of the Related Art A quantity optimization problem is a problem in which a value (numerical value) is set for a variable having a discrete value. ) Is defined as an evaluation function, and the problem is to find a value setting for a variable group that minimizes the evaluation value calculated by the evaluation function.

That is, there are n variables X _i (i = 1,... N) and m constraints C _j (j = 1,... M), and the constraint C _j is k _j
This is a k _j term constraint that depends on the values of 1 (1 ≦ k _j ≦ n) variables. The variable is given a candidate set of values, and the value is selected from the candidate set. The constraint C _j includes a function FC _j for calculating a constraint violation value, and a state in which values are set to n variables so that the sum of m violation values of the constraints is minimized is an optimal solution.

[0004] As devices for finding solutions to the quantity optimization problem, there are known devices that apply linear programming and devices that apply integer programming.

[0005]

When considering the application of an apparatus utilizing linear programming, the problem to be dealt with here is that the values set for variables take discrete values, and the variables are given a candidate set of values. Therefore, first, the optimal solution is determined assuming that the variable takes a continuous value, then the discrete value is used as an approximate solution, but the continuous value is approximated by a discrete value selected from a candidate set of values. The results obtained are not always close to the optimal solution (for example, see “Method for Creating Integer Programming Model”, Sangyo Shuppan, H .;
P. Williams, pp. 178), there is a problem as an application method.

When an application using an integer programming method is considered, since a candidate set of values exists, it is formulated as a 0-1 integer programming problem. If the problem is treated as a 0-1 integer programming problem, the problem can be simplified, but the search space becomes very large. When the number of variables is large, the computation time is very long (for example, "Integer programming and combinatorial optimization"
Nikkagiren, 1982.6, Konno Hiroshi, Suzuki Hisatoshi, pp.
297. See), not practical.

Further, it is difficult to express the constraint condition that it is desirable that the number of variables having a value of 0 is close to a predetermined number in the prior art. For example, in the problem of calculating the combination of varieties to be manufactured at the factory on the next day and the quantity distribution of each varieties,
It is important that the number of varieties produced daily is preferably leveled to some extent, and that it is not preferable that the number of varieties be extremely small or extremely large depending on the day.

According to the present invention, there is provided an apparatus for searching a sub-optimal solution in a short time for a large-scale problem in which a value set as a variable takes a discrete value and a candidate set of values is given. Also, there is provided an apparatus capable of incorporating a condition that the number of variables having a value of 0 approaches a predetermined number.

[0009]

According to a first aspect of the present invention, there is provided a quantity setting device, wherein a variable value takes a discrete value, a candidate set of values of each variable is given in advance, and an absolute constraint and a constraint violation that do not permit constraint violation as a constraint are set. Quantity setting device that has at least a constraint with a constraint violation degree among two types of constraints with an evaluation function that returns a degree, and sets the value of each variable so as to minimize the total of the constraint violation degrees An initial solution generating means for setting an initial value that satisfies the absolute condition for each of the variables; and a local for searching for a local optimal solution by repeatedly increasing and decreasing the value of each of the variables so as to reduce the total of the constraint violation degrees. Optimizing means, storage means for storing the local optimal solution, escape means for escaping from the vicinity of the local optimal solution and deteriorating the solution,
A local optimal solution newly obtained by the local optimizing unit from the deteriorated solution is compared with a local optimal solution stored in the storage unit, and a local optimal solution with a small degree of constraint violation is stored in the storage unit. Comparing and evaluating means for storing, and starting from the first local optimal solution obtained by the local optimizing means from the initial value set by the initial solution generating means, performing the deteriorating operation of the local optimal solution by the escaping means; And a control unit for sequentially controlling an optimum solution search operation including a local optimization operation by the optimization unit and a storing operation of a better local optimum solution by the comparison operation by the comparison evaluation unit.

A quantity setting device according to a second aspect of the present invention is the quantity setting device according to the first aspect, wherein the initial solution generating means is a polynomial or a variable whose absolute constraint is positive and all coefficients are positive. When the left side of a monomial is represented by an inequality expressed as more than the right side of a constant, that is, when all absolute constraints constrain the lower limit, the maximum value of each variable is set as the initial value. .

A quantity setting device according to a third aspect of the present invention is the quantity setting device according to the first aspect, wherein the initial solution generating means is a polynomial or a variable whose absolute constraint is positive and all coefficients are positive. When the left side of a monomial is represented by an inequality that is less than or equal to the right side of a constant, that is, when all the absolute constraints constrain the upper limit, the maximum value of each variable is set as the initial value. .

According to a fourth aspect of the present invention, in the quantity setting device according to the first aspect, the control means stops the optimal solution search operation when the number of repetitions of the optimal solution search operation reaches a predetermined value. Features.

A quantity setting device according to a fifth aspect of the present invention is the quantity setting device according to the third aspect, wherein the local optimizing means collects zero-valued variables and divides the variables into predetermined portions. Each time, the value of each variable is repeatedly increased / decreased to search for a partial local optimal solution, and then the partial division is released to collect non-zero valued variables and to repeatedly increase / decrease the value of each variable to search for a local optimal solution It is characterized by doing.

A quantity setting device according to a sixth aspect of the present invention is the quantity setting device according to the first or fifth aspect, wherein the local optimizing means is capable of calculating the degree of violation of the constraint with the constraint violation degree independently for each variable, and In the case of a variable independent constraint in which the same constraint expression is applied to the variable of, the local optimal solution is searched by repeatedly increasing and decreasing the value in order from the variable having the highest degree of constraint violation.

A quantity setting device according to a seventh aspect of the present invention is the quantity setting device according to the first or fifth or sixth aspect, wherein the number of repetitions of the optimal solution search operation, the number of variables belonging to the portion when the variable is partially divided, It is characterized in that it has a parameter storage means for storing in advance parameters such as the number of times the value of a variable has been increased or decreased in the search for a station optimum solution.

[0016]

Next, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing an embodiment of a quantity setting device according to the present invention.

As shown in FIG. 1, the quantity setting device 1 according to the present embodiment sets an initial solution generator 3 for setting an initial value for each variable.
And a local optimizing unit 4 that repeatedly increases and decreases the value of each variable so as to reduce the total of constraint violation values to obtain a local optimum solution;
A parameter storage unit 8 for storing various parameters used in the quantity setting device 1 of the present embodiment, a storage unit 5 for storing a solution, an escape unit 6 for escaping from the vicinity of the local optimum solution, and a newly obtained solution And a solution stored in the storage unit 5. The comparison and evaluation unit 7 stores a better solution in the storage unit 5, and the control unit 2 controls the above units.

In order to properly describe the present embodiment, appropriate examples will be used in accordance with the problems to be described.

As an example 1, five variables W, V, X,
The problem of setting values for Y and Z is used. The definition of Example 1 will be described with reference to FIG.

The reference numeral 401 indicates that the range of the variable W is [0, 1
152, 1500], reference numeral 402 has a range of variable V of [0, 100, 500, 698], reference numeral 403 has a range of variable X of [0, 1152, 3000], reference numeral 4
04 is the range of the variable Y [0, 215], reference numeral 405
Indicates that the value range of the variable Z is [0, 400]. The value of each variable must be selected from a range.

The reference numeral 406 and the reference numeral 407 describe absolute conditions which are conditions that must always be observed, and the reference numeral 406 indicates the absolute condition 1 "the sum of W and Y must be 1300 or less. And the reference numeral 407 represents the absolute condition 2 “the sum of V, X, and Z must be 1700 or less”.

Reference numerals 408 to 413 describe conditions with constraint violation values. Reference numeral 40
8 is condition 1 with constraint violation value “the total value of Y and Z is 500
The constraint violation value is 0 when the total value of Y and Z is 500 or more, and Y and Z
Is less than 500, then 500-YZ
Becomes Reference numeral 409 expresses condition 2 with constraint violation value “the total value of Y and Z must be 600 or less”, and the constraint violation value becomes 0 when the total value of Y and Z is 600 or less. , Y and Z are greater than 600, then Y + Z-600. Reference numeral 410 represents the condition 3 with constraint violation values “the total value of W, V, and X must be 600 or more”, and the constraint violation values are W, V, and X.
Is 0 when the total value of W is greater than or equal to 600, and 600−W− when the total value of W, V and X is smaller than 600.
VX. Reference numeral 411 is condition 4 with constraint violation value.
The expression "the total value of W, V, and X must be 1500 or less", and the constraint violation value is 0 when the total value of W, V, and X is 1500 or less, and W, V, and X Is greater than 1500, then W + V + X-1500
Becomes Reference numeral 412 represents the condition 5 with constraint violation value 5 “the total value of all variables must be 900 or more”, and the constraint violation value is 0 when the total value of all variables is 900 or more, and If the total value is smaller than 900, it becomes 900-WVXYZ. Reference numeral 413
Expresses the condition 6 with constraint violation value "the total value of all variables must be 1500 or less", and the constraint violation value is 0 when the total value of all variables is 1500 or less, and the total value of all variables is If it is larger than 1500, W + V + X + Y +
Z-1500.

The formula for calculating the constraint violation value in Example 1 is expressed using the excess quantity from the upper limit or the shortage quantity from the lower limit. For example, in the condition 1 with the constraint violation value, the shortage quantity up to the lower limit value 500 is set as the constraint violation value. In addition to the calculation formula directly using the excess (shortage) quantity, a calculation formula using an excess (shortage) ratio, a calculation formula considering the importance of each condition, or the like may be used. Furthermore, a calculation formula using the excess (deficiency) ratio or a calculation formula considering the importance of the condition may be used in some cases.

A specific example of a calculation formula for calculating the violation value of condition 1 with constraint violation value of example 1 using a calculation formula using an excess (deficiency) ratio is to divide the shortage quantity up to the lower limit value by the lower limit value. (500-Y-
Z) / 500.

Further, as a specific example of a calculation formula for calculating the violation value of Condition 1 with constraint violation value of Example 1 by using a calculation formula taking into account the importance of the condition, the violation value of Condition 1 with constraint violation value is determined in advance. In the calculation of the constraint violation value, the degree of importance is multiplied by the importance to calculate the violation degree calculation formula (500-YZ).
× 1000.

FIG. 2 shows a processing flow of the quantity setting device 1 according to this embodiment. FIG. 5 shows a specific example of these processes in Example 1. In FIG. 5, column A shows the change in the value of the variable W, column B shows the change in the value of the variable V, and column C shows the change in the value of the variable X.
, The column D indicates a change in the value of the variable Y, and the column E indicates a change in the value of the variable Z. Absolute condition 1 in column F
If the absolute condition 2 is satisfied, ○ is indicated. If the condition is not satisfied, × is indicated. The total of up to 6 violation values is described. The first row describes each column, and the second row contains 0 for all variables.
Is set, and the third and subsequent lines show the progress of increasing or decreasing the value of the variable.

First, an initial solution is generated in an initializing process 21 using the initial solution generating unit 3. The second row in FIG. 5 shows the state of the initial solution, in which five variables W, V, X, Y, and Z are set to zero. All the absolute conditions are satisfied in a state in which all variables are set to 0, and a state in which all variables are set to 0 is satisfied as a solution. The total violation degree is 2000.

In Example 1, since all of the absolute conditions are limiting expressions of the upper limit, setting 0 to all variables always solves the problem.
Therefore, the specific process of the initial solution generation unit 1 in Example 1 is a process of setting 0 to all variables. The specific processing content performed by the initial solution generation unit 1 differs depending on the nature of the target problem, and can be set as a specific processing example in the case where the defined absolute conditions are all targets for the problem of limiting the lower limit. There is a process of setting the maximum value to each variable.

As described above, the algorithm for generating one solution that satisfies all the absolute conditions included in the target problem is incorporated in the initial solution generating unit 1 in advance.

In Example 1, the variable takes a value greater than or equal to 0, and the absolute condition is that the sum of variables having positive coefficients is a restriction formula having an upper limit, but the variable takes a value greater than or equal to 0. As an absolute condition, the sum of variables having positive coefficients may be a limiting expression having a lower limit.
Such a problem is often encountered when a problem of planning a production plan of a factory that produces a plurality of types of products is represented by a quantity combination optimization problem. In other words, in the example where the upper limit is a limiting formula, if the variables are individual products and the variable value is the product production volume, the limit on the product production volume due to the operating hours of the equipment or the The production amount is limited by the stock amount of the raw material to be used.

Next, in the first optimization process 22 using the local optimization unit 4, the value is increased or decreased so that the total violation value is reduced, and a local optimum solution is calculated. For convenience, the initial setting of the variable selection order is WVXYZ in alphabetical order. The initial setting of the variable selection order does not need to be in alphabetical order, and the user may define the initial setting procedure of the variable selection order.

The processing of the first optimization processing 22 in Example 1 is as follows. If an attempt is made to increase or decrease the value of the variable according to the default variable order, changing the variable W to 1152 in the third row decreases the total violation degree to 500, so the value of W is set to 1152. Next, when the value of the variable V is changed to 100 in the fourth line, the total violation degree becomes 500.
Since the value does not change, the value of V is set to 0 without changing. Next, when the value of the variable X is changed to 1152 in the fifth line, the total violation value increases to 2108, so the value of X is set to 0 without changing. Next, when the value of the variable Y is changed to 215 in the sixth line, the absolute constraint is not satisfied.
And Next, when the value of the variable Z is changed to 400 in the seventh line, the total of the violation values is reduced to 152.
Set to. Next, line 8 to line 13 attempt to change the value continuously, but cannot reach the total violation value smaller than line 7.

Therefore, W described on the seventh line is 115
The state where 2, Z is 400, and the other variables are 0 is the local optimal solution, and the first optimization process 22 using the local optimization unit 4 ends.

Next, in the storage process 23 using the storage unit 5, the local optimum solution searched in the local optimization process 22 is stored in the storage unit 5 as the best solution at the present time.
In Example 1, a solution in which W is 1152, Z is 400, and other variables are 0 is stored in the storage unit 5.

Next, in the deteriorating process 24 using the escape unit 6, a resolving / deteriorating operation of changing the total violation value to be larger is performed. In Example 1, in the process of randomly selecting one variable from a variable group in which a value other than 0 is set and resetting the value to 0, the total value of the values of all variables is reduced by 20% or more. Repeat until (end condition). Specifically, when the variable W is selected and changed from 1152 to 0, the sum of the values of all the variables is reduced from 1552 to 400 and the end condition is satisfied. , And the other variables are 0. The total violation value of this solution is 1200, which is worse than the total violation value 152 of the local optimal solution in the seventh row.

In Example 1, since the absolute conditions are all upper limit expressions, the result of resetting the value of an arbitrary variable included in an arbitrary solution to 0 is satisfied as a solution. As the operation, “processing for resetting the value of a variable to 0” is employed, but the specific processing content differs depending on the nature of the target problem. For example, as a specific example of a process in which all defined absolute conditions limit the lower limit, there is a "process of setting the maximum value that can be set to a selected variable".

In Example 1, "a process of randomly selecting one variable from a variable group in which a value other than 0 is set" is adopted as a variable selection process. A specific example of a process in which all defined absolute conditions are limited to the lower limit is as follows: "One variable is randomly selected from a group of variables to which 0 is set." Process of selecting the "."

That is, the selection of a variable and the manipulation of modifying a variable value differ depending on the nature of the target problem. A variable that satisfies the group of absolute conditions included in the target problem and is significantly different from the current value is set as a variable. The process of resetting to is set in the escape unit 6 in advance.

Further, in Example 1, the end condition that the repetition is performed until the sum of the values of all the variables decreases to a predetermined ratio (20%) or more is adopted. However, the end condition is not limited to this. Conditions such as until the number of variables whose values have been changed become equal to or more than a certain number can also be used.

Next, in an optimization process 25 using the local optimization unit 4, the value of the solution deteriorated in the escape process 24 is increased or decreased to search for a local optimum solution again. The variable selection order is such that VXYZ is set so that
W. If the processing is started from the state of the 14th line and an attempt is made to increase or decrease the value of the variable, the total of the violation values is 152 in the 20th line. After that, the value is repeatedly increased and decreased up to the 25th line, but it is not possible to reach a smaller total violation value. Therefore, the local optimal solution that reaches the second time is a state in which X is 1152, Z is 400, and all other variables are 0.

Next, the replacement process 2 using the comparative evaluation unit 7
In step 6, the solution stored in the storage unit 5 is compared with the local optimum solution calculated in the optimization processing 25, and the better solution is selected. In Example 1, since the total violation value does not change to 152,
The solution stored in the storage unit 5 is not replaced.

As described above, the deterioration processing 24 and the optimization processing 2
One optimization loop is completed by 5 and the exchange processing 26. The user defines in advance an integer greater than or equal to 0 for the number of times of the optimization loop, and ends the processing if it is determined in the inspection under the loop inspection condition 27 that the optimization loop of the defined number of times has been completed. In Example 1, if the number of loops is defined as two, the optimization loop is repeated again because the loop has been passed only once at this point.

In the repetition, in the deteriorating process 24, some variables are selected and the values are changed so as to increase the total violation value. The result of performing the solution modification operation in Example 1 is as shown in line 26, and the value of X is changed from 1152 to 0. By this deterioration processing, the total violation value becomes 1200.

Next, in the optimization process 25, the value of the solution deteriorated in the deterioration process 24 is increased or decreased to search for a local optimum solution again. The variable selection order is the variable X operated by the bad action.
VYZWX. If the process is started from the state on the 26th line and an attempt is made to increase or decrease the value of the variable, the total of the violation values is 15 on the 33rd line. Also,
Thereafter, the value is repeatedly increased and decreased up to the 38th line, but it is not possible to reach a total of the violation values smaller than that. Therefore,
The local optimal solution that reaches the third time has V of 698 and Y of 21
5, Z is 400 and all other variables are 0.

Next, in the replacement process 26, the solution stored in the storage unit 5 is compared with the local optimum solution searched in the optimization process 25, and the better solution is selected. In Example 1, since the total violation value decreases from 152 to 15, the solutions stored in the storage unit 5 are replaced, and V is 698 and Y is 21
5, 400 is newly stored in the storage unit 5, and all other variables are 0.

In this way, the optimization loop is performed until the preset number of loops is completed, and if it is determined in the inspection under the loop inspection condition 27 that the optimization loop of the defined number of times has been completed, it is stored in the storage unit 5. The solution found is presented to the user as a search result. In Example 1, the preset number of loops is 2, and
At the time of the 38th line, the processing of the quantity setting device 1 according to the present embodiment ends, and the user is presented with a solution that V is 698, Y is 215, Z is 400, and all other variables are 0.

Next, Example 2 will be set in order to provide a detailed description of the local optimization processing when adjusting the number of zero-valued variables.

In Example 2, five variables A, B, C, D, and E
Set the value to. The problem definition will be described with reference to FIG.

Reference numerals 61 to 65 indicate that the variable is ABCD
E is defined as five, indicating that the range of each variable is an integer from 0 to 10.

Reference numeral 66 represents condition 1 with constraint violation value, "the total value of all variables must be 10 or more", and the constraint violation value is 0 when the total value of all variables is 10 or more, 1 if the sum of all variables is less than 10
0-ABBCDE is the violation value. Reference numeral 67
Expresses condition 2 with constraint violation value, "the total value of all variables must be 15 or less", and the constraint violation value is 0 when the total value of all variables is 15 or less, and the total value of all variables is If it is larger than 15, A + B + C + D + E-15 is the violation value. The reference numeral 68 represents the condition 3 with the constraint violation value “variable A must be 9 or more”. The constraint violation value is 0 when the variable A is 9 or more, and when the variable A is less than 9 9-A is the violation value.

In Example 2, if the number of groupings (the number of variables belonging to one group) is 2 and the value increase / decrease number is 5, the grouping number is 5 and the value increase / decrease number is 2, if the grouping number is 3 and the value increase / decrease number is 3, In the case of, the obtained result will be described for the three cases.

A specific example of a method of controlling the operation of the search algorithm for local optimization with parameters so that the number of variables having 0 as a value approaches the number desired by the user will be described below.

In the processing of the local optimization unit 4 in Example 1, the condition of the number of zero-valued variables was not taken into consideration. However, the same processing as the processing to be described using Example 2 is applied to the local optimization unit 4. It becomes possible to consider the zero value variable number condition. Hereinafter, a processing procedure of the local optimization unit 4 for enabling consideration of the condition of the number of zero-valued variables will be described.
As the necessary parameters, two of the number of groupings and the number of times of value increase / decrease operations are defined in advance and stored in the parameter storage unit 8.

FIG. 3 shows a processing flow of the local optimization unit 4 when the condition of the number of zero-valued variables is considered.

First, the case where the number of groupings is 2 and the number of times of value increase / decrease is 5 is considered.

In the variable group division 31, variables having the value of 0 are collected and the partial problem is divided into a predetermined number of groupings. Since the number of groupings is 2, 2 for each group
Grouping is performed so that variables can be entered individually. The order of variables is ABCDE in alphabetical order. Therefore, there are three groups of A and B, C and D, and E alone. A
The group of E and B is a first group, the group of C and D is a second group, and the group of E alone is a third group.

The initial setting of the variable selection order does not need to be in alphabetical order, and the user may define the initial setting procedure of the variable selection order.

FIG. 7 shows a specific example of the processing in Example 2. In FIG. 7, column A shows the state of variable A, column B shows the state of variable B, column C shows the state of variable C, and column D shows the variable D
Column E shows the state of variable E, column F shows the total value of all variables, column G shows the constraint violation value of condition 1 with constraint violation values, and column H shows constraint violation values. The constraint violation value of condition 2 with value, the constraint violation value of condition 3 with constraint value in column I,
Column J shows the total constraint violation value. The first row shows the description of each column, and the second and subsequent rows show the violation value situation when a value is set to a variable. In Example 2, the violation value in a state where 0 is set to all variables in the initial state of the second row is 19.

In the sub-problem processing 32, an attempt is made to increase or decrease the value of each variable by the number of times of value increase / decrease operation predetermined by a parameter for each partial problem. First, the first group: A
As a result of trying to increase or decrease the value from B and repeating the value increase / decrease operation five times set by the parameter, as shown in the third line, A
Is 5, B is 5, and the total violation value is 4. Then the second
For the group and the third group, the value is increased / decreased five times set by the parameter. However, the value is not changed because the violation value does not become small even if any change is made.

Next, all groups are released by a group release 33. Finally, in the overall improvement operation 34, non-zero value variables are collected, and the values are increased or decreased until only the non-zero value variables reach the local optimum solution. Repeat the operation. In the case of example 2, A and B
Is a value increase / decrease target, and as shown in the fourth row, a local optimal solution is reached in which A is 9, B is 5, and other variables are 0.

That is, when the number of groupings is 2 and the number of times of value increase / decrease is 5, the local optimal solution shown in the fourth row is 9 for A, 5 for B, and 0 for other variables.

Next, the case where the number of groupings is 5 and the number of times of value increase / decrease is 2 is considered.

In the variable group division 31, variables having the value of 0 are collected and the partial problem is divided into a predetermined number of groupings. Since the number of groupings is 5, grouping is performed so that each group contains 5 variables. That is, all variables are grouped into one group. When the search for the local solution is started from the initial state of the second row, a situation is reached in which all variables are set to 2 as shown in the fifth row.

Next, all the groups are released by the group release 33, and finally, the non-zero value variables are collected by the overall improvement operation 34, and the value is increased or decreased until only the non-zero value variables reach the local optimum solution. Repeat the operation. Here, all variables are subject to value increase / decrease, but the values are not changed except for A.
As shown in the row, a local optimal solution is reached in which A is 7 and other variables are 2.

That is, when the number of groupings is 5 and the number of times of value increase / decrease is 2, the local optimum solution shown in the sixth row is A = 7 and other variables = 2.

Next, the case where the number of groupings is 3 and the number of times of value increase / decrease is 3 is considered.

In a variable group division 31, variables having zero values are collected and a partial problem division is performed with a predetermined number of groupings. Since the number of groupings is 3, grouping is performed so that three variables are included in each group. That is, there are two groups, A, B and C, and D and E. First, the first group: ABC was tried to increase / decrease the value, and as a result of repeating the value increase / decrease operation three times set by the parameter, as shown in the third row, A was 3, B was 3, and C was 3. , The total violation value is 7. Next, for the second group, three value increase / decrease operations set by parameters are performed, and as shown in the seventh row, A, B and C are 3, D is 1, and E is 0.

Next, all groups are released by a group release 33. Finally, in the overall improvement operation 34, non-zero-valued variables are collected, and only the non-zero-valued variables are subjected to value increase / decrease until a local optimal solution is reached. Repeat the operation. Here, ABCD is a value increase / decrease target, but the value is not changed except for A. As shown in the eighth row, A is 8, B and C are 3, D is 1, and E is 0.
To reach the local optimal solution.

That is, if the number of groupings is 3 and the number of times of value increase / decrease is 3, A shown in the eighth row is 8, B and C are 3, and
The local optimal solution is D = 1 and E = 0.

As described above in Example 2 with three types of searches, when the number of groupings is set to be small and the number of times of value increase / decrease is set to be large, the number of variables taking 0 as a value tends to increase. Also, when the number of groupings is set to be large and the number of times of value increase / decrease is set to be small, the number of variables that take 0 tends to decrease. By repeating the change of the parameter value and the solution calculation process based on the above tendency, the operation of the system can be adjusted so that the number of variables taking zero becomes close to the desired number.

Next, a specific example of means for realizing the processing speedup of the quantity setting device 1 of the present embodiment capable of adjusting the number of zero-valued variables using variable independent conditions will be described. Example 3 is set.

In Example 3, values are set for three variables A, B, and C. The problem definition of Example 3 will be described with reference to FIG.

Reference numerals 81 to 83 indicate that three variables, ABC, are defined, and the range of each variable is an integer from 0 to 10. Also, the minimum values preset for each variable are shown.

The reference numeral 84 represents the condition 1 with constraint violation value "the total value of all variables must be 10 or more". The constraint violation value is 0 when the total value of all variables is 10 or more. 1 if the sum of all variables is less than 10
0-ABC is the violation value. Condition 1 with constraint violation value
Is defined as 1. The reference numeral 85 represents the condition 2 with the constraint violation value “the total value of all the variables must be 20 or less”.
If it is less than 0, it becomes 0, and if the total value of all variables is larger than 20, it becomes A + B + C-20. The importance of the condition 2 with the constraint violation value is defined as 1. Reference numeral 86
Expresses condition 3 with constraint violation value: "A minimum value is defined for each variable and it is desired to set the minimum value or more".

Further, the condition 3 with the constraint violation value is of importance 1
000. For the variable A, the minimum value is 0
Thus, no violation value is generated for the condition 3 with the constraint violation value. Considering the variable B, when the value of B becomes smaller than 5, (5-B) × 1000 becomes B
Violation value, and when the value of B is 5 or more, the violation value is 0. Considering the variable C, if the value of C is smaller than 10, (10−C) × 1000 is the violation value for C, and if the value of C is 10 or more, the violation value is 0.

The condition 3 with a constraint violation value is a condition in which a violation value can be calculated independently for each variable and the same conditional expression is applied to all variables. Example 3 is characterized in that a condition classified as a variable independent condition has a high degree of importance.

In Example 3, the processing is performed with the number of groupings 1 / the number of times of increase / decrease of 10 times.

When the grouping number 1 / value increase / decrease number 10 is applied, in the processing of the local optimization unit 4, the first group to which the variable A belongs, the second group to which the variable B belongs, and the third group to which the variable C belongs Then, the problem is divided, and the value is increased or decreased ten times for each group. The setting of “grouping number 1 / value increase / decrease number 10” is a specific example of setting used when it is desired to adjust the solution in a direction to increase the number of variables for which 0 is set.

FIG. 9 shows a specific example of the processing in Example 3. In FIG. 9, column A shows the change in variable A, column B shows the change in variable B, column C shows the change in variable C, and column D shows the change in variable A.
Column E shows the violation value for condition 3 of variable B, column F shows the violation value for condition 3 of variable C, column G shows the violation value for condition 1 and column H Indicates the violation value for condition 2, and column I indicates the total of the violation values from condition 1 to condition 3. The first row describes each column, the second row shows a state in which all variables are set to 0, and the third and subsequent rows show changes when the value of a variable is increased or decreased.

As shown in the second row, in the situation where all variables are set to 0 by default, the violation value of condition 3 with constraint violation value of A is 0, and the violation value of condition 3 with constraint violation value of B is 0. The value is 5000 and the violation value of condition 3 with constraint violation value of C is 100.
00. In the case where the selection order of the variables is set to ABC in alphabetical order as in Example 1, the increase and decrease of the variable values until reaching the local optimal solution are as shown in the second to sixth rows. Is processed as CBAs in descending order of the violation value of the variable independent condition, the increase and decrease of the variable values until the local optimal solution is reached is increased from the seventh row to 9
Will be up to the line. This will be described below.

In the case where the variable selection order is set as ABC in alphabetical order as in Example 1, first,
The variable A is selected in the processing of the group 1 and the value is increased or decreased within 10 times, the variable A is set to 10 as a value setting that minimizes the total violation value, the result of the third row is obtained, and the processing of the group 1 is performed. Ends. Next, in the processing of the group 2, the variable B belonging to the group 2 is selected, the value is increased or decreased within 10 times, and the variable B is set to 5 as a value setting that minimizes the violation value. Result, group 2
Is completed. Next, the variable C is selected in the processing of the group 3 and the value is increased or decreased within 10 times, and 10 is set as the variable setting that minimizes the total violation value.
The result is the fifth row, and the processing of group 3 ends.

Next, the group is released, and the value is increased or decreased for the entire variable group. If the variable A is selected in alphabetical order and 9 is set, the violation value decreases from 5 to 4. Even if the values of the variables B and C are changed, they are not changed because the total violation value does not decrease. When the variable A is selected again and 8 is set, the violation value decreases from 4 to 3. When the process is repeated in this manner, the local optimal solution is reached when the value of the variable A becomes 5, and the result of the sixth row is obtained.

On the other hand, when the variable selection order is processed as CBA in descending order of the violating value of the variable independent condition,
First, in the processing of the group 1, the variable C is selected and the value is increased or decreased within 10 times, and the variable C is set to 10 as a value setting that minimizes the total violating value. Is completed. Next, in the processing of the group 2, the variable B belonging to the group 2 is selected, the value is increased or decreased within 10 times, 5 is set as the value setting that minimizes the violation value, and the result of the ninth line is obtained. Group 2
Is completed. Next, the variable A is selected in the processing of the group 3, but if the value is made larger than 0, the total violation value increases, so that the value is not changed, and the processing of the group 3 ends. Next, the group is released, and the value is increased or decreased for the entire variable group. However, a better solution is not reached, and the result in the ninth row is obtained.

As described above, the case where the processing is performed with the alphabet selection order of ABC as the variable selection order and the case where the processing is performed with the variable selection order as the CBA having the largest violation value of the variable independent condition are the latter. In the selection order, the number of processing steps is smaller, and the processing speed is higher.

As described above, the numerical value setting device according to the present embodiment sets the initial solution satisfying all the absolute constraints as the starting point of the search for the quantity optimization problem in which the variable takes a discrete value. By searching for a solution by limiting the search space to a range that does not violate the absolute constraints, it is possible to reach the solution desired by the user in a shorter time than in the conventional device.
The number of variables set to 0 is adjusted by providing a mechanism for dividing the local optimization process into subproblems and allowing the user to set the number of variables constituting the subproblem and the number of times the variable value is increased or decreased. Also, there is an effect that the processing can be speeded up by using the variable independent condition when using the function of adjusting the number of variables for which 0 is set.

[0087]

As described above, the numerical value setting device according to the present invention sets the initial solution satisfying all the absolute constraints as a starting point for the search for the quantity optimization problem in which the variable takes a discrete value. By searching for a solution by limiting the search space to a range that does not violate the absolute constraint, there is an effect that the user can reach a desired solution in a shorter time than in the conventional device.

Further, by providing a mechanism for dividing the local optimization process into subproblems and allowing the user to set the number of variables constituting the subproblem and the number of times the variable value increases / decreases, a variable in which 0 is set Can be adjusted.

Also, when using the function of adjusting the number of variables to which 0 is set, there is an effect that the processing can be sped up by using the variable independent condition.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of a quantity setting device according to the present invention.

FIG. 2 is a flowchart showing an example of an operation in the quantity setting device 1 of the present embodiment.

FIG. 3 is a flowchart showing an operation of a local optimization unit 4;

FIG. 4 is a diagram illustrating a range of variables and constraints in Example 1.

FIG. 5 is a diagram showing a quantity setting process of Example 1 along the flow of processing by the quantity setting device 1 of the present embodiment.

FIG. 6 is a diagram showing a range of variables and constraints in Example 2.

FIG. 7 is a diagram showing a quantity setting process of Example 2 along a processing flow based on various number of groupings and the number of times of value increase / decrease.

FIG. 8 is a diagram illustrating a range of variables and constraints in Example 3.

FIG. 9 is a diagram showing a quantity setting process of Example 3 showing the effect of value increase / decrease and variable selection.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Quantity setting apparatus 2 Control part 3 Initial solution generation part 4 Local optimization part 5 Storage part 6 Escape part 7 Comparison evaluation part 8 Parameter storage part 21 Initialization processing 22 1st optimization processing 23 Storage processing 24 Deterioration processing 25 Optimization Processing 26 Replacement processing 27 Loop inspection conditions 31 Variable group division 32 Partial problem processing 33 Group release 34 Overall improvement operation

Claims (7)

[Claims] 1. A constraint with a constraint violation degree having a discrete value of a variable value, a candidate set of values of each variable being given in advance, and an absolute constraint not permitting constraint violation as a constraint and an evaluation function returning a constraint violation degree. In a quantity setting device that has at least a constraint with a constraint violation degree among the two types and sets the value of each variable so as to minimize the total of the constraint violation degrees, an initial value that satisfies the absolute condition is set for each variable. Initial solution generating means to be set, local optimizing means for searching for a local optimum solution by repeatedly increasing and decreasing the value of each of the variables so that the total of the constraint violation degrees decreases, and storage means for storing the local optimum solution Escape means for escaping the solution by escaping from the vicinity of the local optimum solution, and a local optimum solution newly obtained from the deteriorated solution by the local optimization means and stored in the storage means. Local optimal solution And a local evaluation solution for storing a local optimal solution having a small degree of constraint violation in the storage unit; and a first local optimal solution obtained by the local optimization unit from an initial value set by the initial solution generating unit. Starting from the above, an optimal solution search operation consisting of a deteriorating operation of the local optimal solution by the escape unit, a local optimizing operation by the local optimizing unit, and a storing operation of a better local optimal solution by the comparing operation by the comparing and evaluating unit is performed. And a control means for repeatedly controlling the order. 2. An initial solution generating means is represented by an inequality in which a left side of a polynomial or a monomial whose absolute constraint is positive and all coefficients are positive and whose absolute value is greater than or equal to 0 is expressed as a right side or more of a constant. 2. The quantity setting device according to claim 1, wherein when the absolute constraint constrains the lower limit, the maximum value of each variable is set as an initial value. 3. The initial solution generating means is represented by an inequality in which the left side of a polynomial or a monomial whose absolute constraints are all positive and all coefficients are positive is expressed as the right side of a constant or less. 2. The quantity setting device according to claim 1, wherein when the absolute constraint constrains the upper limit, zero is set as an initial value for each variable. 4. The quantity setting device according to claim 1, wherein the control means stops the optimal solution search operation when the number of repetitions of the optimal solution search operation reaches a certain value. 5. The local optimization means collects zero-valued variables, divides them into predetermined number of parts, and repeats increasing and decreasing the value of each variable for each part to search for a partial local optimum solution. ,
4. The quantity setting device according to claim 3, wherein the partial division is canceled to collect non-zero-valued variables and to repeatedly increase and decrease the values of the respective variables to search for a local optimum solution. 6. The local optimizing means, when a constraint with a constraint violation degree is a variable independent constraint in which the violation degree can be calculated independently for each variable and the same constraint expression is applied to all variables, 2. A local optimum solution is searched for by repeatedly increasing and decreasing values in order from a larger variable.
Or the quantity setting device according to 5. 7. A parameter storage for storing in advance parameters such as the number of repetitions of the optimal solution search operation, the number of variables belonging to the part at the time of partial division of the variable, and the number of times the value of the variable increases or decreases during the local optimal solution search. 7. The quantity setting device according to claim 1, further comprising means.