JP2014059804A - Evaluation support method, information processor, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To visualize influence on an analysis result in the case of suppressing a load of formula manipulation.SOLUTION: A storage part 11 stores information of a plurality of first functions 13a, 13b which correspond to a plurality of evaluation indexes and respectively show a relation between a parameter and one of the plurality of evaluation indexes. A calculation part 12 calculates a plurality of second functions 14a, 14b corresponding to a plurality of evaluation indexes by performing approximation processing of one or more of the plurality of first functions 13a, 13b. The calculation part 12 generates first range information 15a, 15b showing a range in which a combination of values of the plurality of evaluation indexes changes in accordance with a change in the parameter by using the plurality of first functions 13a, 13b, and generates second range information 16a, 16b showing a range in which a combination of values of the plurality of evaluation indexes changes in accordance with a change in the parameter by using the plurality of second functions 14a, 14b. The calculation part 12 displays the first range information 15a, 15b and the plurality of range information 16a, 16b in a comparable format.

Description

  The present invention relates to an evaluation support method, an information processing apparatus, and a program.

  Currently, computer simulation is used in various fields as the computing power of computers increases. For example, in order to support the design of mechanical products and electronic products, product indices such as response speed and manufacturing cost when parameters such as temperature and pressure are set to certain values are predicted through computer simulation. As a result, it becomes easy to find the optimal combination of parameters and optimal product indexes, and it is possible to efficiently design mechanical products and electronic products by reducing the number of times of producing prototypes.

  Mathematical optimization techniques are often used when analyzing simulation results. The mathematical optimization technique includes numerical analysis that receives a numerical value as an input and outputs a numerical value as a calculation result, and mathematical expression processing that receives a mathematical expression as an input and processes the mathematical expression symbolically. Examples of formula processing methods include Cylindrical Algebraic Decomposition (CAD) and Quantifier Elimination (QE). By using mathematical expression processing technology, for example, a region or boundary that satisfies a specific condition on a graph can be calculated.

  In order to evaluate design specifications from multiple viewpoints, a system has been proposed that evaluates trade-offs between evaluation items using analysis results for each evaluation item and a predetermined evaluation function, and obtains optimal design parameters. Yes. Also, a method has been proposed in which the weight of each objective function is automatically determined and changed when optimizing the combination of a plurality of objective functions. In addition, a system that supports carbon dioxide emission trading by displaying a graph describing a long-term marginal cost curve and a short-term marginal cost curve has been proposed.

  A method of designing a structure such as a tire in consideration of a plurality of performances that are in a trade-off relationship, wherein at least one design variable and two or more objective functions are defined, and a simulation operation is performed to determine the objective function. A method for obtaining a Pareto optimal solution for is proposed. In addition, in order to support the design of the slider shape of the hard disk, a plurality of objective functions represented by polynomials are mathematically processed using the QE method to calculate and display areas where the values of the plurality of objective functions can be obtained. A method has been proposed.

Japanese Patent Laid-Open No. 5-41443 JP-A-6-332883 JP 2002-149978 A JP 2006-285181 A JP 2009-169557 A

  As described above, it is conceivable to analyze the trade-off relationship between a plurality of evaluation indexes by mathematically processing a plurality of functions corresponding to these evaluation indexes. By using the mathematical expression processing technique, a combination of a plurality of evaluation indexes can be handled as a boundary line or a region instead of a point, so that the number of simulations required for the analysis can be reduced as compared with the numerical analysis technique.

  However, in the analysis using the mathematical expression processing technique, the complexity of the function corresponding to the evaluation index becomes a problem. In general, the more complicated the function to be used (for example, the higher the order of the polynomial), the more accurately the characteristics of the evaluation index can be expressed. On the other hand, the more complex the function, the greater the load on mathematical processing, so the product design user may want to make the function used in design work after a certain point less complex There is.

  Therefore, in one aspect, an object of the present invention is to provide an evaluation support method, an information processing apparatus, and a program capable of visualizing an influence on an analysis result when the load of mathematical expression processing is suppressed.

  In one aspect, an evaluation support method executed by a computer is provided. The computer approximates one or more of the plurality of first functions from the plurality of first functions corresponding to the plurality of evaluation indexes, each indicating a relationship between the parameter and one of the plurality of evaluation indexes. Thus, a plurality of second functions corresponding to the plurality of evaluation indexes are calculated. In addition, the computer uses the plurality of first functions to generate first range information indicating a range in which the combination of the values of the plurality of evaluation indexes changes according to the change in the parameter. In addition, the computer uses the plurality of second functions to generate second range information indicating a range in which the combination of the values of the plurality of evaluation indices changes according to the change in the parameter. In addition, the computer displays the first range information and the second range information in a format that can be compared.

  In one aspect, another evaluation support method executed by a computer is provided. The computer uses a plurality of functions corresponding to a plurality of evaluation indexes, each of which indicates a relationship between a parameter and one of the plurality of evaluation indexes, and the plurality of evaluation indexes when the parameter changes in the first parameter range. First range information indicating a range in which the combination of values changes is generated. In addition, the computer obtains, from a plurality of functions, second range information indicating a range in which a combination of a plurality of evaluation index values changes when the parameter changes in a second parameter range wider than the first parameter range. Generate. In addition, the computer displays the first range information and the second range information in a format that can be compared.

  In one aspect, it is possible to visualize the influence on the analysis result when the load of mathematical expression processing is suppressed.

It is the figure which showed the example of the information processing apparatus which concerns on 1st Embodiment. It is the figure which showed the example of the evaluation assistance system which concerns on 2nd Embodiment. It is the figure which showed the example of the hardware of the information processing apparatus which concerns on 2nd Embodiment. It is the figure which showed the example of the functional block of the information processing apparatus which concerns on 2nd Embodiment. It is the figure which showed the calculation method of the objective function which concerns on 2nd Embodiment. It is the figure which showed the simplification method which concerns on 2nd Embodiment. It is the figure which showed the example of the numerical formula process which concerns on 2nd Embodiment. It is the figure which showed the flow of the process by the information processing apparatus which concerns on 2nd Embodiment. It is the figure which showed the flow of the calculation process of the objective function which concerns on 2nd Embodiment. It is the figure which showed the flow of the simplification process of the objective function which concerns on 2nd Embodiment. It is the figure which showed the flow of the numerical formula process which concerns on 2nd Embodiment. It is the figure which showed the display method of the calculation result which concerns on 2nd Embodiment. It is the figure which showed the example of the simplification calculation which concerns on 2nd Embodiment. It is the figure which showed the display method of the calculation result which concerns on 2nd Embodiment. It is the figure which showed the example of a setting of the extended parameter range which concerns on 3rd Embodiment. It is the figure which showed the example of the functional block of the information processing apparatus which concerns on 3rd Embodiment. It is the figure which showed the flow of the numerical formula process which concerns on 3rd Embodiment. It is the figure which showed the 1st display method of the calculation result which concerns on 3rd Embodiment. It is the figure which showed the 2nd display method of the calculation result which concerns on 3rd Embodiment. It is the figure which showed the display method of the calculation result which concerns on 3rd Embodiment. It is the figure which showed the example of the functional block of the information processing apparatus which concerns on 4th Embodiment. It is the figure which showed the example of the numerical formula process which concerns on 4th Embodiment. It is the figure which showed the flow of the process by the information processing apparatus which concerns on 4th Embodiment. It is the figure which showed the flow of the numerical formula process which concerns on 4th Embodiment. It is the figure which showed the display method of the calculation result which concerns on 4th Embodiment.

Hereinafter, embodiments will be described with reference to the drawings.
[First Embodiment]
First, the first embodiment will be described.

FIG. 1 is a diagram illustrating an example of an information processing apparatus according to the first embodiment. As illustrated in FIG. 1, the information processing apparatus 10 includes a storage unit 11 and a calculation unit 12.
The storage unit 11 stores information on a plurality of first functions 13a and 13b that correspond to a plurality of evaluation indexes and each indicate a relationship between a parameter and one of the plurality of evaluation indexes. The parameter may be, for example, a parameter related to the design of the evaluation object, a parameter that defines the setting contents in the manufacturing process of the evaluation object, a parameter that defines the actual operating condition of the evaluation object, or the like. The evaluation index may be, for example, an index that represents the performance of the evaluation target, an index that represents the cost that occurs during the manufacture of the evaluation target, or the like.

  The first functions 13a and 13b may be polynomials or rational expressions, for example. The first functions 13a and 13b may be, for example, mathematical formulas arbitrarily given by the user or approximate formulas obtained by fitting data obtained by simulation or experiment using a method such as the least square method. Good. The storage unit 11 may be a volatile storage device such as a Random Access Memory (RAM), or may be a nonvolatile storage device such as a Hard Disk Drive (HDD) or a flash memory.

  The computing unit 12 calculates a plurality of second functions 14a and 14b corresponding to a plurality of evaluation indexes by approximating one or more of the plurality of first functions 13a and 13b. For example, when the first functions 13a and 13b are expressed by polynomials, the arithmetic unit 12 calculates an approximate polynomial having an order smaller than that of the first functions 13a and 13b, and uses the approximate polynomial as the second function. You may set to 14a and 14b. The approximation process may be, for example, a method for lowering the degree of a polynomial, a method for reducing the number of terms in a polynomial, or the like.

  The computing unit 12 generates first range information 15a and 15b indicating a range in which the combination of the values of the plurality of evaluation indexes changes according to the change of the parameter using the plurality of first functions 13a and 13b. For example, the first range information 15a and 15b may be calculated by mathematically processing a first logical expression indicating a plurality of first functions 13a and 13b and a parameter changing range. . In addition, the first logical expression includes, for example, a variable corresponding to a parameter among variables included in the first functions 13a and 13b, and other variables and output values of the first functions 13a and 13b. A logical expression including a constraint condition indicating that the bound variable exists may be used as the free variable.

  The computing unit 12 generates second range information 16a and 16b indicating a range in which the combination of the values of the plurality of evaluation indices changes according to the change of the parameter using the plurality of second functions 14a and 14b. For example, the second range information 16a and 16b may be calculated by mathematically processing a second logical expression indicating the plurality of second functions 14a and 14b and the range in which the parameter changes. . The second logical expression is, for example, a variable corresponding to a parameter among variables included in the second functions 14a and 14b, and other variables and output values of the second functions 14a and 14b. A logical expression including a constraint condition indicating that the bound variable exists may be used as the free variable.

  The calculation unit 12 displays the first range information 15a, 15b and the second range information 16a, 16b in a comparable format. For example, the calculation unit 12 may display only the first range information 15a and the second range information 16a indicating the inside of the range on the same screen. Moreover, the calculating part 12 may display only the 1st range information 15b and the 2nd range information 16b which show a boundary on the same screen. Moreover, the calculating part 12 may display all the 1st range information 15a and 15b and the 2nd range information 16a and 16b on the same screen.

  The calculation unit 12 may be a processor such as a central processing unit (CPU) or a digital signal processor (DSP). The computing unit 12 may be an electronic circuit other than a processor such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA). For example, the calculation unit 12 executes a program stored in the storage unit 11 or another memory.

  According to the information processing apparatus 10 according to the first embodiment, a format in which part or all of the first range information 15a and 15b can be compared with part or all of the second range information 16a and 16b. By displaying with, it becomes possible to visualize the influence on the analysis result when the load of the mathematical expression processing is suppressed. In addition, it is possible to perform appropriate design and evaluation using the second functions 14a and 14b, which have a low load of mathematical expression processing, in consideration of the effect of approximation processing.

[Second Embodiment]
Next, a second embodiment will be described.
FIG. 2 is a diagram illustrating an example of an evaluation support system according to the second embodiment. As shown in FIG. 2, the evaluation support system 100 according to the second embodiment includes a simulator 110, a network 120, an information processing device 130, and a display device 140.

  The simulator 110 is a device that simulates an object to be evaluated and an environment to be evaluated. For example, the simulator 110 may be a dedicated device designed for simulation, or a general-purpose computer in which a simulation program is installed. For example, the simulator 110 may be a computer having the same hardware as the information processing apparatus 130.

  In the second embodiment, a method for obtaining an evaluation index by using a simulation result by the simulator 110 is introduced. However, a method for obtaining an evaluation index by using an actual experimental result is also conceivable. However, in the following, for the sake of explanation, the description will be made on the assumption that the simulation result in the simulator 110 is used.

  The simulator 110 simulates the object and the environment based on the input parameters, and calculates a predetermined evaluation index for the object and the environment. For example, when the evaluation is performed in order to optimize the head shape of the hard disk, the object is the head of the hard disk. The environment is the assumed internal environment of the hard disk. In this case, the simulator 110 simulates the internal environment of the hard disk, and calculates an evaluation index related to the performance of the head in accordance with input of parameters related to the shape of the head.

  As the evaluation index, for example, an index such as performance or cost is used. Examples of performance evaluation indexes include durability, power consumption, and operating environment (temperature, humidity, atmospheric pressure). In addition, as an evaluation index related to cost, there are cost, manufacturing period, yield, and the like. In the second embodiment, multi-objective optimization that solves an optimization problem by simultaneously considering a plurality of evaluation indexes that are in a trade-off relationship with each other will be considered.

  Multi-objective optimization is often used in the design and evaluation scenes of manufacturing sites such as hard disk head design, semiconductor memory design, and automobile crash safety design. The evaluation support system 100 can be used in various design and evaluation situations. For example, the evaluation support system 100 can be used for designing a semiconductor memory (for example, optimizing a substrate material, a substrate shape, a wiring pattern, etc.). The evaluation support system 100 can also be used for collision safety design of an automobile (for example, optimization of body material, body shape, etc.).

  The value of the evaluation index calculated by the simulator 110 and the parameters input to the simulator 110 when calculating the evaluation index are input to the information processing apparatus 130 via the network 120. At this time, a set of parameters and evaluation index values (hereinafter referred to as index data) is input to the information processing apparatus 130 in association with each other. In addition, a plurality of index data corresponding to a plurality of parameters used for calculation by the simulator 110 is input to the information processing apparatus 130. In addition, in order to handle a plurality of evaluation indices, index data is input to the information processing apparatus 130 for each evaluation index.

  The network 120 may be formed of a wired communication network or a wireless communication network. 2 shows an example in which the simulator 110 and the information processing apparatus 130 are connected via the network 120. However, the simulator 110 and the information processing apparatus 130 may be directly connected via a cable or the like. . Further, the simulator 110 and the information processing apparatus 130 may be integrally formed. For example, a software module that causes a computer to operate may be incorporated in the information processing apparatus 130 in the same manner as the simulator 110, and the information processing apparatus 130 may be operated as the simulator 110.

  The information processing apparatus 130 calculates an objective function for each evaluation index using the index data. Further, the information processing apparatus 130 simplifies the objective function for each evaluation index. Further, the information processing apparatus 130 generates a first logical expression including the objective function before simplification and a second logical expression including the objective function after simplification, and performs mathematical expression processing on the first and second logical expressions. Execute. Then, the information processing device 130 causes the display device 140 to display the result of the mathematical expression processing.

  The display device 140 displays the result of mathematical expression processing under the control of the information processing device 130. The display device 140 is a display device such as a Cathode Ray Tube (CRT) display, a Liquid Crystal Display (LCD), a Plasma Display Panel (PDP), or an Organic Electro-Luminescence Display (OELD).

  FIG. 3 is a diagram illustrating an example of hardware of the information processing apparatus according to the second embodiment. As illustrated in FIG. 3, the information processing apparatus 130 includes, for example, a CPU 901, a RAM 902, an HDD 903, an image signal processing unit 904, an input signal processing unit 905, a disk drive 906, and a communication interface 907. The CPU 901 is an example of the calculation unit 12 according to the first embodiment. The RAM 902 and the HDD 903 are an example of the storage unit 11 according to the first embodiment.

  The CPU 901 is a processor including an arithmetic unit that executes instructions described in a program. The CPU 901 loads at least a part of the program and data stored in the HDD 903 into the RAM 902 and executes instructions described in the program. Note that the CPU 901 may include a plurality of processor cores. Further, the information processing apparatus 130 may be equipped with a plurality of CPUs 901. In this case, the information processing apparatus 130 can execute processes in parallel.

  The RAM 902 is a volatile memory for temporarily storing programs executed by the CPU 901 and data used for processing. Note that the information processing apparatus 130 may have a different type of memory from the RAM 902. Further, the information processing apparatus 130 may include a plurality of memories.

  The HDD 903 is an example of a nonvolatile storage device that stores programs such as an operating system (OS), firmware, or application software, data used for processing, and the like. Note that the information processing apparatus 130 may have a different type of storage device from the HDD 903, such as a flash memory or a solid state drive (SSD). Further, the information processing apparatus 130 may include a plurality of storage devices.

  The image signal processing unit 904 is controlled by the CPU 901 and outputs an image to the display device 140 connected to the information processing device 130. As the display device 140, for example, a CRT display, LCD, PDP, OELD, or the like can be used.

  The input signal processing unit 905 acquires an input signal from the input device 92 connected to the information processing apparatus 130 and notifies the CPU 901 of the input signal. As the input device 92, for example, a mouse, a keyboard, a touch panel, a touch pad, a trackball, a remote controller, a button switch, or the like can be used.

  The disk drive 906 is a reading device that reads programs and data recorded on the recording medium 93. As the recording medium 93, for example, a magnetic disk such as a Flexible Disk (FD) or HDD, an optical disk such as a Compact Disc (CD) or a Digital Versatile Disc (DVD), or a magneto-optical disk such as a Magneto-Optical disk (MO) is used. be able to. For example, the disk drive 906 is controlled by the CPU 901 and stores a program and data read from the recording medium 93 in the RAM 902 or the HDD 903.

  The communication interface 907 is an interface for communicating with other computers via the network 120. The communication interface 907 may be a wired interface or a wireless interface. For example, the information processing apparatus 130 communicates with the simulator 110 using the communication interface 907.

  FIG. 4 is a diagram illustrating an example of functional blocks of the information processing apparatus according to the second embodiment. As illustrated in FIG. 4, the information processing apparatus 130 according to the second embodiment includes an objective function calculation unit 131, a storage unit 132, a simplification unit 133, a mathematical expression processing unit 134, and a display control unit 135. The objective function calculation unit 131, the simplification unit 133, the mathematical expression processing unit 134, and the display control unit 135 can be realized as modules of a program executed by the CPU 901. However, some or all of the functions of the objective function calculation unit 131, the simplification unit 133, the mathematical expression processing unit 134, and the display control unit 135 can be realized as an electronic circuit instead of software.

  The objective function calculation unit 131 uses the input index data to calculate an objective function that outputs the value of the evaluation index according to the input of parameters. For example, the objective function calculation unit 131 calculates an approximate expression (for example, a polynomial or a rational expression) that fits a set of index data by a method such as a least square method, and sets the approximate expression as an objective function. In the second embodiment, a plurality of objective functions respectively corresponding to a plurality of evaluation indexes are generated.

The objective function calculated by the objective function calculation unit 131 is stored in the storage unit 132. The storage unit 132 is a storage area secured in the RAM 902 or the HDD 903.
The simplification unit 133 reads the objective function stored in the storage unit 132. Note that the simplification unit 133 may directly acquire the objective function from the objective function calculation unit 131. The simplification unit 133 simplifies the objective function. As a simplification method, for example, a method of lowering the order of the objective function or a method of reducing the number of terms of the objective function can be considered.

  By reducing the order of the objective function, it is possible to reduce the calculation load when executing mathematical expression processing on the logical expression including the objective function. In addition, by reducing the number of terms in the objective function, even when the maximum order of the objective function cannot be reduced, it is possible to reduce the computation load when executing mathematical processing on a logical expression including the objective function. become.

  When applying the method of reducing the order of the objective function, the simplification unit 133 calculates a low-order approximation expression that approximates the objective function before simplification in a predetermined parameter range (hereinafter referred to as parameter range D). Then, the approximate expression is set as a simplified objective function. For example, the simplification unit 133 calculates a low-order approximation expression in which the difference between the objective function before simplification and the objective function after simplification is smaller than a predetermined value (hereinafter, approximate determination value) in the parameter range D, The approximate expression is set to a simplified objective function.

  When the objective function is a polynomial, the simplification unit 133 prepares a lower-order polynomial than the objective function before simplification, and the difference from the objective function before simplification is greater than the approximate determination value in the entire parameter range D. The coefficient of the polynomial is calculated so as to be small. Then, the simplification unit 133 sets a low-order polynomial to which the calculated coefficient is assigned as a simplified objective function. Note that the highest order of the polynomial, the order of each term included in the polynomial, etc. may be set in advance, or minimum under the condition that the difference from the objective function before simplification is smaller than the approximate judgment value. The simplification unit 133 may automatically determine the order of

  In the method of reducing the number of terms of the objective function, the simplification unit 133 calculates an approximate expression with a small number of terms that approximates the objective function before the simplification in the parameter range D, and the objective function after the simplification is simplified. Set to. For example, the simplification unit 133 calculates an approximate expression in which the difference between the objective function before simplification and the objective function after simplification is smaller than the approximate determination value and has a small number of terms, and after the simplification of the approximate expression Set to the objective function of. At this time, the simplification unit 133 reduces the number of terms so as to reduce the number of higher-order terms. For example, if the Nth order term or the Mth order term (N> M) can be omitted, the simplification unit 133 sets an approximate expression in which the Nth order term is omitted as a simplified objective function.

  The parameter range D assumes, for example, an environment in which an object is actually used, an environment defined by safety standards, an environment requested by a provider or consumer of the object, or other environments. It is set in advance. In many cases, a parameter range having a margin is set in advance as the parameter range D in consideration of an environment where the use of the object is assumed. The approximate determination value may be arbitrarily set by the user, for example, or may be determined based on the degree of variation in the index data. As an example, a method of setting the maximum value of the distance between the objective function before the simplification and the index data as an approximate determination value can be considered.

  The difference between the objective function before simplification and the objective function after simplification can be expressed by a norm. For example, when each objective function is represented by a polynomial, consider a vector whose elements are polynomial coefficients, and use the norm of the difference between two vectors corresponding to both objective functions as the difference between the objective functions. It is done. In this case, a p-order average norm or maximum norm can be used. Further, when the norm of the polynomial difference is used as the difference between the two objective functions, an H∞ norm or the like can be used.

  If the vector v is defined by the following formula (1), the p-order average norm of the vector v is expressed as the following formula (2). Further, the maximum value norm of the vector v is expressed as the following equation (3). Further, the H∞ norm of the polynomial F is expressed as the following equation (4). However, j included in the following formula (4) is an imaginary unit.

A method for evaluating the degree of approximation of both objective functions by comparing the R ² value of the objective function before simplification for the set of index data with the R ² value of the objective function after simplification for the set of index data Is also possible. However, the R ² value represents a determination coefficient that is the square of the correlation coefficient R. In this method, for example, the simplified objective function is determined from the set of index data so that the difference between the R ² values of both objective functions is smaller than the approximate determination value.

  The simplified objective function calculated by the simplification unit 133 is stored in the storage unit 132. The mathematical expression processing unit 134 acquires the objective function before simplification and the objective function after simplification from the storage unit 132. Note that the mathematical expression processing unit 134 may directly obtain the simplified objective function from the simplification unit 133.

  As shown in FIG. 4, the mathematical expression processing unit 134 includes a first region calculation unit 1341, a first Pareto calculation unit 1342, a second region calculation unit 1343, and a second Pareto calculation unit 1344. The objective function before simplification is input to the first region calculation unit 1341. On the other hand, the objective function after simplification is input to the second region calculation unit 1343.

  The first area calculation unit 1341 generates a logical expression that is a target of mathematical expression processing using the objective function before simplification. As the logical expression, for example, a first-order predicate logical expression can be used. First-order predicate logical expressions are atomic expressions (algebraic equations, algebraic inequalities), quantifiers (generic symbols, existence symbols), and logical connectors (logical sums, logical products, negations, implications, etc.) It is a logical expression expressed by using.

  For example, the first region calculation unit 1341 sets a variable to which a parameter is substituted among variables included in the objective function before simplification as a bound variable, and sets the output value of the objective function before simplification as a free variable. To do. Further, the first region calculation unit 1341 sets the constraint condition that the bound variable is included in the parameter range D. Then, the first region calculation unit 1341 sets a logical expression expressing that there is a bound variable that satisfies the objective function before simplification under the set constraint conditions.

  The first area calculation unit 1341 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and generates a logical expression that represents a range of values that can be taken by the set of free variables (hereinafter, executable area). To do. For example, when two evaluation indices are considered, there are two objective functions before simplification. If only the output value of the objective function before simplification is set as a free variable, a logical expression expressing an executable area representing a range of values that can be taken by a set of two output values by a predetermined mathematical process Is generated. This feasible region can be drawn on a two-dimensional plane.

  For example, CAD or QE can be used as the predetermined mathematical expression processing. Regarding QE, for example, the basic idea is published in [Hirokazu Anai, Kazuhiro Yokoyama, “QE calculation algorithm and its application”, University of Tokyo Press].

Here, the solution of the optimization problem by QE is introduced. QE is a technique for generating a logical expression that does not include a quantification symbol from a logical expression that includes a quantification symbol by a computer. As a simple example, when a logical expression shown in the following expression (5) is given, applying QE to this logical expression yields a logical expression shown in the following expression (6). In this example, x ₁ , x ₂ , and x ₃ with a quantifier symbol are bound variables, and y without a quantifier symbol is a free variable. The logical expression shown in the following equation (5) includes a quantifier, but the logical equation shown in the following equation (6) does not include a quantifier.

  As in this example, when QE is applied, a logical expression that does not include a quantifier symbol can be generated from a logical expression that includes a quantifier symbol. Moreover, when QE is used, the optimization problem shown in the following equation (7) can be solved from the result of the above equation (6). That is, since the range of y for which the minimum value is to be obtained is given by the above equation (6), the minimum value −4 can be accurately obtained. Similarly, it is possible to solve the optimization problem in a similar manner for more complicated problems.

For example, when the objective functions F ₀ (x) and G ₀ (x) before simplification are given, the first region calculation unit 1341 shows the following equation (8) in the same manner as in the above example. Mathematical expression processing is performed on the logical expression, and a logical expression indicating a possible range of the free variables y ₁ and y ₂ is generated. However, in the following equation (8), the variable x is a variable to which a parameter is substituted, and φ (x) represents a constraint condition indicating that the variable x is included in the parameter range D. The variable x may be a scalar or a vector. Further, when the objective function includes a variable other than the variable x, the variable can be set as a free variable.

  A logical expression representing the executable area generated by the first area calculation unit 1341 is input to the first Pareto calculation unit 1342. The first pareto calculator 1342 calculates the pareto front based on a logical expression representing the executable area. The Pareto front is a boundary reached when at least one free variable advances in a predetermined direction in the executable region. However, when the executable region is widened in the direction in which the free variable increases, the predetermined direction is the direction in which it decreases. On the other hand, when the executable region is widened in the direction in which the free variable decreases, the predetermined direction is the direction in which it increases. This boundary is represented by a line when there are two free variables, a plane when there are three free variables, and a hyperplane when there are four or more free variables.

  On the other hand, the second region calculation unit 1343 generates a logical expression that is a target of mathematical expression processing using the simplified objective function. For example, the second region calculation unit 1343 sets a variable to which a parameter is substituted among variables included in the simplified objective function as a bound variable, and sets the output value of the simplified objective function as a free variable. To do. Further, the second region calculation unit 1343 sets the constraint condition that the bound variable is included in the parameter range D. Then, the second region calculation unit 1343 sets a logical expression expressing that there is a bound variable that satisfies the objective function before simplification under the set constraint conditions.

  The second area calculation unit 1343 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and generates a logical expression that represents an executable area that is a range of values that can be taken by the set of free variables. For example, when two evaluation indices are considered, there are two simplified objective functions. If only the output value of the objective function after simplification is set as a free variable, a logical expression representing an executable region that is a range of values that can be taken by a set of two output values is obtained by predetermined mathematical processing. Generated. This feasible region can be drawn on a two-dimensional plane.

  A logical expression representing the executable area generated by the second area calculation unit 1343 is input to the second Pareto calculation unit 1344. The second pareto calculator 1344 calculates the pareto front based on a logical expression representing the executable area.

  Information on logical expressions representing executable areas generated by the first area calculator 1341 and the second area calculator 1343, information on the Pareto front calculated by the first pareto calculator 1342 and the second pareto calculator 1344, and Is input to the display control unit 135. Based on the input information, the display control unit 135 causes the display device 140 to display an executable area related to the objective function before simplification and an executable area related to the objective function after simplification.

  At this time, the display control unit 135 displays the two executable areas so as to overlap each other on the same screen. In addition, the display control unit 135 displays two Pareto fronts respectively corresponding to the two executable areas on the same screen.

  In this way, by displaying the two executable areas so as to overlap each other on the same screen, the user can visually recognize the influence accompanying simplification of the objective function. Therefore, it becomes possible to easily estimate the influence of simplification. As a result, it is possible to design and evaluate in consideration of the influence of simplification when performing design and evaluation using an executable region related to the objective function after simplification. For example, it is possible to grasp the common part of two executable areas and determine the optimum design and evaluation conditions within the common part.

  Further, when performing design and evaluation, a Pareto front representing an optimal solution is often referred to. Also in such a case, by displaying the two Pareto fronts on the same screen, the user can easily grasp the influence of simplification on the Pareto front. As a result, it is possible to realize design and evaluation in consideration of the influence of simplification while reducing the load of mathematical expression processing.

  As described above, by simplifying the objective function, the load of mathematical expression processing is reduced, and the time required for calculating the executable region is shortened. On the other hand, when performing design and evaluation using a simplified objective function, it is preferable that the influence of simplification on the calculation result of mathematical expression processing can be easily grasped. In view of these circumstances, an information processing apparatus 130 has been devised that allows the effects of simplification to be visually recognized. When the information processing apparatus 130 is used, the influence on the calculation result due to simplification becomes clear, and it becomes easy to determine the optimum design and evaluation conditions in consideration of the influence of simplification.

  Hereinafter, the processing performed by the information processing apparatus 130 will be described in consideration of two evaluation indexes (index # 1, index # 2) that are in a trade-off relationship with each other. In this description, it is assumed that the objective function is a polynomial. The simplification method is a method for reducing the order. Of course, these assumptions are merely examples, and the number of evaluation indexes, the type of mathematical expression processing, the function form of the objective function, the simplification method, and the like can be changed as appropriate.

FIG. 5 is a diagram illustrating an objective function calculation method according to the second embodiment. As shown in FIG. 5, when a parameter is given, the simulator 110 generates index data including a parameter value and an index # 1 value, and index data including a parameter value and an index # 2 value. The Further, the objective function calculation unit 131 calculates the objective function F ₀ using the index data related to the index # 1, and calculates the objective function G ₀ using the index data related to the index # 2. At this time, the objective function calculation unit 131 uses an least square method or the like to calculate approximate polynomials that respectively fit the index data related to the index # 1 and the index data related to the index # 2, and each of the calculated two approximate polynomials Set to functions F ₀ and G ₀ .

FIG. 6 is a diagram illustrating a simplification method according to the second embodiment. In the graph of FIG. 6A, the white circles represent the index data, the solid line represents the objective function F ₀ , and the chain line represents the simplified objective function F ₁ . In the graph of FIG. 6B, the black circles represent the index data, the solid line represents the objective function G ₀ , and the chain line represents the simplified objective function G ₁ .

When the objective function F ₀ is obtained, the simplification unit 133 calculates an objective function F ₁ obtained by simplifying the objective function F ₀ as shown in FIG. At this time, the simplification unit 133 calculates the objective function F ₁ whose difference from the objective function F ₀ in the parameter range D is smaller than the approximate determination value and whose order is lower than the objective function F ₀ . Similarly, when the objective function G ₀ is obtained, the simplification unit 133 calculates an objective function G ₁ obtained by simplifying the objective function G ₀ as shown in FIG. 6B. At this time, the simplification unit 133 calculates an objective function G ₁ whose difference from the objective function G ₀ in the parameter range D is smaller than the approximate determination value and whose order is lower than the objective function G ₀ .

FIG. 7 is a diagram illustrating an example of mathematical expression processing according to the second embodiment. As shown in FIG. 7, when the objective functions F ₀ and G ₀ are obtained, the first area calculation unit 1341 sets a logical expression shown in the following expression (9). The first region calculation unit 1341 performs a QE to the logical expression set, the objective function F ₀ and a set of output values of _{G 0 (y 1, y 2} ) can be executed is a possible range area [Phi ₀ A logical expression representing (y ₁ , y ₂ ) is calculated. Furthermore, the first pareto calculator 1342 calculates the pareto front PF ₀ of the executable region Φ ₀ (y ₁ , y ₂ ).

Similarly, when the objective functions F ₁ and G ₁ are obtained, the second area calculation unit 1343 sets a logical expression shown in the following expression (10). The second area calculation unit 1343 performs QE on the set logical expression, and the executable area Φ ₁ that is a range that the set of output values (y ₁ , y ₂ ) of the objective functions F ₁ and G ₁ can take. A logical expression representing (y ₁ , y ₂ ) is calculated. In addition, the second Pareto calculation unit 1344 calculates the Pareto front PF ₁ of the executable region Φ ₁ (y ₁ , y ₂ ).

The display control unit 135 causes the display device 140 to display the two executable areas Φ ₀ (y ₁ , y ₂ ) and Φ ₁ (y ₁ , y ₂ ) in a comparable form. The display control unit 135 causes the display device 140 to display the two Pareto fronts PF ₀ and PF ₁ in a comparable format. With this process, the user can visually recognize the influence of the simplification on the calculation result. As a result, it becomes possible to perform design and evaluation taking into account the effects of simplification when performing design and evaluation using the executable region based on the simplified objective function and the Pareto front calculation results .

Next, the flow of processing by the information processing apparatus 130 will be described.
FIG. 8 is a diagram illustrating a flow of processing by the information processing apparatus according to the second embodiment.
(S101) The objective function calculation unit 131 calculates the objective function.

(S102) The simplification unit 133 simplifies the objective function.
(S103) The mathematical expression processing unit 134 executes mathematical expression processing.
(S104) The calculation result is displayed by the display control unit 135.

Hereinafter, each process shown in FIG. 8 will be further described.
FIG. 9 is a diagram showing a flow of objective function calculation processing according to the second embodiment. The objective function calculation process shown in FIG. 9 is mainly executed by the objective function calculator 131.

  (S111) The objective function calculation unit 131 acquires index data related to the index # 1 and index data related to the index # 2 calculated by the simulator 110. For example, the objective function calculation unit 131 acquires index data regarding each index from the simulator 110 via the network 120.

(S112) The objective function calculation unit 131 calculates the objective function F ₀ from the index data regarding the index # 1. For example, the objective function calculation unit 131 calculates an approximate polynomial that fits a set of index data related to the index # 1 by the least square method or the like, and sets the approximate polynomial as the objective function F ₀ .

(S113) The objective function calculation unit 131 calculates the objective function G ₀ from the index data regarding the index # 2. For example, the objective function calculation unit 131 calculates an approximate polynomial that fits a set of index data related to the index # 2 by the least square method or the like, and sets the approximate polynomial as the objective function G ₀ . Note that the process of S113 may be replaced with the process of S112.

(S114) The objective function calculator 131 outputs the calculated objective functions F ₀ and G ₀ . For example, the objective functions F ₀ and G ₀ are stored in the storage unit 132 or input to the simplification unit 133. When the process of S114 is completed, the objective function calculation process ends.

FIG. 10 is a diagram showing the flow of the objective function simplification process according to the second embodiment. The simplification process of the objective function shown in FIG.
(S121) The simplification unit 133 acquires the parameter range D. The parameter range D may be arbitrarily determined by the user, or may be determined in advance in consideration of the operating conditions to be evaluated. For example, the parameter range D may be input by the user via the input device 92, stored in advance in the HDD 903 or the like, or provided via the network 120. It may be.

(S122) The simplification unit 133 acquires the objective functions F ₀ and G ₀ . For example, the simplification unit 133 reads the objective functions F ₀ and G ₀ stored in the storage unit 132. The simplification unit 133 may directly acquire the objective functions F ₀ and G ₀ from the objective function calculation unit 131 instead of reading the objective functions F ₀ and G ₀ from the storage unit 132. The simplification unit 133 may directly acquire the objective functions F ₀ and G ₀ from the objective function calculation unit 131 in addition to reading the objective functions F ₀ and G ₀ from the storage unit 132.

(S123) The simplification unit 133 calculates an objective function F ₁ obtained by simplifying the objective function F ₀ . For example, simplifying unit 133 prepares a low order polynomial than the objective function F _0, the difference between the polynomial and the objective function F ₀ to determine the coefficients of the polynomial to be smaller than the approximate determination value. At this time, the simplification unit 133 may determine the coefficient of the polynomial so that the difference between the polynomial and the objective function F ₀ is minimized. The simplification unit 133 sets the polynomial assigned the determined coefficient to the objective function F ₁ .

(S124) The simplification unit 133 calculates an objective function G ₁ obtained by simplifying the objective function G ₀ . For example, simplifying unit 133 prepares a low order polynomial than the objective function G _0, the difference between the polynomial and the objective function G ₀ determines the coefficients of the polynomial to be smaller than the approximate determination value. At this time, the simplification unit 133 may determine the coefficient of the polynomial so that the difference between the polynomial and the objective function G ₀ is minimized. The simplification unit 133 sets the polynomial assigned the determined coefficient to the objective function G ₁ . Note that the process of S124 may be replaced with the process of S123.

(S125) The simplification unit 133 outputs the objective functions F ₀ , G ₀ , F ₁ , G ₁ . For example, the objective functions F ₀ , G ₀ , F ₁ , G ₁ are stored in the storage unit 132 or input to the mathematical expression processing unit 134. When the process of S125 is completed, the simplification of the objective function ends.

FIG. 11 is a diagram showing a flow of mathematical expression processing according to the second embodiment. The mathematical formula processing shown in FIG. 11 is mainly executed by the mathematical formula processing unit 134.
(S131) The mathematical expression processing unit 134 acquires the parameter range D.

(S132) The mathematical expression processor 134 obtains objective functions F ₀ , G ₀ , F ₁ , G ₁ . For example, the mathematical expression processing unit 134 reads part or all of the objective functions F ₀ , G ₀ , F ₁ , G ₁ stored in the storage unit 132. Incidentally, formula manipulation unit 134, the objective function F ₀ from the storage unit 132, G _0, F _1, purpose simplifying unit 133 instead of reading a part or the whole in G ₁ function F _0, G _0, F ₁ , part or all of G ₁ may be directly acquired. Further, the mathematical expression processing unit 134 reads out part or all of the objective functions F ₀ , G ₀ , F ₁ , G ₁ from the storage unit 132, and at the same time reads out the objective functions F ₀ , G ₀ , F from the simplification unit 133. ₁ , part or all of G ₁ may be directly acquired.

The objective functions F ₀ and G ₀ are input to the first area calculation unit 1341. The objective functions F ₁ and G ₁ are input to the second area calculation unit 1343.
(S133) The first region calculation unit 1341 sets a logical expression L ₀ based on the objective functions F ₀ and G ₀ . For example, the logical expression L ₀ is expressed by the above expression (9).

(S134) The first area calculation unit 1341 executes mathematical expression processing on the logical expression L ₀ and calculates a logical expression representing the executable area Φ ₀ . The first pareto calculation unit 1342 calculates the pareto front PF ₀ of the executable region Φ ₀ based on the logical expression calculated by the first region calculation unit 1341.

(S135) The second region calculation unit 1343 sets a logical expression L ₁ based on the objective functions F ₁ and G ₁ . For example, the logical expression L ₁ is expressed by the above expression (10).
(S136) The second area calculation unit 1343 performs mathematical expression processing on the logical expression L ₁ and calculates a logical expression representing the executable area Φ ₁ . The second pareto calculator 1344 calculates the pareto front PF ₁ of the executable region Φ ₁ based on the logical expression calculated by the second region calculator 1343. Note that the processes of S135 and S136 may be replaced in order with the processes of S133 and S134.

(S137) The mathematical expression processing unit 134 outputs information on the executable regions Φ ₀ and Φ ₁ and information on the Pareto fronts PF ₀ and PF ₁ . For example, information on the executable regions Φ ₀ and Φ ₁ and information on the Pareto fronts PF ₀ and PF ₁ are input to the display control unit 135. Note that the information on the executable areas Φ ₀ and Φ _{1 and} the information on the Pareto fronts PF ₀ and PF ₁ may be stored in the storage unit 132. When the process of S137 is completed, the execution of the mathematical expression process is completed.

FIG. 12 is a diagram illustrating a calculation result display method according to the second embodiment. As shown in FIG. 12, the display control unit 135 that has obtained the information on the executable areas Φ ₀ and Φ _{1 and} the information on the Pareto fronts PF ₀ and PF ₁ places the executable areas Φ ₀ and Φ ₁ on the same screen. Overlapping display. In addition, the display control unit 135 displays the Pareto fronts PF ₀ and PF ₁ on the same screen. In the example of FIG. 12, an area (hatched area) that expands in the direction in which the free variables y ₁ and y ₂ become larger with the Pareto front as a boundary represents an executable area. Further, in the example of FIG. 12, it is represented by different hatching the feasible region [Phi ₀ and [Phi ₁ common region feasible region [Phi ₀ and [Phi ₁ overlap.

As in the display example shown in FIG. 12, by displaying the executable regions Φ ₀ and Φ ₁ in the same coordinate system, it is possible to easily visually recognize the common region where the executable regions Φ ₀ and Φ ₁ overlap. It becomes possible. Further, by displaying the Pareto fronts PF ₀ and PF ₁ in an overlapping manner, the influence of simplification in the vicinity of the optimum solution can be easily recognized. A part of the executable areas Φ ₀ and Φ ₁ excluding the common area represents the influence of simplification. For example, by estimating the area of this partial region, the magnitude of the effect of simplification can be evaluated. In addition, by setting parameters so that the free variables are within the common area, it becomes possible to perform design and evaluation that are not easily affected by simplification.

In the example of FIG. 12, the display method of displaying the executable areas Φ ₀ and Φ ₁ and the Pareto fronts PF ₀ and PF ₁ in the same coordinate system is shown, but only the Pareto fronts PF ₀ and PF ₁ are the same. A display method that displays the image in a coordinate system is also conceivable. A display method in which only the executable regions Φ ₀ and Φ ₁ are displayed in the same coordinate system is also conceivable. Further, when there are three or more evaluation indexes, a display method for displaying the executable regions Φ ₀ and Φ ₁ and the Pareto fronts PF ₀ and PF ₁ in a three-dimensional display, a display method for displaying contour lines, and the like are also conceivable. As an expression method, for example, shading, color, line type, three-dimensional expression, transparent expression, and the like are conceivable.

Here, a calculation example is shown in which the executable regions Φ ₀ and Φ ₁ and the Pareto fronts PF ₀ and PF ₁ are calculated for the objective functions F ₀ and G ₀ shown in the following formulas (11) and (12).

FIG. 13 is a diagram illustrating an example of simplified calculation according to the second embodiment. The objective function F ₀ shown in the above equation (11) is expressed by the graph shown by the solid line in FIG. For example, when a quadratic polynomial that approximates the objective function F ₀ in the range of the parameter x from 3 to 9 is obtained, a quadratic polynomial F ₁ expressed by the following equation (13) is obtained. Therefore, this quadratic polynomial F ₁ is set as a simplified objective function. The objective function F ₁ is expressed by a chain line in FIG.

On the other hand, the objective function G ₀ shown in the above equation (12) is expressed by the graph shown by the solid line in FIG. Similar to the case of obtaining the quadratic polynomial F ₁ , when obtaining a quadratic polynomial that approximates the objective function G ₀ in the range of the parameter x from 3 to 9, the quadratic polynomial G expressed by the following equation (14): ₁ is obtained. Therefore, this quadratic polynomial G ₁ is set as a simplified objective function. The objective function G ₁ is expressed by a chain line in FIG.

FIG. 14 is a diagram illustrating a calculation result display method according to the second embodiment. When the objective functions F ₀ , G ₀ , F ₁ , G ₁ are obtained, the executable areas Φ ₀ and Φ ₁ can be calculated by mathematical processing. When the objective functions F ₀ , G ₀ , F ₁ , G ₁ are given by the above equations (11) to (14) and the parameter range D is given by the following equation (15), the feasible region Φ ₀ and Φ ₁ is as shown in FIG. However, FIG. 14B is an enlarged view of a part R of FIG. For reference, the executable area Φ ₁ is expressed by a logical expression shown in the following expression (16).

  As described above, when the technique according to the second embodiment is applied, the user can visually recognize the influence on the calculation result due to the simplification. As a result, it becomes possible to perform design and evaluation taking into account the effects of simplification when performing design and evaluation using the executable region based on the simplified objective function and the Pareto front calculation results . In other words, it is possible to use the simplified objective function with a low calculation load after fully recognizing the influence of the simplification. In addition, it is possible to determine a simplification method with little influence on the calculation result while checking the influence of simplification.

[Third Embodiment]
Next, a third embodiment will be described.
FIG. 15 is a diagram illustrating an example of setting an extended parameter range according to the third embodiment.

In the description of the second embodiment, as an example, a method for obtaining the objective function F ₁ by simplifying the objective function F ₀ was introduced. In this method, an approximate expression that approximates the objective function F ₀ in the parameter range D is obtained, and the approximate expression is set as the objective function F ₁ . Therefore, in the parameter range D, the objective function F ₀ and the objective function F ₁ are sufficiently approximated. However, when the parameter deviates from the parameter range D, the difference between the objective function F ₀ and the objective function F ₁ may be greatly increased. The same applies to the difference between the objective function G ₀ and the objective function G ₁ .

For example, when designing a product or the like, the parameter range D to be considered in simplification is more than the parameter range (actual usage range D _r ) assuming an environment where the product is actually used, as shown in FIG. Are often set widely. For example, the parameter ranges D is broadly set than the actual use range D _r envisaged on the basis of such a guaranteed operating environment and product specification limits. That is, the parameter range D is set with a margin so that even if the product user uses it in an environment slightly different from the operation guarantee environment, the product will not immediately fail. However, since the approximate expression is used, it is preferable to grasp in advance the influence when the parameter deviates from the parameter range D.

  Therefore, the present inventor examined a method for estimating the influence on the calculation result due to the deviation of the parameter. In the third embodiment, a method for visualizing the influence when the parameter deviates from the parameter range D will be introduced.

In the following description, the expression shown in FIG. 15 is used, and the amount of deviation in which the parameter exceeds the upper limit of the parameter range D is expressed as δ ₁ , and the amount of deviation in which the parameter falls below the lower limit of the parameter range D is expressed as δ ₂ . Note that δ ₁ and δ ₂ may be set to the same value δ. In addition, a parameter range in consideration of deviation is expressed as an extended parameter range Dδ. The evaluation support system according to the third embodiment is obtained by replacing the information processing apparatus 130 with the information processing apparatus 230 according to the third embodiment in the evaluation support system 100 according to the second embodiment. is there.

  FIG. 16 is a diagram illustrating an example of functional blocks of the information processing apparatus according to the third embodiment. As illustrated in FIG. 16, the information processing apparatus 230 according to the third embodiment includes an objective function calculation unit 231, a storage unit 232, a simplification unit 233, a mathematical expression processing unit 234, and a display control unit 235.

  The information processing device 230 has the same hardware as the information processing device 130 according to the second embodiment. The objective function calculation unit 231, the simplification unit 233, the mathematical expression processing unit 234, and the display control unit 235 can be realized as a program module executed by the CPU 901. In addition, some or all of the functions of the simplification unit 233, the mathematical expression processing unit 234, and the display control unit 235 can be realized as an electronic circuit instead of software. The storage unit 232 is a storage area secured in the RAM 902 or the HDD 903.

  However, the objective function calculation unit 231, the storage unit 232, and the simplification unit 233 perform substantially the same processing as the objective function calculation unit 131, the storage unit 132, and the simplification unit 133 according to the second embodiment, respectively. Run. Therefore, description of substantially the same items as those of the second embodiment will be omitted, and description will be made focusing on items that are different from those of the second embodiment. Hereinafter, the mathematical expression processing unit 234 and the display control unit 235 will be mainly described.

  As illustrated in FIG. 16, the mathematical expression processing unit 234 includes a first region calculation unit 2341, a first Pareto calculation unit 2342, a second region calculation unit 2343, and a second Pareto calculation unit 2344. Further, the mathematical expression processing unit 234 includes a third region calculation unit 2345, a third Pareto calculation unit 2346, a fourth region calculation unit 2347, and a fourth Pareto calculation unit 2348.

The objective functions F ₀ and G ₀ before simplification are input to the first region calculation unit 2341 and the third region calculation unit 2345. On the other hand, the simplified objective functions F ₁ and G ₁ are input to the second region calculation unit 2343 and the fourth region calculation unit 2347.

The first region calculation unit 2341, a variable x parameter in the variables included in the objective function F ₀ and G ₀ before simplification is substituted as bound variables, and, prior to simplified objective function F ₀ and G Set the output value of ₀ to the free variables y ₁ and y ₂ . Further, the first region calculation unit 2341 sets the constraint condition that the bound variable is included in the parameter range D. The first region calculation unit 2341 then expresses a logical expression shown in the following equation (17) that expresses that there are bound variables that satisfy the objective functions F ₀ and G ₀ before simplification under the set constraint conditions. Set.

The first region calculation unit 2341 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and the executable region Φ ₀ which is a range of values that the free variable pair (y ₁ , y ₂ ) can take. Generate a logical expression that represents A logical expression representing the executable area Φ ₀ generated by the first area calculation unit 2341 is input to the first Pareto calculation unit 2342. The first pareto calculation unit 2342 calculates the pareto front PF ₀ based on a logical expression representing the executable region Φ ₀ .

The second region calculation unit 2343 uses the variable x to which the parameter is substituted among the variables included in the simplified objective functions F ₁ and G ₁ as a bound variable, and the simplified objective functions F ₁ and G ₁ Set the output value of ₁ to the free variables y ₁ and y ₂ . Further, the second region calculation unit 2343 sets the constraint condition that the bound variable is included in the parameter range D. The second region calculation unit 2343 then expresses a logical expression shown in the following equation (18) that expresses that there are bound variables that satisfy the simplified objective functions F ₁ and G ₁ under the set constraints. Set.

The second region calculation unit 2343 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and the executable region Φ ₁ that is a range of values that the free variable pair (y ₁ , y ₂ ) can take. Generate a logical expression that represents A logical expression representing the executable area Φ ₁ generated by the second area calculation unit 2343 is input to the second Pareto calculation unit 2344. The second pareto calculation unit 2344 calculates the pareto front PF ₁ based on a logical expression representing the executable region Φ ₁ .

The third region calculation unit 2345, a variable x parameter in the variables included in the objective function F ₀ and G ₀ before simplification is substituted as bound variables, and, prior to simplified objective function F ₀ and G Set the output value of ₀ to the free variables y ₁ and y ₂ . In addition, the third region calculation unit 2345 sets the constraint condition that the bound variable is included in the extended parameter range Dδ. Then, the third region calculation unit 2345 expresses that there is a bound variable that satisfies the objective functions F ₀ and G ₀ before simplification under the set constraint condition, and is expressed by the following logical expression (19). Set.

The third region calculation unit 2345 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and the executable region Φ ₀ which is a range of values that the free variable pair (y ₁ , y ₂ ) can take. A logical expression expressing δ is generated. A logical expression representing the executable region Φ ₀ δ generated by the third region calculation unit 2345 is input to the third Pareto calculation unit 2346. The third pareto calculation unit 2346 calculates the pareto front PF ₀ δ based on a logical expression representing the executable region Φ ₀ δ.

The fourth region calculation unit 2347 uses the variable x into which the parameter is substituted among the variables included in the simplified objective functions F ₁ and G ₁ as a bound variable, and the simplified objective functions F ₁ and G ₁ Set the output value of ₁ to the free variables y ₁ and y ₂ . Further, the fourth region calculation unit 2347 sets the constraint condition that the bound variable is included in the extended parameter range Dδ. Then, the fourth area calculation unit 2347 expresses that the bound variable satisfying the objective functions F ₁ and G ₁ after the simplification exists under the set constraint condition, and the logical formula shown in the following formula (20) Set.

The fourth region calculation unit 2347 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and the executable region Φ ₁ that is a range of values that the free variable pair (y ₁ , y ₂ ) can take. A logical expression expressing δ is generated. A logical expression representing the executable region Φ ₁ δ generated by the fourth region calculation unit 2347 is input to the fourth Pareto calculation unit 2348. The fourth pareto calculation unit 2348 calculates the pareto front PF ₁ δ based on a logical expression representing the executable region Φ ₁ δ.

The display control unit 235 includes executable regions Φ ₀ (y ₁ , y ₂ ), Φ ₁ (y ₁ , y ₂ ), Φ ₀ δ (y ₁ , y ₂ ), and Φ ₁ δ (y ₁ , y ₂ ). At least two of them are displayed on the display device 140 in a comparable format. Further, the display control unit 235 causes the display device 140 to display at least two of the pareto fronts PF ₀ , PF ₁ , PF ₀ δ, and PF ₁ δ in a comparable form.

For example, if the Pareto fronts PF ₀ and PF ₀ δ are displayed on the same screen, it is possible to visually grasp the influence on the executable region Φ ₀ due to the deviation of the parameters. Further, if the Pareto fronts PF ₁ and PF ₁ δ are displayed on the same screen, it is possible to visually grasp the influence on the executable region Φ ₁ due to the deviation of the parameters. If the Pareto fronts PF ₀ and PF ₁ δ are displayed on the same screen, it is possible to visually grasp the influence on the executable area Φ ₀ due to parameter deviation and simplification.

  As described above, according to the information processing apparatus 230 according to the third embodiment, the user can visually recognize the influence on the calculation result due to the deviation of the parameter. As a result, it is possible to perform more robust design and evaluation in consideration of the effect of parameter deviation.

  Next, the flow of processing by the information processing apparatus 230 will be described. However, the processing executed by the information processing device 230 includes calculation of the objective function, simplification of the objective function, execution of mathematical expression processing, and display of the result, as in the processing according to the second embodiment (see FIG. 8). reference). The contents of the processing related to the calculation of the objective function and the simplification of the objective function are substantially the same as the processing related to the calculation of the objective function and the simplification of the objective function according to the second embodiment. Therefore, the flow of mathematical expression processing by the information processing apparatus 230 will be described here.

FIG. 17 is a diagram illustrating a flow of mathematical expression processing according to the third embodiment. The formula processing shown in FIG. 17 is mainly executed by the formula processing unit 234.
(S231) The mathematical expression processing unit 234 acquires the parameter range D and the extended parameter range Dδ. The parameter range D and the extended parameter range Dδ may be arbitrarily determined by the user, or may be determined in advance in consideration of the operation condition to be evaluated. For example, the parameter range D and the extended parameter range Dδ may be input by the user via the input device 92, may be stored in advance in the HDD 903 or the like, or may be stored via the network 120. May be provided.

(S232) The mathematical expression processing unit 234 acquires the objective functions F ₀ , G ₀ , F ₁ , G ₁ . For example, the mathematical expression processing unit 234 reads part or all of the objective functions F ₀ , G ₀ , F ₁ , G ₁ stored in the storage unit 232. Note that the mathematical expression processing unit 234 reads the objective functions F ₀ , G ₀ , F ₁ , and G ₁ from the storage unit 232 in place of all or part of the objective functions F ₀ , G ₀ , G ₁ , A part or all of F ₁ and G ₁ may be acquired directly. In addition, the mathematical expression processing unit 234 reads out part or all of the objective functions F ₀ , G ₀ , F ₁ , G ₁ from the storage unit 232, and at the same time reads out the objective functions F ₀ , G ₀ , A part or all of F ₁ and G ₁ may be acquired directly.

The objective functions F ₀ and G ₀ are input to the first region calculation unit 2341 and the third region calculation unit 2345. The objective functions F ₁ and G ₁ are input to the second region calculation unit 2343 and the fourth region calculation unit 2347.

(S233) The first region calculation unit 2341 sets a logical expression L ₀ based on the objective functions F ₀ and G ₀ . However, the logical expression L ₀ is expressed by the above expression (17). The third region calculation unit 2345 sets a logical expression L ₀ δ based on the objective functions F ₀ and G ₀ . However, the logical expression L ₀ δ is expressed by the above expression (19).

(S234) The first area calculation unit 2341 executes mathematical expression processing on the logical expression L ₀ to calculate a logical expression representing the executable area Φ ₀ . The first pareto calculator 2342 calculates the pareto front PF ₀ of the executable region Φ ₀ based on the logical expression calculated by the first region calculator 2341.

(S235) The third region calculation unit 2345 executes mathematical expression processing on the logical expression L ₀ δ to calculate a logical expression representing the executable region Φ ₀ δ. The third pareto calculation unit 2346 calculates the pareto front PF ₀ δ of the executable region Φ ₀ δ based on the logical expression calculated by the third region calculation unit 2345. Note that the process of S235 may be replaced with the process of S234.

(S236) The second region calculation unit 2343 sets a logical expression L ₁ based on the objective functions F ₁ and G ₁ . However, the logical expression L ₁ is expressed by the above expression (18). The fourth region calculation unit 2347 sets a logical expression L ₁ δ based on the objective functions F ₁ and G ₁ . However, the logical expression L ₁ δ is expressed by the above expression (20).

(S237) The second area calculation unit 2343 performs mathematical expression processing on the logical expression L ₁ and calculates a logical expression representing the executable area Φ ₁ . The second Pareto calculation unit 2344 calculates the Pareto front PF ₁ of the executable region Φ ₁ based on the logical expression calculated by the second region calculation unit 2343.

(S238) The fourth area calculation unit 2347 executes mathematical expression processing on the logical expression L ₁ δ to calculate a logical expression representing the executable area Φ ₁ δ. The fourth Pareto calculation unit 2348 calculates the Pareto front PF ₁ δ of the executable region Φ ₁ δ based on the logical expression calculated by the fourth region calculation unit 2347. Note that the process of S238 may be replaced with the process of S237.

(S239) The mathematical expression processing unit 234 outputs information on the executable regions Φ ₀ , Φ ₁ , Φ ₀ δ, Φ ₁ δ and information on the Pareto fronts PF ₀ , PF ₁ , PF ₀ δ, PF ₁ δ. . For example, information on the executable areas Φ ₀ , Φ ₁ , Φ ₀ δ, Φ ₁ δ and information on the Pareto fronts PF ₀ , PF ₁ , PF ₀ δ, PF ₁ δ are input to the display control unit 235. . Note that information on the executable areas Φ ₀ , Φ ₁ , Φ ₀ δ, Φ ₁ δ and information on the Pareto fronts PF ₀ , PF ₁ , PF ₀ δ, PF ₁ δ may be stored in the storage unit 232. Good. When the process of S239 is completed, the execution of the mathematical expression process is completed. Note that the processing of S233 to S235 may be replaced with the processing of S236 to S238.

FIG. 18 is a diagram illustrating a first display method of calculation results according to the third embodiment. Figure 18 (A), the feasible region [Phi ₀ and [Phi ₀ [delta] Information and Pareto front PF ₀ and PF ₀ [delta] Information and display control unit 235 to obtain a can feasible region [Phi ₀ and [Phi ₀ δ is displayed on the same screen. Further, the display control unit 235 displays the Pareto fronts PF ₀ and PF ₀ δ on the same screen. In the example of FIG. 18, a display method is adopted in which the display of the common area where the executable areas Φ ₀ and Φ ₀ δ overlap is omitted and the difference between the executable areas Φ ₀ and Φ ₀ δ is displayed. According to this display method, the influence on the executable area Φ ₀ due to the deviation of the parameter can be easily visually confirmed.

Further, as shown in FIG. 18 (B), the display control unit 235 obtains information of the feasible region [Phi ₁ and [Phi ₁ [delta] and the information of the Pareto front PF ₁ and PF ₁ [delta] is feasible region [Phi ₁ and Φ ₁ δ is displayed on the same screen. Further, the display control unit 235 displays the Pareto fronts PF ₁ and PF ₁ δ on the same screen. In the example of FIG. 18, a display method is adopted in which the display of the common area where the executable areas Φ ₁ and Φ ₁ δ overlap is omitted and the difference between the executable areas Φ ₁ and Φ ₁ δ is displayed. According to this display method, the influence on the executable area Φ ₁ due to the deviation of the parameter can be easily visually confirmed.

FIG. 19 is a diagram showing a second display method of calculation results according to the third embodiment. As shown in FIG. 19, the display control unit 235 that has obtained the information on the executable regions Φ ₀ and Φ ₁ δ and the information on the Pareto fronts PF ₀ and PF ₁ δ has the same executable regions Φ ₀ and Φ ₁ δ. Overlay on the screen. In addition, the display control unit 235 displays the Pareto fronts PF ₀ and PF ₁ δ on the same screen. In the example of FIG. 19, a display method is adopted in which the display of the common area where the executable areas Φ ₀ and Φ ₁ δ overlap is omitted and the difference between the executable areas Φ ₀ and Φ ₁ δ is displayed. According to this display method, it is possible to easily visually recognize the influence on the executable region Φ ₀ due to the deviation and simplification of parameters.

FIG. 20 is a diagram illustrating a calculation result display method according to the third embodiment. Here, the feasible regions Φ ₀ and Φ ₀ δ with respect to the objective functions F ₀ and G ₀ expressed by the above formulas (11) and (12) exemplified in the description of the second embodiment and a Pareto front PF ₀ and PF ₀ [delta] shows a calculation example of calculation. However, the parameter range D is given by the above formula (15), and the extended parameter range Dδ is given by the following formula (21). In this case, the executable regions Φ ₀ and Φ ₀ δ are as shown in FIG. However, FIG. 20B is an enlarged view of a part R of FIG. In the example of FIG. 20, a display method is employed in which the display of the common area where the executable areas Φ ₀ and Φ ₀ δ overlap is omitted and the difference between the executable areas Φ ₀ and Φ ₀ δ is displayed.

  As described above, when the technique according to the third embodiment is applied, the user can visually recognize the influence on the calculation result due to the deviation of the parameter. As a result, it is possible to perform robust design and evaluation in consideration of the effect of parameter deviation when performing design and evaluation using the executable region and Pareto front calculation results.

It is also possible to determine a simplification method with little influence on the calculation result while confirming the influence due to the deviation of the parameter. For example, it is possible to evaluate the influence of the parameter deviation by checking the area sandwiched between the two Pareto fronts PF ₀ and PF ₀ δ while changing the values of the deviations δ ₁ and δ ₂ prepared in advance. become. Therefore, it is possible to quantitatively estimate the range of the allowable deviations δ ₁ and δ ₂ .

[Fourth Embodiment]
Next, a fourth embodiment will be described. In the fourth embodiment, as in the third embodiment, a method for visualizing the influence of parameter deviation is introduced. Also in the fourth embodiment, the expression of the extended parameter range Dδ introduced in the description according to the third embodiment is used similarly. The evaluation support system according to the fourth embodiment is obtained by replacing the information processing apparatus 130 with the information processing apparatus 330 according to the fourth embodiment in the evaluation support system 100 according to the second embodiment. Suppose there is.

  FIG. 21 is a diagram illustrating an example of functional blocks of the information processing apparatus according to the fourth embodiment. As illustrated in FIG. 21, the information processing apparatus 330 according to the fourth embodiment includes an objective function calculation unit 331, a mathematical expression processing unit 332, and a display control unit 333.

  Note that the information processing apparatus 330 has the same hardware as the information processing apparatus 130 according to the second embodiment. The objective function calculation unit 331, the mathematical expression processing unit 332, and the display control unit 333 can be realized as a module of a program executed by the CPU 901. However, some or all of the functions of the objective function calculation unit 331, the mathematical expression processing unit 332, and the display control unit 333 can be realized as an electronic circuit instead of software.

  However, the objective function calculation unit 331 executes substantially the same processing as the objective function calculation unit 131 according to the second embodiment. Therefore, description of substantially the same items as those of the second embodiment will be omitted, and description will be made focusing on items that are different from those of the second embodiment. Hereinafter, the mathematical expression processing unit 332 and the display control unit 333 will be mainly described.

  As illustrated in FIG. 21, the mathematical expression processing unit 332 includes a first region calculation unit 3321, a first Pareto calculation unit 3322, a second region calculation unit 3323, and a second Pareto calculation unit 3324. The objective functions F and G calculated by the objective function calculator 331 are input to the first area calculator 3321 and the second area calculator 3323, respectively.

The first region calculation unit 3321 sets a variable x to which a parameter is substituted among variables included in the objective functions F and G as a bound variable, and sets output values of the objective functions F and G as free variables y ₁ and y _2. Set to. Further, the first region calculation unit 3321 sets the constraint condition that the bound variable is included in the parameter range D. Then, the first region calculation unit 3321 sets a logical expression represented by the following expression (22) expressing that there are bound variables that satisfy the objective functions F and G under the set constraint conditions.

The first area calculation unit 3321 performs a predetermined mathematical process on the set logical expression to delete the bound variable, and determines the executable area Φ that is a range of values that the set of free variables (y ₁ , y ₂ ) can take. Generate the expressed logical expression. A logical expression representing the executable region Φ generated by the first region calculation unit 3321 is input to the first Pareto calculation unit 3322. The first pareto calculation unit 3322 calculates the pareto front PF based on a logical expression representing the executable area Φ.

The second region calculation unit 3323 uses a variable x to which a parameter is substituted among variables included in the objective functions F and G as a bound variable, and outputs the output values of the objective functions F and G as free variables y ₁ and y _2. Set to. In addition, the second region calculation unit 3323 sets the constraint condition that the bound variable is included in the extended parameter range Dδ. Then, the second region calculation unit 3323 sets a logical expression shown in the following expression (23) that expresses that there are bound variables that satisfy the objective functions F and G under the set constraint conditions.

The second region calculation unit 3323 performs predetermined mathematical processing on the set logical expression to delete the bound variable, and determines the executable region Φδ that is a range of values that the free variable pair (y ₁ , y ₂ ) can take. Generate the expressed logical expression. A logical expression representing the executable region Φδ generated by the second region calculation unit 3323 is input to the second Pareto calculation unit 3324. The second pareto calculation unit 3324 calculates the pareto front PFδ based on a logical expression representing the executable region Φδ.

The display control unit 333 causes the display device 140 to display the executable areas Φ (y ₁ , y ₂ ) and Φδ (y ₁ , y ₂ ) in a comparable format. Further, the display control unit 333 causes the display device 140 to display the Pareto fronts PF and PFδ in a comparable format. For example, if the Pareto fronts PF and PFδ are displayed on the same screen, it is possible to visually grasp the influence on the executable area Φ due to the deviation of the parameters.

  As described above, according to the information processing apparatus 330 according to the fourth embodiment, the user can visually recognize the influence on the calculation result due to the deviation of the parameter. As a result, it is possible to perform more robust design and evaluation in consideration of the effect of parameter deviation.

  FIG. 22 is a diagram illustrating an example of mathematical expression processing according to the fourth embodiment. As shown in FIG. 22, in the fourth embodiment, mathematical formulas for the logical expressions related to the objective functions F and G and the parameter range D and the logical expressions related to the objective functions F and G and the extended parameter range Dδ are shown. Processing is executed. Then, the executable areas Φ and Φδ obtained as a result of the mathematical expression processing for each logical expression are displayed in a comparable format. Further, the Pareto fronts PF and PFδ calculated from the executable regions Φ and Φδ are displayed in a comparable format.

Next, the flow of processing by the information processing apparatus 330 will be described.
FIG. 23 is a diagram illustrating a flow of processing performed by the information processing apparatus according to the fourth embodiment.
(S301) The objective function calculation unit 331 calculates the objective function.

(S302) The mathematical expression processing unit 332 executes mathematical expression processing.
(S303) The display control unit 333 displays the calculation result.
Hereinafter, each process shown in FIG. 23 will be further described. However, among the processes executed by the information processing apparatus 330, the objective function calculation process is substantially the same as the objective function calculation process executed by the information processing apparatus 130 according to the second embodiment. Therefore, the flow of mathematical expression processing by the information processing apparatus 330 will be described in detail here.

FIG. 24 is a diagram illustrating a flow of mathematical expression processing according to the fourth embodiment. The mathematical expression processing shown in FIG. 24 is mainly executed by the mathematical expression processing unit 332.
(S311) The mathematical expression processing unit 332 acquires the parameter range D and the extended parameter range Dδ. The parameter range D and the extended parameter range Dδ may be arbitrarily determined by the user, or may be determined in advance in consideration of the operation condition to be evaluated. For example, the parameter range D and the extended parameter range Dδ may be input by the user via the input device 92, may be stored in advance in the HDD 903 or the like, or may be stored via the network 120. May be provided.

(S312) The mathematical expression processing unit 332 acquires the objective functions F and G. The objective functions F and G are input to the first region calculation unit 3321 and the second region calculation unit 3323.
(S313) The first region calculation unit 3321 sets a logical expression L based on the objective functions F and G. However, the logical expression L is expressed by the above expression (22). The second region calculation unit 3323 sets a logical expression Lδ based on the objective functions F and G. However, the logical expression Lδ is expressed by the above expression (23).

  (S314) The first area calculation unit 3321 executes mathematical expression processing on the logical expression L, and calculates a logical expression representing the executable area Φ. The first pareto calculator 3322 calculates the pareto front PF of the executable area Φ based on the logical expression calculated by the first area calculator 3321.

  (S315) The second area calculation unit 3323 performs mathematical expression processing on the logical expression Lδ to calculate a logical expression representing the executable area Φδ. The second pareto calculator 3324 calculates the pareto front PFδ of the executable region Φδ based on the logical expression calculated by the second region calculator 3323. Note that the process of S315 may be replaced with the process of S314.

  (S316) The mathematical expression processing unit 332 outputs information on the executable areas Φ and Φδ and information on the Pareto fronts PF and PFδ. For example, information on the executable regions Φ and Φδ and information on the Pareto fronts PF and PFδ are input to the display control unit 333. When the process of S316 is completed, the execution of the mathematical expression process is completed.

  FIG. 25 is a diagram showing a calculation result display method according to the fourth embodiment. As shown in FIG. 25, the display control unit 333 that has obtained the information on the executable regions Φ and Φδ and the information on the Pareto fronts PF and PFδ displays the executable regions Φ and Φδ on the same screen. In addition, the display control unit 333 displays the Pareto front PF and PFδ on the same screen. In the example of FIG. 25, a display method is adopted in which the display of the common area where the executable areas Φ and Φδ overlap is omitted and the difference between the executable areas Φ and Φδ is displayed. According to this display method, it is possible to easily visually recognize the influence on the executable area Φ due to the deviation of the parameter.

  As described above, when the technique according to the fourth embodiment is applied, it becomes possible for the user to visually recognize the influence on the calculation result due to the deviation of the parameter. As a result, it is possible to perform robust design and evaluation in consideration of the effect of parameter deviation when performing design and evaluation using the executable region and Pareto front calculation results.

It is also possible to determine a simplification method with little influence on the calculation result while confirming the influence due to the deviation of the parameter. For example, by checking the area sandwiched between the two Pareto fronts PF and PFδ while changing the values of the deviations δ ₁ and δ ₂ prepared in advance, it is possible to estimate the influence of the parameter deviation. Accordingly, the range of allowable deviations δ ₁ and δ ₂ can be quantitatively evaluated.

10, 130, 230, 330 Information processing device 11, 132, 232 Storage unit 12 Calculation unit 13a, 13b First function 14a, 14b Second function 15a, 15b First range information 16a, 16b Second range information DESCRIPTION OF SYMBOLS 100 Evaluation support system 110 Simulator 120 Network 131,231,331 Objective function calculation part 133,233 Simplification part 134,234,332 Formula processing part 1341,2341,3321 1st area | region calculation part 1342,2342,3322 1st Pareto calculation Part 1343, 2343, 3323 second area calculation part 1344, 2344, 3324 second Pareto calculation part 2345 third area calculation part 2346 third Pareto calculation part 2347 fourth area calculation part 2348 fourth Pareto calculation part 135, 235, 333 Display control unit 14 Display device

Claims (8)

An evaluation support method executed by a computer,
By approximating one or more of the plurality of first functions from a plurality of first functions corresponding to a plurality of evaluation indices and each indicating a relationship between a parameter and one of the plurality of evaluation indices. Calculating a plurality of second functions corresponding to the plurality of evaluation indices;
Using the plurality of first functions, first range information indicating a range in which a combination of values of the plurality of evaluation indexes changes according to a change in the parameters, and the plurality of second functions Using a function, generate second range information indicating a range in which a combination of values of the plurality of evaluation indices changes according to a change in the parameter,
Displaying the first range information and the second range information in a comparable format;
Evaluation support method. The plurality of first functions and the plurality of second functions are respectively polynomials;
When calculating one second function by approximating one first function, the one second function to be calculated is a polynomial having a lower order than the first function.
The evaluation support method according to claim 1. The first range information is calculated by mathematically processing a first logical expression indicating the plurality of first functions and a range in which the parameter changes,
The second range information is calculated by mathematically processing a second logical expression indicating the plurality of second functions and the range in which the parameter changes.
The evaluation support method according to claim 1 or 2. The comparable format is a display format in which at least one of the region and boundary indicated by the first range information and at least one of the region and boundary indicated by the second range information are displayed in an overlapping manner.
The evaluation support method according to any one of claims 1 to 3. The first and second range information is calculated by setting a range in which the parameter changes as a first parameter range,
Further, a range in which the parameter changes is set to a second parameter range wider than the first parameter range, and third range information is generated using the plurality of first functions, To generate the fourth range information using the second function of
Displaying at least two of the first to fourth range information in a comparable format;
The evaluation support method according to any one of claims 1 to 4. An evaluation support method executed by a computer,
The values of the plurality of evaluation indices when the parameter changes in the first parameter range from a plurality of functions corresponding to the plurality of evaluation indices, each indicating a relationship between the parameter and one of the plurality of evaluation indices. Generating a first range information indicating a range in which a combination of the plurality of combinations is changed, and evaluating the plurality of evaluations when the parameter changes in a second parameter range wider than the first parameter range from the plurality of functions. Generating second range information indicating a range in which the combination of index values changes,
Displaying the first range information and the second range information in a comparable format;
Evaluation support method. A storage unit that stores information on a plurality of first functions corresponding to a plurality of evaluation indexes, each indicating a relationship between a parameter and one of the plurality of evaluation indexes;
A plurality of second functions corresponding to the plurality of evaluation indices are calculated by approximating one or more of the plurality of first functions, and a change in the parameter is performed using the plurality of first functions. And generating a first range information indicating a range in which a combination of values of the plurality of evaluation indices changes, and using the plurality of second functions, the plurality of evaluation indices according to a change in the parameter Generating a second range information indicating a range in which a combination of values changes, and displaying the first range information and the second range information in a comparable format;
An information processing apparatus. On the computer,
By approximating one or more of the plurality of first functions from a plurality of first functions corresponding to a plurality of evaluation indices and each indicating a relationship between a parameter and one of the plurality of evaluation indices. Calculating a plurality of second functions corresponding to the plurality of evaluation indices;
Using the plurality of first functions, first range information indicating a range in which a combination of values of the plurality of evaluation indexes changes according to a change in the parameters, and the plurality of second functions Using a function, generate second range information indicating a range in which a combination of values of the plurality of evaluation indices changes according to a change in the parameter,
Displaying the first range information and the second range information in a comparable format;
A program that executes processing.

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