Pareto solution search device and Pareto solution search method

Abstract

An evaluation value acquisition unit (1) that acquires the evaluation values in the envelope analysis for M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is obtained by a genetic algorithm using envelope analysis, and a distance calculation unit (2) that calculates the relative distances between the M Pareto solution candidates are provided to configure a Pareto solution search device. Further, the Pareto solution search device selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distances calculated by the distance calculation unit (2) and the evaluation values acquired by the evaluation value acquisition unit (1). The Pareto solution search device further includes a Pareto solution candidate creation unit (4) that newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates by using any one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit (3).

Description

Technical Field

[0001] The present disclosure relates to a Pareto solution search device and a Pareto solution search method.

Background Art

[0002] There is a Pareto solution search device that executes a genetic algorithm for obtaining solutions to multi-objective problems, and repeatedly updates M (where M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to the multi-objective problem. A Pareto solution candidate is a candidate for a solution close to an ideal solution in a multi-objective problem. As such a Pareto solution search device, for example, Patent Document 1 discloses a device that executes a multi-objective optimization method including a selection step and a modification step. The selection step acquires evaluation values of M Pareto solution candidates in a plurality of objective functions from a simulator that calculates the evaluation values of the M Pareto solution candidates. Then, the selection step executes a selection process of selecting G (where G is an integer of 1 or more and less than M) Pareto solution candidates having relatively high evaluation values from among the M Pareto solution candidates. The modification step executes a creation process of newly creating (M - G) Pareto solution candidates different from the G Pareto solution candidates by using any one or more of the G Pareto solution candidates selected in the selection step. The modification step gives the G Pareto solution candidates selected in the selection step and the newly created (M - G) Pareto solution candidates to the simulator. The simulator calculates the evaluation values of the respective Pareto solution candidates given from the modification step. The selection process in the selection step and the creation process in the modification step are repeatedly performed a plurality of times.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the multi-objective optimization method executed by the apparatus disclosed in Patent Document 1, the selection process in the selection step and the creation process in the change step are repeatedly performed a plurality of times, so that the G Pareto solution candidates finally selected by the selection step are limited to Pareto solution candidates with relatively high evaluation values. As a result, there has been a problem that the diversity of the G Pareto solution candidates finally selected may be lacking.

[0005] The present disclosure has been made to solve the above-described problems, and an object thereof is to obtain a Pareto solution search apparatus that can select more diverse Pareto solution candidates than the apparatus disclosed in Patent Document 1.

Means for Solving the Problems

[0006] The Pareto solution search apparatus according to the present disclosure includes an evaluation value acquisition unit that acquires the evaluation values in the envelope analysis method of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem in which a solution is obtained by a genetic algorithm using the envelope analysis method, from a simulator that calculates the evaluation values in the envelope analysis method of each Pareto solution candidate, and a distance calculation unit that calculates the relative distance between the M Pareto solution candidates. Further, the Pareto solution search apparatus includes a Pareto solution candidate selection unit that selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit and the evaluation value acquired by the evaluation value acquisition unit, and a Pareto solution candidate creation unit that newly creates (M−G) Pareto solution candidates different from the G Pareto solution candidates using any one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit. , the Pareto solution candidate selection unit includes a first selection processing unit that selects N (N is an integer greater than or equal to 1 and less than or equal to M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit, and based on the respective evaluation values of the N Pareto solution candidates selected by the first selection processing unit, a second selection processing unit that selects G (G is an integer greater than or equal to 1 and less than N) Pareto solution candidates from among the N Pareto solution candidates are provided.

Effects of the Invention

[0007] According to the present disclosure, it is possible to select more diverse Pareto solution candidates than the apparatus disclosed in Patent Document 1.

Brief Description of the Drawings

[0008]

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Mode for Carrying Out the Invention

[0009] Hereinafter, in order to explain the present disclosure in more detail, modes for carrying out the present disclosure will be described with reference to the accompanying drawings.

[0010] Embodiment 1. FIG. 1 is a configuration diagram showing a Pareto solution search device according to Embodiment 1. FIG. 2 is a hardware configuration diagram showing the hardware of the Pareto solution search device according to Embodiment 1. The Pareto solution search device shown in FIG. 1 is a device for executing a genetic algorithm using data envelopment analysis (DEA), and includes an evaluation value acquisition unit 1, a distance calculation unit 2, a Pareto solution candidate selection unit 3, and a Pareto solution candidate creation unit 4. As methods included in DEA, several methods are known. The Pareto solution search device shown in FIG. 1 is for executing, for example, a genetic algorithm using super CCR or a genetic algorithm using CCR among the methods included in DEA. However, the genetic algorithm used by the Pareto solution search device shown in FIG. 1 is not limited to super CCR or CCR.

[0011] The evaluation value acquisition unit 1 is realized, for example, by the evaluation value acquisition circuit 11 shown in FIG. 2. The evaluation value acquisition unit 1 acquires the evaluation values of each Pareto solution candidate in DEA from a simulator that calculates the evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem for which a solution is obtained by a genetic algorithm using DEA. The evaluation value acquisition unit 1 outputs each Pareto solution candidate to the distance calculation unit 2 and the Pareto solution candidate selection unit 3 respectively, and outputs the evaluation value of each Pareto solution candidate in DEA to the Pareto solution candidate selection unit 3.

[0012] The distance calculation unit 2 is realized by, for example, the distance calculation circuit 12 shown in FIG. 2. The distance calculation unit 2 acquires M Pareto solution candidates from the evaluation value acquisition unit 1. The distance calculation unit 2 calculates the relative distances between the M Pareto solution candidates. The distance calculation unit 2 outputs the relative distances between the M Pareto solution candidates to the Pareto solution candidate selection unit 3.

[0013] The Pareto solution candidate selection unit 3 is realized by, for example, the Pareto solution candidate selection circuit 13 shown in FIG. 2. The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3b. The Pareto solution candidate selection unit 3 acquires each Pareto solution candidate and the evaluation value of each Pareto solution candidate in DEA from the evaluation value acquisition unit 1, and acquires the relative distances between the M Pareto solution candidates from the distance calculation unit 2. Based on the relative distances between the M Pareto solution candidates and the evaluation values of each Pareto solution candidate in DEA, the Pareto solution candidate selection unit 3 selects G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates from the M Pareto solution candidates. The Pareto solution candidate selection unit 3 outputs the selected G Pareto solution candidates to the Pareto solution candidate creation unit 4.

[0014] Based on the relative distances calculated by the distance calculation unit 2, the first selection processing unit 3a selects N (N is an integer greater than or equal to 1 and less than or equal to M) Pareto solution candidates from the M Pareto solution candidates acquired by the evaluation value acquisition unit 1. The second selection processing unit 3b selects the evaluation values of the N Pareto solution candidates selected by the first selection processing unit 3a from the evaluation values of the M Pareto solution candidates output from the evaluation value acquisition unit 1. The second selection processing unit 3b selects G (where G is an integer greater than or equal to 1 and less than N) Pareto solution candidates from among the N Pareto solution candidates based on the respective evaluation values of the N Pareto solution candidates. M ≧ N > G ≧ 1.

[0015] The Pareto solution candidate creation unit 4 is realized, for example, by the Pareto solution candidate creation circuit 14 shown in FIG. 2. The Pareto solution candidate creation unit 4 includes a crossover processing unit 4a and a mutation processing unit 4b. The Pareto solution candidate creation unit 4 acquires G Pareto solution candidates from the Pareto solution candidate selection unit 3. The Pareto solution candidate creation unit 4 newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates by using any one or more of the G Pareto solution candidates. The Pareto solution candidate creation unit 4 outputs the G Pareto solution candidates selected by the Pareto solution candidate selection unit 3 and the (M - G) Pareto solution candidates newly created to the simulator.

[0016] The crossover processing unit 4a acquires any two Pareto solution candidates from among the G Pareto solution candidates. The crossover processing unit 4a performs a crossover process of swapping some values in one of the two Pareto solution candidates with some values in the other Pareto solution candidate. The mutation processing unit 4b acquires any one of the G Pareto solution candidates. The mutation processing unit 4b performs a mutation process of changing some values in the acquired Pareto solution candidate.

[0017] The simulator acquires the G Pareto solution candidates selected by the Pareto solution candidate selection unit 3 and the (M - G) Pareto solution candidates created by the Pareto solution candidate creation unit 4, and calculates the evaluation values of each Pareto solution candidate in terms of DEA. The simulator outputs the evaluation values of each Pareto solution candidate in terms of DEA to the evaluation value acquisition unit 1. As a result, the evaluation value acquisition process by the evaluation value acquisition unit 1, the distance calculation process by the distance calculation unit 2, the Pareto solution candidate selection process by the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation process by the Pareto solution candidate creation unit 4 are repeated.

[0018] In FIG. 1, it is assumed that each of the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4, which are components of the Pareto solution search device, is realized by dedicated hardware as shown in FIG. 2. That is, it is assumed that the Pareto solution search device is realized by an evaluation value acquisition circuit 11, a distance calculation circuit 12, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate creation circuit 14. Each of the evaluation value acquisition circuit 11, the distance calculation circuit 12, the Pareto solution candidate selection circuit 13, and the Pareto solution candidate creation circuit 14 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field-Programmable Gate Array), or a combination thereof.

[0019] The components of the Pareto solution search device are not limited to those realized by dedicated hardware, and the Pareto solution search device may be realized by software, firmware, or a combination of software and firmware. Software or firmware is stored in the memory of a computer as a program. A computer means the hardware that executes the program, and for example, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a DSP (Digital Signal Processor) corresponds to it.

[0020] FIG. 3 is a hardware configuration diagram of a computer when the Pareto solution search device is implemented by software, firmware, or the like. When the Pareto solution search device is implemented by software, firmware, or the like, a program for causing a computer to execute the respective processing procedures in the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 is stored in the memory 21. Then, the processor 22 of the computer executes the program stored in the memory 21.

[0021] Further, FIG. 2 shows an example in which each component of the Pareto solution search device is implemented by dedicated hardware, and FIG. 3 shows an example in which the Pareto solution search device is implemented by software, firmware, or the like. However, this is only an example, and some components of the Pareto solution search device may be implemented by dedicated hardware and the remaining components may be implemented by software, firmware, or the like.

[0022] Next, the operation of the Pareto solution search device shown in FIG. 1 will be described. FIG. 4 is a flowchart showing a Pareto solution search method which is a processing procedure of the Pareto solution search device. When the Pareto solution search device is applied to a pumping plan of a sewage treatment plant as shown in FIG. 5, for example, the following three goals (1) to (3) are set as multiple goals. FIG. 5 is an explanatory diagram showing an example of a pumping system in a sewage treatment plant. However, the three goals (1) to (3) are merely examples, and other goals may be set. In the pumping system shown in FIG. 5, after rainwater or the like flows into the inflow channel, it flows into the pump well, and the pump pumps the water accumulated in the pump well into the water treatment tank. Then, the water accumulated in the water treatment tank is discharged into a river or the sea.

[0023] ·Goal (1) Avoidance of the flooding risk is set as a goal so that the sewage treatment plant is not flooded by rainwater or the like. ·Objective (2) Cost reduction of power consumption is set as an objective so that the power consumption of the sewage treatment plant is reduced. ·Objective (3) Water quality regulations for rivers, etc. are set as an objective when rainwater, etc. is discharged from the sewage treatment plant into rivers or the sea.

[0024] When three objectives (1) to (3) are set as multi-objectives, as shown in the following formulas (1) to (3) for example, an objective function f1 regarding avoidance of flooding risk, an objective function f2 regarding cost reduction of power consumption, and an objective function f3 regarding water quality regulations for rivers, etc. are set as the objective functions of the genetic algorithm. The setting of the objective functions f1, f2, and f3 may be performed by, for example, the evaluation value acquisition unit 1 or the simulator.

[0025] TIFF0007714155000001.tif75166

[0026] In formulas (1) to (4), mean(x) is a mathematical symbol representing the average value of x. max(x, y) is a mathematical symbol representing the selection of the larger one between x and y. y1(t) indicates the water level (m) of the inflow channel at time t, and y STD indicates the water level (m) in the standard state of the inflow channel, and WLW STD indicates the water level width (m) in the standard state of the inflow channel. y2(t) indicates the power consumption of the sewage treatment plant at time t. COD(t) indicates the chemical oxygen demand (g / L) of rivers, etc. at time t, TN(t) indicates the total nitrogen amount (g / L) of rivers, etc. at time t, and TP(t) indicates the total phosphorus amount (g / L) of rivers, etc. at time t. COD Rv indicates the regulated value (g / L) of the chemical oxygen demand, and TN Rv indicates the regulated value (g / L) of the total nitrogen amount, and TP Rv indicates the regulated value (g / L) of the total phosphorus amount. COD Gv(t) represents the total value (Kg) of the chemical oxygen demand in a river, etc. at time t, and TN Gv (t) represents the total value (Kg) of the total nitrogen in a river, etc. at time t, and TP Gv (t) represents the total value (Kg) of the total phosphorus in a river, etc. at time t. COD TotalGv (t) represents the regulatory value (Kg) of the total value of the chemical oxygen demand, and TN TotalGv represents the regulatory value (Kg) of the total value of the total nitrogen, and TP TotalGv represents the regulatory value (Kg) of the total value of the total phosphorus.

[0027] The simulator calculates the evaluation values Ev M in the DEA for M (M is an integer of 2 or more) Pareto solution candidates PS1 to PS m (m = 1, ···, M). If the multiple objective functions are f1, f2, and f3, the respective evaluation values Ev M in the M Pareto solution candidates PS1 to PS m in the objective functions f1, f2, and f3 are calculated. The process by which the simulator calculates the evaluation value Ev m of the Pareto solution candidate PS m (m = 1, ···, M) is a known technique, so detailed description is omitted. Incidentally, if the multiple objective functions are, for example, two, f1 and f2, the evaluation value Ev m of the Pareto solution candidate PS m is obtained, for example, by the following evaluation formula. However, the following evaluation formula is only an example, and the evaluation value Ev m of the Pareto solution candidate PS m may be obtained by other evaluation formulas. [Evaluation formula] Ev m =(Wa × f1)+(Wb × f2) Wa is the weight coefficient for the objective function f1, and Wb is the weight coefficient for the objective function f2. For the Pareto solution candidate PS m where the objective function f1 is more emphasized than the objective function f2, the evaluation value Ev mWhen it is calculated, the weight coefficient Wa is set to a value larger than the weight coefficient Wb. On the other hand, for the Pareto solution candidate PS where the objective function f2 is more emphasized than the objective function f1 m evaluation value Ev m When it is calculated, the weight coefficient Wa is set to a value smaller than the weight coefficient Wb.

[0028] The evaluation value acquisition unit 1 obtains from the simulator the Pareto solution candidate PS m (m = 1, ···, M) and the evaluation value Ev m of the Pareto solution candidate PS m (step ST1 in FIG. 4). However, when the evaluation value acquisition unit 1 has set the Pareto solution candidate PS m , it transmits the Pareto solution candidate PS m to the simulator. In this case, the evaluation value acquisition unit 1 does not obtain the Pareto solution candidate PS m from the simulator and only obtains the evaluation value Ev m of the Pareto solution candidate PS m . FIG. 6 is an explanatory diagram showing an example of M Pareto solution candidates PS m (m = 1, ···, M) in a multi-objective problem. In FIG. 6, for the sake of simplicity of explanation, an example where there are two objective functions, f1 and f2, and M = 10 is shown. In FIG. 6, the black circles indicate the Pareto solution candidates PS m . The horizontal axis in FIG. 6 indicates the value f1(x, y) of the objective function f1 that changes depending on the design variables x and y when the design variables of the objective function f1 are, for example, x and y. For example, -1 ≤ x ≤ 1 and -1 ≤ y ≤ 1. The vertical axis in FIG. 6 indicates the value f2(x, y) of the objective function f2 that changes depending on the design variables x and y when the design variables of the objective function f2 are, for example, x and y. The evaluation value acquisition unit 1 outputs the Pareto solution candidate PS m to each of the distance calculation unit 2 and the Pareto solution candidate selection unit 3, and outputs the evaluation value Ev m of the Pareto solution candidate PS m to the Pareto solution candidate selection unit 3.

[0029] The distance calculation unit 2 acquires the Pareto solution candidates PS m (m = 1, ···, M) from the evaluation value acquisition unit 1. The distance calculation unit 2 calculates the relative distances L M between the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) (step ST2 in FIG. 4). The distance calculation unit 2 outputs the relative distance L m to the Pareto solution candidate selection unit 3.

[0030] Hereinafter, the calculation process of the relative distance L m by the distance calculation unit 2 will be specifically described. Among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS1, the distance calculation unit 2 calculates the distance L m between the Pareto solution candidate PS1 and the Pareto solution candidates PS 1,m (m = 2, ···, M). The distance L m between the Pareto solution candidate PS1 and the Pareto solution candidate PS 1,m is, for example, the Euclidean distance between the Pareto solution candidate PS1 and the Pareto solution candidate PS m . Among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS2, the distance calculation unit 2 calculates the distance L m between the Pareto solution candidate PS2 and the Pareto solution candidates PS 2,m (m = 1, 3, ···, M). The distance L m between the Pareto solution candidate PS2 and the Pareto solution candidate PS 2,m is, for example, the Euclidean distance between the Pareto solution candidate PS2 and the Pareto solution candidate PS m . Among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS M , the distance calculation unit 2 calculates the distance L M between the Pareto solution candidate PS m and the Pareto solution candidates PS M,m (m = 1, ···, M - 1).Calculate the Pareto solution candidate PS M and the Pareto solution candidate PS m and the distance L M,m For example, as the distance between the Pareto solution candidate PS M and the Pareto solution candidate PS m the Euclidean distance is calculated.

[0031] The first selection processing unit 3a of the Pareto solution candidate selection unit 3 acquires the Pareto solution candidates PS m (m = 1, ···, M) from the evaluation value acquisition unit 1, and acquires the relative distances PS M between the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) from the distance calculation unit 2. For each Pareto solution candidate PS m (m = 1, ···, M), the first selection processing unit 3a calculates the congestion distance ΣL m as the sum of (M - 1) distances L m . Specifically, among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS1, the first selection processing unit 3a calculates the congestion distance ΣL1 as the sum of (M - 1) distances L 1,m as shown in the following formula (5). ΣL1 = L 1,2 + L 1,3 + ··· + L 1,M (5) Among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS2, the first selection processing unit 3a calculates the congestion distance ΣL2 as the sum of (M - 1) distances L 2,m as shown in the following formula (6). ΣL2 = L 2,1 + L 2,3 + ··· + L 2,M (6) Among the M Pareto solution candidates PS1 to PS M , for example, focusing on the Pareto solution candidate PS M , the first selection processing unit 3a calculates the congestion distance ΣL MAs (M - 1) distances L M,m are summed up. ΣL M = L M,1 + L M,2 + ··· + L M,M-1 (7)

[0032] The first selection processing unit 3a compares M congestion distances ΣL1 to ΣL M with each other. The first selection processing unit 3a, based on the comparison results of the congestion distances ΣL1 to ΣL M prioritizes and selects N (N is an integer from 1 to M) Pareto solution candidates PS1 to PS M from among those with a relatively large congestion distance ΣL (step ST3 in FIG. 4). The first selection processing unit 3a outputs the selected N Pareto solution candidates PS’1 to PS’ N to the second selection processing unit 3b. By the first selection processing unit 3a selecting N Pareto solution candidates PS’1 to PS’ N based on the congestion distance ΣL, the diversity of the Pareto solution candidates is improved.

[0033] The second selection processing unit 3b obtains the evaluation values Ev m of the Pareto solution candidates PS m (m = 1, ···, M) from the evaluation value acquisition unit 1, and obtains N Pareto solution candidates PS’1 to PS’ N from the first selection processing unit 3a. The second selection processing unit 3b selects, from among the M evaluation values Ev1 to Ev M the evaluation values Ev’1 to Ev’ N corresponding to the N Pareto solution candidates PS’1 to PS’ N . The second selection processing unit 3b, based on the respective evaluation values Ev’ N in the N Pareto solution candidates PS’1 to PS’ n (n = 1, ···, N), selects G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ GSelect it (step ST4 in FIG. 4). Specifically, the second selection processing unit 3b selects the top G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ n with relatively high evaluation values Ev’. G The second selection processing unit 3b outputs the selected G Pareto solution candidates PS”1 to PS” G to the Pareto solution candidate creation unit 4.

[0034] The Pareto solution candidate creation unit 4 acquires the G Pareto solution candidates PS”1 to PS” G from the Pareto solution candidate selection unit 3. The Pareto solution candidate creation unit 4 newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates using one or more of the G Pareto solution candidates. G The Pareto solution candidate creation unit 4 outputs the G Pareto solution candidates and the (M - G) Pareto solution candidates to the simulator.

[0035] Hereinafter, the creation process of the (M - G) Pareto solution candidates by the Pareto solution candidate creation unit 4 will be specifically described. The crossover processing unit 4a acquires any two Pareto solution candidates from among the G Pareto solution candidates PS”1 to PS” G For the sake of convenience of explanation, assume that any two Pareto solution candidates are PS”1 and PS”2. As shown in FIG. 7, the crossover processing unit 4a performs a crossover process of swapping some values in the Pareto solution candidate PS”1 and some values in the Pareto solution candidate PS”2 according to the crossover probability (step ST5 in FIG. 4). Since the crossover process itself is a known technique, a detailed description thereof will be omitted. FIG. 7 is an explanatory diagram showing an example of the crossover process by the crossover processing unit 4a. By the crossover processing unit 4a performing the crossover process, the diversity of the Pareto solution candidates is improved. ​​​In the example of FIG. 7, the "111" from the fourth bit to the sixth bit in the Pareto solution candidate PS”1 and the "000" from the fourth bit to the sixth bit in the Pareto solution candidate PS”2 are swapped.

[0036] Here, the crossover processing unit 4a performs a crossover process of swapping some values in the Pareto solution candidate PS”1 and some values in the Pareto solution candidate PS”2. However, this is only an example, and in addition to the crossover process of swapping some values in the Pareto solution candidate PS”1 and some values in the Pareto solution candidate PS”2, the crossover processing unit 4a may perform, for example, a crossover process of swapping some values in the Pareto solution candidate PS”3 and some values in the Pareto solution candidate PS”4. Hereinafter, the Pareto solution candidate after the crossover process by the crossover processing unit 4a is referred to as PS Cr and so on.

[0037] The mutation processing unit 4b obtains any one of the G Pareto solution candidates PS”1 to PS” G from among them. Here, for the sake of convenience of explanation, it is assumed that any one of the Pareto solution candidates is PS”3. As shown in FIG. 8, the mutation processing unit 4b performs a mutation process of randomly changing some values in the Pareto solution candidate PS”3 according to the mutation probability (step ST6 in FIG. 4). Since the mutation process itself is a known technique, a detailed description thereof is omitted. FIG. 8 is an explanatory diagram showing an example of the mutation process by the mutation processing unit 4b. By the mutation processing unit 4b performing the mutation process, the diversity of the Pareto solution candidates is improved. In the example of FIG. 8, the "0" in the third bit of the Pareto solution candidate PS”3 is changed to "2", and the "0" in the fifth bit of the Pareto solution candidate PS”3 is changed to "3". Hereinafter, the Pareto solution candidate after the mutation process by the mutation processing unit 4b is referred to as PS Mu and so on.

[0038] If the number of times of a series of processes in the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 has not reached H times (in the case of NO in step ST7 of FIG. 4), G Pareto solution candidates PS”1 to PS” selected by the Pareto solution candidate selection unit 3 G and the Pareto solution candidate PS after the crossover process Cr and the Pareto solution candidate PS after the mutation process Mu are given to the simulator. H is an integer of 1 or more. The simulator calculates the respective evaluation values Ev M for each of the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) in a plurality of objective functions, the respective evaluation values for the G Pareto solution candidates PS”1 to PS” G the evaluation value of the Pareto solution candidate PS after the crossover process Cr and the evaluation value of the Pareto solution candidate PS after the mutation process Mu . The simulator outputs the M Pareto solution candidates PS1 to PS M and the respective evaluation values Ev M for each of the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) to the evaluation value acquisition unit 1. Each of the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 performs the processes of steps ST1 to ST6 in FIG. 4. If the number of times of a series of processes in the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 has reached H times (in the case of YES in step ST7 of FIG. 4), as the final selection result of the Pareto solution, G Pareto solution candidates PS”1 to PS” selected by the Pareto solution candidate selection unit 3 G are displayed, for example, on a display device (not shown).

[0039] In the above-described Embodiment 1, from a simulator that calculates evaluation values in the envelope analysis method for M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is obtained by a genetic algorithm using the envelope analysis method, an evaluation value acquisition unit 1 that acquires the evaluation values in the envelope analysis method for each Pareto solution candidate, and a distance calculation unit 2 that calculates the relative distance between the M Pareto solution candidates are provided, and the Pareto solution search device is configured. Further, the Pareto solution search device, based on the relative distance calculated by the distance calculation unit 2 and the evaluation value acquired by the evaluation value acquisition unit 1, selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from among the M Pareto solution candidates, and a Pareto solution candidate creation unit 4 that newly creates (M−G) Pareto solution candidates different from the G Pareto solution candidates using any one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit 3. Therefore, the Pareto solution search device can select more diverse Pareto solution candidates than the device disclosed in Patent Document 1.

[0040] In the Pareto solution search device shown in FIG. 1, the first selection processing unit 3a calculates the sum of (M−1) distances L as the congestion distance ΣL m (m = 1, ···, M). However, this is merely an example, and the first selection processing unit 3a may calculate the average value of (M−1) distances L, for example, as the congestion distance ΣL m . Also in this case, the first selection processing unit 3a preferentially selects N Pareto solution candidates with a relatively large congestion distance ΣL from among the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) based on the comparison result of the congestion distances ΣL1 to ΣL m . M M .

[0041] In the Pareto solution search device shown in FIG. 1, the second selection processing unit 3b selects the top G Pareto solution candidates PS”1 to PS” with relatively high evaluation values Ev’ N from among the N Pareto solution candidates PS’1 to PS’ n .G is selected. However, this is just an example, and the second selection processing unit 3b may select, for example, G Pareto solution candidates PS”1 to PS” G by means of the binary tournament method. The binary tournament method randomly selects two Pareto solution candidates PS’ from among N Pareto solution candidates PS’1 to PS’ N and performs a process of selecting the Pareto solution candidate with the higher evaluation value Ev’ among the two Pareto solution candidates PS’. Then, the binary tournament method repeats the said process until G Pareto solution candidates PS”1 to PS” n are selected. G are selected.

[0042] Embodiment 2. In Embodiment 2, a Pareto solution search device including a rank specifying unit 5 that determines the superiority or inferiority of M Pareto solution candidates PS1 to PS m (m = 1, ···, M) based on the evaluation values Ev obtained by the evaluation value acquisition unit 1 and specifies the rank Rk to which each Pareto solution candidate PS M belongs among a plurality of ranks Rk based on the determination result of the superiority or inferiority will be described. m FIG. 9 is a configuration diagram showing a Pareto solution search device according to Embodiment 2. In FIG. 9, the same reference numerals as those in FIG. 1 denote the same or corresponding parts, and thus detailed description thereof is omitted.

[0043] FIG. 10 is a hardware configuration diagram showing the hardware of the Pareto solution search device according to Embodiment 2. In FIG. 10, the same reference numerals as those in FIG. 2 denote the same or corresponding parts, and thus detailed description thereof is omitted. The Pareto solution search device shown in FIG. 9 is a device for executing a genetic algorithm using DEA, and includes an evaluation value acquisition unit 1, a distance calculation unit 2, a rank specifying unit 5, a Pareto solution candidate selection unit 3, and a Pareto solution candidate creation unit 4. The rank specifying unit 5 is realized, for example, by a rank specifying circuit 15 shown in FIG. 10.

[0044] The rank specifying unit 5 is realized, for example, by a rank specifying circuit 15 shown in FIG. 10. The rank determination unit 5 receives from the evaluation value acquisition unit 1 the Pareto solution candidates PS m (m = 1, ···, M) and the evaluation values Ev m of the Pareto solution candidates PS m and acquires them. Based on the evaluation values Ev m , the rank determination unit 5 determines the superiority and inferiority of the M Pareto solution candidates PS1 to PS M . Based on the determination result of superiority and inferiority, the rank determination unit 5 specifies the rank Rk to which the Pareto solution candidates PS m (m = 1, ···, M) belong among the plurality of ranks Rk. The rank determination unit 5 outputs the rank Rk to which the Pareto solution candidates PS m (m = 1, ···, M) belong to the Pareto solution candidate selection unit 3.

[0045] The Pareto solution candidate selection unit 3 is realized, for example, by the Pareto solution candidate selection circuit 13 shown in FIG. 10. The Pareto solution candidate selection unit 3 includes a first selection processing unit 3c and a second selection processing unit 3b. Similar to the first selection processing unit 3a shown in FIG. 1, the first selection processing unit 3c receives from the evaluation value acquisition unit 1 the Pareto solution candidates PS m (m = 1, ···, M) and receives from the distance calculation unit 2 the relative distances L M between the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) and acquires them. Similar to the first selection processing unit 3a shown in FIG. 1, based on the relative distances L m (m = 1, ···, M), the first selection processing unit 3c selects N Pareto solution candidates PS'1 to PS' M from among the M Pareto solution candidates PS1 to PS N acquired by the evaluation value acquisition unit 1. However, unlike the first selection processing unit 3a shown in FIG. 1, the first selection processing unit 3c selects the Pareto solution candidates PS' from among the Pareto solution candidates PS belonging to each rank Rk so that the total number of selected Pareto solution candidates PS' is N, based on the relative distances L m (m = 1, ···, M).

[0046] In FIG. 9, it is assumed that each of the evaluation value acquisition unit 1, distance calculation unit 2, rank identification unit 5, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4, which are components of the Pareto solution search device, is realized by dedicated hardware as shown in FIG. 10. That is, it is assumed that the Pareto solution search device is realized by an evaluation value acquisition circuit 11, a distance calculation circuit 12, a rank identification circuit 15, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate creation circuit 14. Each of the evaluation value acquisition circuit 11, distance calculation circuit 12, rank identification circuit 15, Pareto solution candidate selection circuit 13, and Pareto solution candidate creation circuit 14 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, an ASIC, an FPGA, or a combination thereof.

[0047] The components of the Pareto solution search device are not limited to those realized by dedicated hardware, and the Pareto solution search device may be realized by software, firmware, or a combination of software and firmware. When the Pareto solution search device is realized by software or firmware, etc., a program for causing a computer to execute each processing procedure in the evaluation value acquisition unit 1, distance calculation unit 2, rank identification unit 5, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4 is stored in the memory 21 shown in FIG. 3. Then, the processor 22 shown in FIG. 3 executes the program stored in the memory 21.

[0048] Also, FIG. 10 shows an example in which each component of the Pareto solution search device is realized by dedicated hardware, and FIG. 3 shows an example in which the Pareto solution search device is realized by software or firmware, etc. However, this is only an example, and some components of the Pareto solution search device may be realized by dedicated hardware, and the remaining components may be realized by software or firmware, etc.

[0049] Next, the operation of the Pareto solution search device shown in FIG. 9 will be described. However, except for the rank determination unit 5 and the first selection processing unit 3c, it is the same as the Pareto solution search device shown in FIG. 1. Therefore, here, mainly the operations of the rank determination unit 5 and the first selection processing unit 3c will be described.

[0050] The rank determination unit 5 receives, from the evaluation value acquisition unit 1, the Pareto solution candidates PS m (m = 1, ···, M) and the evaluation values Ev m of the Pareto solution candidates PS m and acquires them. The rank determination unit 5 determines the superiority and inferiority of the M Pareto solution candidates PS1 to PS m based on the evaluation value Ev M . Hereinafter, the determination process of superiority and inferiority by the rank determination unit 5 will be specifically described. Here, for convenience of explanation, an example in which the rank determination unit 5 determines the superiority and inferiority between the Pareto solution candidate PS m and the Pareto solution candidate PS m+1 will be described.

[0051] The rank determination unit 5 compares the evaluation value Ev m of the Pareto solution candidate PS m with the evaluation value Ev m+1 of the Pareto solution candidate PS m+1 . If the evaluation value Ev m of the Pareto solution candidate PS m is higher than the evaluation value Ev m+1 of the Pareto solution candidate PS m+1 , the rank determination unit 5 determines that the Pareto solution candidate PS m is superior to the Pareto solution candidate PS m+1 . If the evaluation value Ev m of the Pareto solution candidate PS m is lower than the evaluation value Ev m+1 of the Pareto solution candidate PS m+1 , the rank determination unit 5 determines that the Pareto solution candidate PS m is inferior to the Pareto solution candidate PS m+1 .

[0052] Based on the determination result of superiority and inferiority, the Pareto solution candidate PS m (m = 1, ···, M) calculates the rank Rk. Hereinafter, the calculation process of the rank Rk by the rank determination unit 5 will be specifically described.

[0053] In the example of FIG. 6, focusing on the Pareto solution candidate PS1, assume that there are two Pareto solution candidates having the same evaluation value as the evaluation value Ev1 of the Pareto solution candidate PS1, namely the Pareto solution candidates PS2 and PS3. Also, assume that the evaluation values Ev4 to Ev 10 of the Pareto solution candidates PS4 to PS 10 are lower than the evaluation value Ev1 of the Pareto solution candidate PS1. In this case, each of the Pareto solution candidates PS1, PS2, and PS3 is classified into the highest rank Rk1 as shown in FIG. 11. FIG. 11 is an explanatory diagram showing the rank Rk of the Pareto solution candidate PS m (m = 1, ···, M). Focusing on the Pareto solution candidate PS4, assume that there are four Pareto solution candidates having the same evaluation value as the evaluation value Ev4 of the Pareto solution candidate PS4, namely the Pareto solution candidates PS5 to PS8. Also, assume that the evaluation values Ev9 to Ev 10 of the Pareto solution candidates PS9 to PS 10 are lower than the evaluation value Ev4 of the Pareto solution candidate PS4. In this case, each of the Pareto solution candidates PS4 to PS8 is classified into the second highest rank Rk2.

[0054] Focusing on the Pareto solution candidate PS9, assume that there is one Pareto solution candidate having the same evaluation value as the evaluation value Ev9 of the Pareto solution candidate PS9, namely the Pareto solution candidate PS 10 . Also, assume that the evaluation values Ev9 to Ev 10 of the Pareto solution candidates PS9 to PS 10 are lower than the evaluation value Ev4 of the Pareto solution candidate PS4. In this case, the Pareto solution candidates PS9 to PS 10Each of them is classified into rank Rk3 which is the third highest rank. Here, it is assumed that the evaluation value Ev1 of the Pareto solution candidate PS1 is the same as the evaluation value Ev2 of the Pareto solution candidate PS2. The same evaluation value does not necessarily mean that the evaluation value Ev1 and the evaluation value Ev2 are exactly the same. For example, if the difference between the evaluation value Ev1 and the evaluation value Ev2 is less than or equal to a certain threshold, they may be regarded as the same evaluation value. The rank determination unit 5 outputs the rank Rk to which the Pareto solution candidate PS m (m = 1, ···, M) belongs to the Pareto solution candidate selection unit 3.

[0055] The first selection processing unit 3c of the Pareto solution candidate selection unit 3 acquires the Pareto solution candidate PS m (m = 1, ···, M) from the evaluation value acquisition unit 1, and acquires the relative distance L M between the M Pareto solution candidates PS1 to PS m (m = 1, ···, M) from the distance calculation unit 2. Also, the first selection processing unit 3c acquires the rank Rk of the Pareto solution candidate PS m from the rank determination unit 5. If the number of Pareto solution candidates selected by the second selection processing unit 3b is G, the first selection processing unit 3c sets the number N of Pareto solution candidates to be selected from among the M Pareto solution candidates PS1 to PS M to be greater than G and less than or equal to M.

[0056] The first selection processing unit 3c preferentially selects the Pareto solution candidates PS M classified into a high rank from among the M Pareto solution candidates PS1 to PS m , and when selecting one or more Pareto solution candidates PS m classified into a certain rank, all the Pareto solution candidates PS m classified into that certain rank are selected. Therefore, in the example of FIG. 11, if G is any one of 1 to 3, N is set to 3; if G is any one of 4 to 8, N is set to 8; and if G is any one of 9 to 10, N is set to 10.

[0057] The first selection processing unit 3c selects N Pareto solution candidates PS’1 to PS’ M from among the M Pareto solution candidates PS1 to PS N . In the example of FIG. 11, if N = 3, then the first selection processing unit 3c selects the three Pareto solution candidates PS1 to PS3 classified into rank Rk1. If N = 8, then the first selection processing unit 3c selects the three Pareto solution candidates PS1 to PS3 classified into rank Rk1 and the five Pareto solution candidates PS4 to PS8 classified into rank Rk2. For example, if N = 10, then the first selection processing unit 3c selects the three Pareto solution candidates PS1 to PS3 classified into rank Rk1, the five Pareto solution candidates PS4 to PS8 classified into rank Rk2, and the two Pareto solution candidates PS9 to PS 10 .

[0058] The second selection processing unit 3b selects G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ n selected by the first selection processing unit 3c, based on their respective evaluation values Ev’ N (n = 1, ···, N). G . In the example of FIG. 11, if G = 1, then the second selection processing unit 3b selects any one of the three Pareto solution candidates PS1 to PS3 classified into rank Rk1. If there are slight differences in the evaluation values Ev1 to Ev3 of the three Pareto solution candidates PS1 to PS3, then the one Pareto solution candidate with the highest evaluation value is selected. If the evaluation values Ev1 to Ev3 are all the same, then any one Pareto solution candidate is selected. If G = 2, any two of the three Pareto solution candidates PS1 to PS3 classified into rank Rk1 are selected by the second selection processing unit 3b. Also in this case, if there are slight differences in the evaluation values Ev1 to Ev3, two Pareto solution candidates with relatively higher evaluation values are selected. If all of the values Ev1 to Ev3 are the same, any two Pareto solution candidates are selected. If G = 3, all of the three Pareto solution candidates PS1 to PS3 classified into rank Rk1 are selected by the second selection processing unit 3b.

[0059] If G is any one of 4 to 8, one or more and five or fewer Pareto solution candidates are selected by the second selection processing unit 3b from among the three Pareto solution candidates PS1 to PS3 classified into rank Rk1 and the eight Pareto solution candidates PS4 to PS8 classified into rank Rk2. Also in this case, for example, one or more and five or fewer Pareto solution candidates with relatively higher evaluation values are selected from among the five Pareto solution candidates PS4 to PS8. If G is any one of 9 to 10, one or more and two or fewer Pareto solution candidates are selected by the second selection processing unit 3b from among the three Pareto solution candidates PS1 to PS3 classified into rank Rk1, the five Pareto solution candidates PS4 to PS8 classified into rank Rk2, and the two Pareto solution candidates PS9 to PS 10 Also in this case, for example, one or more and two or fewer Pareto solution candidates with relatively higher evaluation values are selected from among the two Pareto solution candidates PS9 to PS 10 The second selection processing unit 3b outputs the selected G Pareto solution candidates PS”1 to PS” to the Pareto solution candidate creation unit 4. G

[0060] In the Pareto solution search device shown in FIG. 9, when the first selection processing unit 3c selects one or more Pareto solution candidates PS m classified into a certain rank, all of the Pareto solution candidates PS mis selected. Specifically, in the example of FIG. 11, if G is any one of 1 to 3, the first selection processing unit 3c sets N = 3, and if G is any one of 4 to 8, the first selection processing unit 3c sets N = 8, and if G is any one of 9 to 10, the first selection processing unit 3c sets N = 10. However, N only needs to be less than or equal to M and greater than G, and is not limited to the above settings. For example, when N = 5 is set, the first selection processing unit 3c selects three Pareto solution candidates PS1 to PS3 classified into rank Rk1 and two Pareto solution candidates from among the five Pareto solution candidates PS4 to PS8 classified into rank Rk2. In this case, from among the five Pareto solution candidates PS4 to PS8, the top two Pareto solution candidates with a large relative distance L m (m = 4, ···, 8) are selected. For example, when N = 9 is set, the first selection processing unit 3c selects three Pareto solution candidates PS1 to PS3 classified into rank Rk1, five Pareto solution candidates PS4 to PS8 classified into rank Rk2, and two Pareto solution candidates PS9 to PS 10 among them. In this case, from among the two Pareto solution candidates PS9 to PS 10 among them, the Pareto solution candidate with a large relative distance L m (m = 9, 10) is selected.

[0061] In the above-described second embodiment, based on the evaluation values acquired by the evaluation value acquisition unit 1, the superiority and inferiority of M Pareto solution candidates are determined, and based on the determination result of the superiority and inferiority, a rank identification unit 5 that identifies the rank to which each Pareto solution candidate belongs among a plurality of ranks is provided. Thus, the Pareto solution search device is configured. Further, the first selection processing unit 3c of the Pareto solution search device selects Pareto solution candidates from among the Pareto solution candidates belonging to each rank based on the relative distance so that the total number of selected Pareto solution candidates is N. Therefore, the Pareto solution search device can select more diverse Pareto solution candidates than the device disclosed in Patent Document 1.

[0062] Embodiment 3. In Embodiment 3, among the M Pareto solution candidates PS1 to PS M a Pareto solution search device is provided with an evaluation value correction unit 6 that corrects the evaluation values of all Pareto solution candidates included in the Pareto frontier so that the evaluation values of all Pareto solution candidates included in the Pareto frontier are 1 or more.

[0063] FIG. 12 is a configuration diagram showing a Pareto solution search device according to Embodiment 3. In FIG. 12, the same reference numerals as those in FIG. 1 denote the same or corresponding parts, and thus detailed description thereof is omitted. FIG. 13 is a hardware configuration diagram showing the hardware of the Pareto solution search device according to Embodiment 3. In FIG. 13, the same reference numerals as those in FIG. 2 denote the same or corresponding parts, and thus detailed description thereof is omitted. The Pareto solution search device shown in FIG. 12 is a device for executing a genetic algorithm using DEA, and includes an evaluation value acquisition unit 1, an evaluation value correction unit 6, a distance calculation unit 7, a Pareto solution candidate selection unit 3, and a Pareto solution candidate creation unit 4.

[0064] The evaluation value correction unit 6 is realized by, for example, an evaluation value correction circuit 16 shown in FIG. 13. The evaluation value correction unit 6 receives, from the evaluation value acquisition unit 1, the Pareto solution candidate PS m (m = 1, ···, M) and the evaluation value Ev m of the Pareto solution candidate PS m and acquires them. The evaluation value correction unit 6 identifies, based on the evaluation value Ev m of the Pareto solution candidate PS m the Pareto solution candidates PS M included in the Pareto frontier PF among the M Pareto solution candidates PS1 to PS PFj (j = 1, ···, J). J is an integer of 1 or more and M or less. The evaluation value correction unit 6 corrects the evaluation values Ev PF1 of all the Pareto solution candidates PS PFJ ~PS PFjAll Pareto solution candidates PS PF1 ~PS PFJ included in the Pareto frontier PF are corrected so that (j = 1, ···, J) becomes 1 or more. PFj The evaluation value correction unit 6 outputs the Pareto solution candidates PS after evaluation value correction to the distance calculation unit 7 and the Pareto solution candidate selection unit 3 respectively, and outputs the corrected evaluation value Ev PF1 ~PS PFJ ’ to the Pareto solution candidate selection unit 3. PFj The distance calculation unit 7 is realized by, for example, the distance calculation circuit 17 shown in FIG. 13.

[0065] The distance calculation unit 7 obtains the Pareto solution candidates PS after evaluation value correction from the evaluation value correction unit 6. PF1 ~PS PFJ The distance calculation unit 7 obtains the Pareto solution candidates PS among the M Pareto solution candidates PS1 to PS M that are not included in the Pareto frontier PF from the evaluation value acquisition unit 1. m The distance calculation unit 7 calculates the relative distance L between the Pareto solution candidates PS PF1 ~PS PFJ after evaluation value correction and the Pareto solution candidates PS m that are not included in the Pareto frontier PF among the M Pareto solution candidates PS1 to PS M The distance calculation unit 7 outputs the relative distance L m between the M Pareto solution candidates PS1 to PS to the Pareto solution candidate selection unit 3. M The Pareto solution candidate selection unit 3 is realized by, for example, the Pareto solution candidate selection circuit 13 shown in FIG. 13. m The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3d.

[0066] The second selection processing unit 3d calculates the respective evaluation values Ev in the N Pareto solution candidates PS’1 to PS’ selected by the first selection processing unit 3a. N in the N Pareto solution candidates PS’1 to PS’n (n = 1, ···, N), based on this, select G Pareto solution candidates PS”1 to PS” from among the N Pareto solution candidates PS’1 to PS’ N G If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is a Pareto solution candidate PS included in the Pareto frontier PF PFj then, the second selection processing unit 3d uses the corrected evaluation value Ev’ by the evaluation value correction unit 6 as the evaluation value Ev n PFj If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is not a Pareto solution candidate PS included in the Pareto frontier PF m then, the second selection processing unit 3d uses the evaluation value Ev obtained by the evaluation value acquisition unit 1 as the evaluation value Ev n m

[0067] In FIG. 12, it is assumed that each of the evaluation value acquisition unit 1, the evaluation value correction unit 6, the distance calculation unit 7, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4, which are components of the Pareto solution search device, is realized by dedicated hardware as shown in FIG. 13. That is, it is assumed that the Pareto solution search device is realized by an evaluation value acquisition circuit 11, an evaluation value correction circuit 16, a distance calculation circuit 17, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate creation circuit 14. Each of the evaluation value acquisition circuit 11, the evaluation value correction circuit 16, the distance calculation circuit 17, the Pareto solution candidate selection circuit 13, and the Pareto solution candidate creation circuit 14 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0068] The components of the Pareto solution search device are not limited to those realized by dedicated hardware, and the Pareto solution search device may be realized by software, firmware, or a combination of software and firmware. ​​​​​​When the Pareto solution search device is realized by software, firmware, etc., a program for causing a computer to execute the respective processing procedures in the evaluation value acquisition unit 1, the evaluation value correction unit 6, the distance calculation unit 7, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 is stored in the memory 21 shown in FIG. 3. Then, the processor 22 shown in FIG. 3 executes the program stored in the memory 21.

[0069] Also, FIG. 13 shows an example in which each component of the Pareto solution search device is realized by dedicated hardware, and FIG. 3 shows an example in which the Pareto solution search device is realized by software, firmware, etc. However, this is only an example, and some components in the Pareto solution search device may be realized by dedicated hardware, and the remaining components may be realized by software, firmware, etc.

[0070] Next, the operation of the Pareto solution search device shown in FIG. 12 will be described. However, except for the evaluation value correction unit 6, the distance calculation unit 7, and the second selection processing unit 3d, it is the same as the Pareto solution search device shown in FIG. 1. Therefore, here, mainly the operations of the evaluation value correction unit 6, the distance calculation unit 7, and the second selection processing unit 3d will be described.

[0071] The evaluation value correction unit 6 receives, from the evaluation value acquisition unit 1, the Pareto solution candidates PS m (m = 1, ···, M) and the evaluation values Ev m of the Pareto solution candidates PS m . The evaluation value correction unit 6 identifies, based on the evaluation value Ev m of the Pareto solution candidate PS m , the Pareto solution candidates PS M among the M Pareto solution candidates PS1 to PS PFj that are included in the Pareto front PF. The Pareto solution candidates PS PFj included in the Pareto front PF belong to, for example, the Pareto solution candidates PS mAssuming that it is so, the evaluation value correction unit 6 may specify the Pareto solution candidate PS belonging to the rank Rk1, similarly to the rank specification unit 5 shown in FIG. 9. m It may be specified.

[0072] The evaluation value correction unit 6 corrects the evaluation values Ev PF1 ~PS PFJ (j = 1, ···, J) of all the Pareto solution candidates PS PFj included in the Pareto frontier PF so that they become 1 or more. PF1 ~PS PFJ included in the Pareto frontier PF. PFj The evaluation value correction unit 6 corrects the evaluation values Ev Here, assuming that the Pareto solution candidates included in the Pareto frontier PF are, for example, PS1 to PS3, and the evaluation value Ev1 of PS1 is “1.1”, the evaluation value Ev2 of PS2 is “1.05”, and the evaluation value Ev3 of PS3 is “0.95”, the correction process by the evaluation value correction unit 6 will be specifically described below.

[0073] The evaluation value correction unit 6 calculates a coefficient α such that the evaluation value Ev3 of the Pareto solution candidate PS3 with the smallest evaluation value among the Pareto solution candidates PS1 to PS3 becomes “1.0” as shown in the following formula (8).

[0074] TIFF0007714155000002.tif16166

[0075] The evaluation value correction unit 6 corrects the respective evaluation values Ev1 to Ev3 of the Pareto solution candidates PS1 to PS3 by multiplying each of the Pareto solution candidates PS1 to PS3 by the coefficient α as shown in the following formula (9). Ev PF1 ’ = Ev1 × α = 1.1 × 1.053 = 1.158 Ev PF2 ’ = Ev2 × α = 1.05 × 1.053 = 1.106 Ev PF3 ’ = Ev3 × α = 0.95 × 1.053 = 1.000 (9) In Equation (9), each of Ev1’, Ev2’, and Ev3’ is the corrected evaluation value. The evaluation value correction unit 6 outputs the corrected evaluation values Ev PF1 ’, Ev PF2 ’, Ev PF3 ’ to the distance calculation unit 7 and the second selection processing unit 3d, respectively.

[0076] The distance calculation unit 7 obtains the Pareto solution candidates PS PF1 ~PS PFJ after the evaluation value is corrected from the evaluation value correction unit 6. The distance calculation unit 7 obtains the Pareto solution candidates PS1 to PS M from the evaluation value acquisition unit 1, among which the Pareto solution candidates PS m not included in the Pareto frontier PF are obtained. The distance calculation unit 7 includes the Pareto solution candidates PS PF1 ~PS PFJ after the evaluation value is corrected and the Pareto solution candidates PS m not included in the Pareto frontier PF, and calculates the relative distance L M between the M Pareto solution candidates PS1 to PS m . The calculation process of the relative distance L M between the M Pareto solution candidates PS1 to PS m is the same as that of the distance calculation unit 2 shown in FIG. 1. The distance calculation unit 7 outputs the relative distance L M between the M Pareto solution candidates PS1 to PS m to the Pareto solution candidate selection unit 3.

[0077] As described in Embodiment 1, the first selection processing unit 3a selects N Pareto solution candidates PS’1 to PS’ M from among the M Pareto solution candidates PS1 to PS N and outputs the N Pareto solution candidates PS’1 to PS’ N to the second selection processing unit 3d.

[0078] The second selection processing unit 3d obtains the N Pareto solution candidates PS’1 to PS’ N from the first selection processing unit 3a. The second selection processing unit 3d obtains the corrected evaluation value Ev PFj ’ (j = 1, ···, J) from the evaluation value correction unit 6, and obtains the evaluation value Ev m of the Pareto solution candidate PS m not included in the Pareto frontier PF from the evaluation value acquisition unit 1. The second selection processing unit 3d selects G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ n based on their respective evaluation values Ev N (n = 1, ···, N). G If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is the Pareto solution candidate PS PFj included in the Pareto frontier PF, the second selection processing unit 3d uses the corrected evaluation value Ev n ’ by the evaluation value correction unit 6 as the evaluation value Ev PFj . If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is the Pareto solution candidate PS m not included in the Pareto frontier PF, the second selection processing unit 3d uses the evaluation value Ev n obtained by the evaluation value acquisition unit 1 as the evaluation value Ev m .

[0079] In the above-described Embodiment 3, based on the evaluation values acquired by the evaluation value acquisition unit 1, all the Pareto solution candidates included in the Pareto frontier are specified among the M Pareto solution candidates, and all the evaluation values of the Pareto solution candidates included in the Pareto frontier are corrected so that the evaluation values of all the Pareto solution candidates included in the Pareto frontier become 1 or more. The Pareto solution search device shown in FIG. 12 is configured to include an evaluation value correction unit 6. Further, the Pareto solution candidate selection unit 3 of the Pareto solution search device shown in FIG. 12 is based on the relative distance calculated by the distance calculation unit 7, the evaluation value after correction by the evaluation value correction unit 6, and the evaluation values of the Pareto solution candidates not included in the Pareto frontier among the M Pareto solution candidates. G Pareto solution candidates are selected from among the M Pareto solution candidates. Therefore, similar to the Pareto solution search device shown in FIG. 1, the Pareto solution search device shown in FIG. 12 can select more diverse Pareto solution candidates than the device disclosed in Patent Document 1. Further, the Pareto solution search device shown in FIG. 12 can increase the probability that the Pareto solution candidates included in the Pareto frontier are selected.

[0080] Embodiment 4. In Embodiment 4, among the M Pareto solution candidates PS1 to PS M A Pareto solution search device including a shape correction unit 8 that corrects the shape of the Pareto frontier by correcting the Pareto solution candidates included in the Pareto frontier will be described.

[0081] FIG. 14 is a configuration diagram showing a Pareto solution search device according to Embodiment 4. In FIG. 14, the same reference numerals as those in FIG. 1 denote the same or corresponding parts, and thus detailed description thereof is omitted. FIG. 15 is a hardware configuration diagram showing the hardware of the Pareto solution search device according to Embodiment 4. In FIG. 15, the same reference numerals as those in FIG. 2 denote the same or corresponding parts, and thus detailed description thereof is omitted. The Pareto solution search device shown in FIG. 14 is a device for executing a genetic algorithm using DEA, and includes an evaluation value acquisition unit 1, a shape correction unit 8, a distance calculation unit 9, a Pareto solution candidate selection unit 3, and a Pareto solution candidate creation unit 4.

[0082] The shape correction unit 8 is realized by, for example, the shape correction circuit 18 shown in FIG. 15. The shape correction unit 8 receives, from the evaluation value acquisition unit 1, the Pareto solution candidates PS m (m = 1, ···, M) and the evaluation values Ev m of the Pareto solution candidates PS m and acquires them. The shape correction unit 8, based on the evaluation values Ev m of the Pareto solution candidates PS m , identifies the Pareto solution candidates PS M among the M Pareto solution candidates PS1 to PS PFj that are included in the Pareto frontier PF. J is an integer greater than or equal to 1 and less than or equal to M. The shape correction unit 8 corrects the shape of the Pareto frontier PF by correcting the Pareto solution candidates PS PFj included in the Pareto frontier PF. The shape correction unit 8 outputs the corrected Pareto solution candidates PS PFj ' to each of the distance calculation unit 9 and the Pareto solution candidate selection unit 3.

[0083] The distance calculation unit 9 is realized by, for example, the distance calculation circuit 19 shown in FIG. 15. The distance calculation unit 9 acquires the corrected Pareto solution candidates PS PFj ' by the shape correction unit 8 and the Pareto solution candidates PS M among the evaluation values of the M Pareto solution candidates PS1 to PS m that have not been corrected by the shape correction unit 8. The distance calculation unit 9 acquires the corrected Pareto solution candidates PS PFj ' and the M Pareto solution candidates PS1 to PS M among which the Pareto solution candidates PS m not corrected by the shape correction unit 8 are included, and calculates the relative distance L M between the M Pareto solution candidates PS1 to PS m . The distance calculation unit 9 calculates the relative distance L M between the M Pareto solution candidates PS1 to PSm Output it to the Pareto solution candidate selection unit 3.

[0084] The Pareto solution candidate selection unit 3 is realized by, for example, a Pareto solution candidate selection circuit 13 shown in FIG. 13. The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3e. The second selection processing unit 3e is based on the respective evaluation values Ev N in the N Pareto solution candidates PS’1 to PS’ n (n = 1, ···, N) selected by the first selection processing unit 3a, and selects G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ G . If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is the Pareto solution candidate PS PFj ’ corrected by the shape correction unit 8, the second selection processing unit 3d uses the evaluation value Ev PFj of the Pareto solution candidate PS PFj ’ corrected by the shape correction unit 8. If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is a Pareto solution candidate whose evaluation value has not been corrected by the shape correction unit 8, the second selection processing unit 3d uses the evaluation value Ev n of the Pareto solution candidate PS n whose evaluation value has not been corrected by the shape correction unit 8.

[0085] In FIG. 14, it is assumed that each of the evaluation value acquisition unit 1, the shape correction unit 8, the distance calculation unit 9, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4, which are components of the Pareto solution search device, is realized by dedicated hardware as shown in FIG. 15. That is, it is assumed that the Pareto solution search device is realized by an evaluation value acquisition circuit 11, a shape correction circuit 18, a distance calculation circuit 19, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate creation circuit 14. Each of the evaluation value acquisition circuit 11, the shape correction circuit 18, the distance calculation circuit 19, the Pareto solution candidate selection circuit 13, and the Pareto solution candidate creation circuit 14 corresponds to, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0086] The components of the Pareto solution search device are not limited to those realized by dedicated hardware, and the Pareto solution search device may be realized by software, firmware, or a combination of software and firmware. When the Pareto solution search device is realized by software or firmware, etc., a program for causing a computer to execute each processing procedure in the evaluation value acquisition unit 1, the shape correction unit 8, the distance calculation unit 9, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4 is stored in the memory 21 shown in FIG. 3. Then, the processor 22 shown in FIG. 3 executes the program stored in the memory 21.

[0087] Also, FIG. 15 shows an example in which each of the components of the Pareto solution search device is realized by dedicated hardware, and FIG. 3 shows an example in which the Pareto solution search device is realized by software or firmware, etc. However, this is only an example, and some components of the Pareto solution search device may be realized by dedicated hardware, and the remaining components may be realized by software or firmware, etc.

[0088] Next, the operation of the Pareto solution search device shown in FIG. 14 will be described. However, except for the shape correction unit 8, the distance calculation unit 9, and the second selection processing unit 3e, it is the same as the Pareto solution search device shown in FIG. 1. Therefore, here, mainly, the operations of the shape correction unit 8, the distance calculation unit 9, and the second selection processing unit 3e will be described.

[0089] The shape correction unit 8 receives from the evaluation value acquisition unit 1 the Pareto solution candidate PS m (m = 1, ···, M), and the Pareto solution candidate PSm The evaluation value Ev m is obtained. The shape correction unit 8 determines the Pareto solution candidates PS m with evaluation values Ev m Based on this, among the M Pareto solution candidates PS1 to PS M the Pareto solution candidates PS PFj (j = 1, ···, J) included in the Pareto frontier PF are specified. The Pareto solution candidates PS PFj included in the Pareto frontier PF belong to, for example, the rank Rk1. The shape correction unit 8 may specify the Pareto solution candidates PS m belonging to the rank Rk1 in the same manner as the rank specification unit 5 shown in FIG. 9. m It may be specified like this.

[0090] In the example of FIG. 11, the Pareto solution candidates PS m belonging to the rank Rk1 are PS1 to PS3, and the shape of the Pareto frontier PF including PS1 to PS3 is a so-called convex shape. The convex shape means that as the value f1(x, y) of the objective function f1 increases, the Pareto solution candidate PS m approaches the x-axis related to the objective function f1, and as the value f2(x, y) of the objective function f2 increases, the Pareto solution candidate PS m approaches the y-axis related to the objective function f2. If the shape of the Pareto frontier PF is a convex shape, the Pareto solution candidate PS PFj included in the Pareto frontier PF is highly likely to be the optimal solution. Also, if the shape of the Pareto frontier PF is a linear shape, the Pareto solution candidate PS PFj included in the Pareto frontier PF is highly likely to be the optimal solution. On the other hand, if the shape of the Pareto frontier PF is a non-convex shape, the Pareto solution candidate PS PFj included in the Pareto frontier PF is less likely to be the optimal solution. The non-convex shape is a shape that is neither a convex shape nor a linear shape. Therefore, when the shape of the Pareto frontier PF is a non-convex shape, if the shape of the Pareto frontier PF is corrected to be a linear shape, the Pareto solution candidates PS PFj included in the Pareto frontier PF are more likely to become the optimal solution.

[0091] The shape correction unit 8 corrects the shape of the Pareto frontier PF by correcting the Pareto solution candidates PS PFj included in the Pareto frontier PF.

[0092] Hereinafter, the shape correction process by the shape correction unit 8 will be specifically described. Here, an example in which the dimension of the shape of the Pareto frontier PF is two-dimensional will be described. For convenience of explanation, the Pareto solution candidates PS PFj included in the Pareto frontier PF are, as shown in FIGS. 16 and 17, PS PF1 to PS PF11 shall be assumed. FIG. 16 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is a non-convex shape. FIG. 17 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is a convex shape. The shape correction unit 8 specifies a parameter p that satisfies the following equation (10). Since the process of specifying the parameter p itself is a known technique, a detailed description thereof will be omitted. The shape correction unit 8 raises each of the Pareto solution candidates PS PF1 to PS PF11 to the p-th power as shown in the following equation (11) to linearly approximate the shape of the Pareto frontier PF. PS PFj ' is the Pareto solution candidate after correction.

[0093] TIFF0007714155000003.tif26166

[0094] In the example of FIG. 16, the shape of the Pareto frontier PF is corrected from a non-convex shape to a linear shape. In the example of FIG. 17, the shape of the Pareto frontier PF is corrected from a convex shape to a linear shape. Here, the shape correction unit 8 identifies a parameter p that satisfies Equation (10), and by raising each of the Pareto solution candidates PS PF1 ~PS PF11 to the p-th power, it shows a method of linearly approximating the shape of the Pareto frontier PF. However, it suffices that the shape of the Pareto frontier PF can be linearly approximated, and it goes without saying that the shape correction unit 8 may linearly approximate the shape of the Pareto frontier PF using a method other than the above method. In FIGS. 16 and 17, an example in which the dimension of the shape of the Pareto frontier PF is two-dimensional is shown. For this reason, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes a linear shape. When the dimension of the shape of the Pareto frontier PF is three-dimensional, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes a plane. When the dimension of the shape of the Pareto frontier PF is four-dimensional or more, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes a hyperplane.

[0095] The distance calculation unit 9 obtains the Pareto solution candidate PS PFj ’ after correction by the shape correction unit 8, and the Pareto solution candidate PS M among the M Pareto solution candidates PS1 to PS m that has not been corrected by the shape correction unit 8. The distance calculation unit 9 obtains the corrected Pareto solution candidate PS PFj ’ and the Pareto solution candidate PS m that has not been corrected by the shape correction unit 8 among the M Pareto solution candidates PS1 to PS M and calculates the relative distance L m between them. The calculation process of the relative distance L M between the M Pareto solution candidates PS1 to PS m itself is the same as that of the distance calculation unit 2 shown in FIG. 1. The distance calculation unit 9 calculates the M Pareto solution candidates PS1 to PSM The relative distance L between m is output to the Pareto solution candidate selection unit 3.

[0096] As described in Embodiment 1, the first selection processing unit 3a selects N Pareto solution candidates PS’1 to PS’ M from among the M Pareto solution candidates PS1 to PS N and outputs the N Pareto solution candidates PS’1 to PS’ N to the second selection processing unit 3e.

[0097] The second selection processing unit 3e acquires the N Pareto solution candidates PS’1 to PS’ N from the first selection processing unit 3a. The second selection processing unit 3e acquires the evaluation values Ev PFj in the DEA of the corrected Pareto solution candidate PS PFj ’ (j = 1, ···, J) from the shape correction unit 8, and acquires the evaluation values Ev m in the DEA of the Pareto solution candidate PS m from the evaluation value acquisition unit 1. Based on the respective evaluation values Ev N in the N Pareto solution candidates PS’1 to PS’ n (n = 1, ···, N), the second selection processing unit 3e selects G Pareto solution candidates PS”1 to PS” N from among the N Pareto solution candidates PS’1 to PS’ G . If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is the Pareto solution candidate PS PFj ’ corrected by the shape correction unit 8, the second selection processing unit 3d uses the evaluation value Ev PFj of the Pareto solution candidate PS PFj ’ corrected by the shape correction unit 8. If the Pareto solution candidate PS’ selected by the first selection processing unit 3a is a Pareto solution candidate whose evaluation value has not been corrected by the shape correction unit 8, the second selection processing unit 3d uses the evaluation value Ev n of the Pareto solution candidate PS n not corrected by the shape correction unit 8.

[0098] In the above-described Embodiment 4, based on the evaluation values acquired by the evaluation value acquisition unit 1, among the M Pareto solution candidates, the Pareto solution candidates included in the Pareto frontier are specified, and the shape of the Pareto frontier is corrected by correcting the Pareto solution candidates included in the Pareto frontier. Thus, the Pareto solution search device shown in FIG. 14 is configured to include a shape correction unit 8. Further, the distance calculation unit 9 of the Pareto solution search device shown in FIG. 14 calculates the relative distance between the M Pareto solution candidates including the Pareto solution candidates after correction by the shape correction unit 8 and the Pareto solution candidates among the M Pareto solution candidates that have not been corrected by the shape correction unit 8. Therefore, similar to the Pareto solution search device shown in FIG. 1, the Pareto solution search device shown in FIG. 14 can select more diverse Pareto solution candidates than the device disclosed in Patent Document 1. Further, the Pareto solution search device shown in FIG. 14 can increase the probability that a Pareto solution candidate that is an optimal solution is selected.

[0099] Note that in the present disclosure, free combinations of the respective embodiments, modifications of any constituent elements of the respective embodiments, or omissions of any constituent elements in the respective embodiments are possible.

Industrial Applicability

[0100] The present disclosure is suitable for a Pareto solution search device and a Pareto solution search method.

Explanation of Signs

[0101] 1 Evaluation value acquisition unit, 2 Distance calculation unit, 3 Pareto solution candidate selection unit, 3a First selection processing unit, 3b Second selection processing unit, 3c First selection processing unit, 3d Second selection processing unit, 3e Second selection processing unit, 4 Pareto solution candidate creation unit, 4a Crossover processing unit, 4b Mutation processing unit, 5 Rank determination unit, 6 Evaluation value correction unit, 7 Distance calculation unit, 8 Shape correction unit, 9 Distance calculation unit, 11 Evaluation value acquisition circuit, 12 Distance calculation circuit, 13 Pareto solution candidate selection circuit, 14 Pareto solution candidate creation circuit, 15 Rank determination circuit, 16 Evaluation value correction circuit, 17 Distance calculation circuit, 18 Shape correction circuit, 19 Distance calculation circuit, 21 Memory, 22 Processor.

Claims

1. An evaluation value acquisition unit that acquires the evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is obtained by a genetic algorithm using the envelope analysis method, from a simulator that calculates the evaluation values of the M Pareto solution candidates in the envelope analysis method; A distance calculation unit that calculates the relative distance between the M Pareto solution candidates; Based on the relative distance calculated by the distance calculation unit and the evaluation value acquired by the evaluation value acquisition unit, a Pareto solution candidate selection unit that selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from among the M Pareto solution candidates; A Pareto solution candidate creation unit that newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates by using any one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit; Comprising: The Pareto solution candidate selection unit: A first selection processing unit that selects N (N is an integer of 1 or more and M or less) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit; A second selection processing unit that selects G (G is an integer of 1 or more and less than N) Pareto solution candidates from among the N Pareto solution candidates based on the respective evaluation values of the N Pareto solution candidates selected by the first selection processing unit. A Pareto solution search device.

2. Based on the evaluation value acquired by the evaluation value acquisition unit, a rank identification unit that determines the superiority or inferiority of the M Pareto solution candidates and identifies the rank to which each Pareto solution candidate belongs among a plurality of ranks based on the determination result of the superiority or inferiority; The first selection processing unit: The Pareto solution search device according to claim 1, characterized in that Pareto solution candidates are selected from among the Pareto solution candidates belonging to each rank based on the relative distance so that the total number of selected Pareto solution candidates is N.

3. An evaluation value acquisition unit that acquires the evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is obtained by a genetic algorithm using the envelope analysis method, from a simulator that calculates the evaluation values of the M Pareto solution candidates in the envelope analysis method; A distance calculation unit that calculates the relative distance between the M Pareto solution candidates; Based on the relative distance calculated by the distance calculation unit and the evaluation value obtained by the evaluation value acquisition unit, a Pareto solution candidate selection unit that selects G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates from among the M Pareto solution candidates; Among the G Pareto solution candidates selected by the Pareto solution candidate selection unit, using any one or more of the Pareto solution candidates, a Pareto solution candidate creation unit that newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates; Based on the evaluation value obtained by the evaluation value acquisition unit, among the M Pareto solution candidates, all Pareto solution candidates included in the Pareto front are specified, and the evaluation values of all Pareto solution candidates included in the Pareto front are corrected so that the evaluation values of all Pareto solution candidates included in the Pareto front are 1 or more. An evaluation value correction unit; The Pareto solution candidate selection unit Based on the relative distance calculated by the distance calculation unit, the evaluation value after correction by the evaluation value correction unit, and the evaluation values of the Pareto solution candidates among the M Pareto solution candidates that are not included in the Pareto front, from among the M Pareto solution candidates, The Pareto solution search device is characterized in that the G Pareto solution candidates are selected.

4. From a simulator that calculates the evaluation values of M (M is an integer greater than or equal to 2) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is obtained by a genetic algorithm using the envelope analysis method, an evaluation value acquisition unit that acquires the evaluation values of each Pareto solution candidate in the envelope analysis method; A distance calculation unit that calculates the relative distance between the M Pareto solution candidates; Based on the relative distance calculated by the distance calculation unit and the evaluation value obtained by the evaluation value acquisition unit, a Pareto solution candidate selection unit that selects G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates from among the M Pareto solution candidates; Among the G Pareto solution candidates selected by the Pareto solution candidate selection unit, using any one or more of the Pareto solution candidates, a Pareto solution candidate creation unit that newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates; Based on the evaluation values obtained by the evaluation value acquisition unit, among the M Pareto solution candidates, identify the Pareto solution candidates included in the Pareto frontier, and correct any of the Pareto solution candidates included in the Pareto frontier, thereby correcting the shape of the Pareto frontier, a shape correction unit; The distance calculation unit A Pareto solution search device characterized in that it calculates the relative distance between M Pareto solution candidates including the Pareto solution candidates after correction by the shape correction unit and the Pareto solution candidates among the M Pareto solution candidates that have not been corrected by the shape correction unit.

5. G Pareto solution candidates selected by the Pareto solution candidate selection unit and (M - G) Pareto solution candidates created by the Pareto solution candidate creation unit are provided to the simulator. The Pareto solution search device according to any one of claims 1 to 4, characterized in that the evaluation value acquisition process by the evaluation value acquisition unit, the distance calculation process by the distance calculation unit, the Pareto solution candidate selection process by the Pareto solution candidate selection unit, and the Pareto solution candidate creation process by the Pareto solution candidate creation unit are repeated.

6. The Pareto solution candidate creation unit A crossover processing unit that obtains any two Pareto solution candidates from the G Pareto solution candidates selected by the Pareto solution candidate selection unit, and exchanges some values in one of the two Pareto solution candidates with some values in the other Pareto solution candidate; The Pareto solution search device according to any one of claims 1 to 4, characterized in that it includes a mutation processing unit that obtains any one of the G Pareto solution candidates selected by the Pareto solution candidate selection unit and changes some values in the obtained Pareto solution candidate.

7. The evaluation value acquisition unit obtains the evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem in which a solution is obtained by a genetic algorithm using the envelope analysis method from a simulator that calculates the evaluation values of the envelope analysis method for each Pareto solution candidate. The distance calculation unit calculates the relative distance between the M Pareto solution candidates. The Pareto solution candidate selection unit selects G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit and the evaluation value acquired by the evaluation value acquisition unit. The Pareto solution candidate creation unit newly creates (M - G) Pareto solution candidates different from the G Pareto solution candidates by using any one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit. The Pareto solution candidate selection unit performs a first selection process of selecting N (N is an integer greater than or equal to 1 and less than or equal to M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit, and performs a second selection process of selecting G (G is an integer greater than or equal to 1 and less than N) Pareto solution candidates from among the N Pareto solution candidates based on the respective evaluation values of the N Pareto solution candidates selected by the first selection processing unit. Pareto solution search method. **Claim 8**: The rank determination unit determines the superiority and inferiority of the M Pareto solution candidates based on the evaluation values acquired by the evaluation value acquisition unit, and based on the determination result of the superiority and inferiority, specifies the rank to which each Pareto solution candidate belongs among a plurality of ranks. The first selection processing unit selects Pareto solution candidates from among the Pareto solution candidates belonging to each rank based on the relative distance so that the total number of selected Pareto solution candidates is N. The Pareto solution search method according to claim 7. **Claim 9**: The evaluation value acquisition unit acquires the evaluation values of the M (M is an integer greater than or equal to 2) Pareto solution candidates in the envelope analysis method from a simulator that calculates the evaluation values of the M Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem in which a solution is obtained by a genetic algorithm using the envelope analysis method, for each Pareto solution candidate. The distance calculation unit calculates the relative distance between the M Pareto solution candidates. The Pareto solution candidate selection unit selects G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit and the evaluation value acquired by the evaluation value acquisition unit. The Pareto solution candidate creation unit uses one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit to newly create (M - G) Pareto solution candidates different from the G Pareto solution candidates. The evaluation value correction unit identifies all Pareto solution candidates included in the Pareto front among the M Pareto solution candidates based on the evaluation values obtained by the evaluation value acquisition unit, and corrects the evaluation values of all Pareto solution candidates included in the Pareto front so that the evaluation values of all Pareto solution candidates included in the Pareto front are 1 or more. The Pareto solution candidate selection unit A Pareto solution search method for selecting the G Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit, the evaluation value after correction by the evaluation value correction unit, and the evaluation values of the Pareto solution candidates not included in the Pareto front among the M Pareto solution candidates.

10. The evaluation value acquisition unit acquires the evaluation values of each Pareto solution candidate in the envelope analysis method from a simulator that calculates the evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem in which a solution is obtained by a genetic algorithm using the envelope analysis method. The distance calculation unit calculates the relative distance between the M Pareto solution candidates. The Pareto solution candidate selection unit selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from among the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit and the evaluation values obtained by the evaluation value acquisition unit. The Pareto solution candidate creation unit uses one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit to newly create (M - G) Pareto solution candidates different from the G Pareto solution candidates. The shape correction unit identifies the Pareto solution candidates included in the Pareto front among the M Pareto solution candidates based on the evaluation values obtained by the evaluation value acquisition unit, and corrects the shape of the Pareto front by correcting any of the Pareto solution candidates included in the Pareto front. The distance calculation unit A Pareto solution search method for calculating a relative distance between M Pareto solution candidates including a Pareto solution candidate after correction by the shape correction unit and a Pareto solution candidate among the M Pareto solution candidates that has not been corrected by the shape correction unit.

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