Pareto solution search device and pareto solution search method

Abstract

This Pareto solution search device is configured to comprise: an evaluation value acquisition unit (1) that acquires an evaluation value in an envelope analysis method for each Pareto solution candidate from a simulator for calculating, by means of a genetic algorithm using an envelope analysis method, an evaluation value in an envelope analysis method for M Pareto solution candidates (M = integer equal to or greater than 2) in a plurality of objective functions corresponding to a multipurpose problem for which a solution is required; and a distance calculation unit (2) that calculates a relative distance between the M Pareto solution candidates. The Pareto solution search device also comprises a Pareto solution candidate selection unit (3) that selects G Pareto solution candidates (G = integer equal to or greater than 1 but less than M) from among the M Pareto solution candidates on the basis of the relative distance calculated by the distance calculation unit (2) and the evaluation value acquired by the evaluation value acquisition unit (1), and 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 Pareto solution candidates among the G Pareto solution candidates selected by the Pareto solution candidate selection unit (3).

Description

Pareto solution search device and Pareto solution search method

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

[0002] There is a Pareto solution search device that executes a genetic algorithm to find a solution to a multi-objective problem, and that repeatedly updates M (M is an integer equal to or greater than 2) Pareto solution candidates for multiple objective functions corresponding to the multi-objective problem. Pareto solution candidates are solution candidates that are close to an ideal solution for the multi-objective problem. Patent Document 1, for example, discloses an example of such a Pareto solution search device that executes a multi-objective optimization method including a selection step and a change step. The selection step acquires evaluation values ​​of the M Pareto solution candidates from a simulator that calculates evaluation values ​​of the M Pareto solution candidates for multiple objective functions. The selection step then executes a selection process to select G (G is an integer equal to or greater than 1 and less than M) Pareto solution candidates with relatively high evaluation values ​​from the M Pareto solution candidates. The change step executes a creation process to create (M-G) new Pareto solution candidates different from the G Pareto solution candidates using one or more Pareto solution candidates from the G Pareto solution candidates selected by the selection step. In the modification step, the G Pareto solution candidates selected in the selection step and the newly created (M-G) Pareto solution candidates are provided to a simulator. The simulator calculates an evaluation value for each of the Pareto solution candidates provided by the modification step. The selection process in the selection step and the creation process in the modification step are repeated multiple times.

[0003] Japanese Patent Application Publication No. 8-36560

[0004] In the multi-objective optimization method executed by the device disclosed in Patent Document 1, the selection process in the selection step and the creation process in the modification step are repeated multiple 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, which results in 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-mentioned problems, and aims to provide a Pareto solution search device that can select a greater variety of Pareto solution candidates than the device disclosed in Patent Document 1.

[0006] A Pareto solution search device according to the present disclosure includes an evaluation value acquisition unit that acquires evaluation values ​​of M (M is an integer equal to or greater than 2) Pareto solution candidates using envelope analysis from a simulator that calculates evaluation values ​​of each Pareto solution candidate using envelope analysis for a plurality of objective functions corresponding to a multi-objective problem whose solution is to be found by a genetic algorithm using envelope analysis, and a distance calculation unit that calculates relative distances between the M Pareto solution candidates. The Pareto solution search device also includes a Pareto solution candidate selection unit that selects G (G is an integer equal to or greater than 1 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 and the evaluation values ​​acquired by the evaluation value acquisition unit, and a Pareto solution candidate creation unit that uses one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit to create new (M-G) Pareto solution candidates different from the G Pareto solution candidates.

[0007] According to the present disclosure, it is possible to select Pareto solution candidates with a greater variety than the device disclosed in Patent Document 1.

[0008] 1 is a configuration diagram showing a Pareto solution search device according to a first embodiment; FIG. 2 is a hardware configuration diagram showing the hardware of the Pareto solution search device according to the first embodiment; FIG. 3 is a hardware configuration diagram of a computer when the Pareto solution search device is realized by software, firmware, or the like; FIG. 4 is a flowchart showing a Pareto solution search method, which is a processing procedure of the Pareto solution search device; FIG. 5 is an explanatory diagram showing an example of a pumping system in a sewage treatment plant; ｍ(m=1, ..., M). An explanatory diagram showing an example of crossover processing by the crossover processing unit 4a. An explanatory diagram showing an example of mutation processing by the mutation processing unit 4b. A configuration diagram showing a Pareto solution search device according to a second embodiment. A hardware configuration diagram showing hardware of a Pareto solution search device according to a second embodiment. Pareto solution candidate PS ｍ FIG. 1 is an explanatory diagram showing a rank Rk of (m=1, ..., M). FIG. 2 is a configuration diagram showing a Pareto solution search device according to embodiment 3. FIG. 3 is a hardware configuration diagram showing hardware of a Pareto solution search device according to embodiment 3. FIG. 4 is a configuration diagram showing a Pareto solution search device according to embodiment 4. FIG. 5 is a hardware configuration diagram showing hardware of a Pareto solution search device according to embodiment 4. FIG. 6 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is non-convex. FIG. 7 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is convex.

[0009] In order to explain the present disclosure in more detail, embodiments of the present disclosure will be described below 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 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. Several methods are known as methods included in DEA. The Pareto solution search device shown in FIG. 1 is for executing, among methods included in DEA, a genetic algorithm using Super CCR or a genetic algorithm using CCR. 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 an 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 the DEA from a simulator that calculates the evaluation values ​​of M (M is an integer equal to or greater than 2) Pareto solution candidates in the DEA for multiple objective functions corresponding to a multi-objective problem whose solution is to be found by a genetic algorithm using the 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, and outputs the evaluation value of each Pareto solution candidate in the 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 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, for example, by the Pareto solution candidate selection circuit 13 shown in FIG. 2 . The Pareto solution candidate selection unit 3 includes a first selection processing unit 3 a and a second selection processing unit 3 b. The Pareto solution candidate selection unit 3 acquires each Pareto solution candidate and its evaluation value in the 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. The Pareto solution candidate selection unit 3 selects G (G is an integer equal to or greater than 1 and less than M) Pareto solution candidates from the M Pareto solution candidates based on the relative distances between the M Pareto solution candidates and the evaluation value in the DEA of each Pareto solution candidate. The Pareto solution candidate selection unit 3 outputs the selected G Pareto solution candidates to the Pareto solution candidate creation unit 4.

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

[0015] The Pareto solution candidate creation unit 4 is realized by, for example, 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 uses one or more of the G Pareto solution candidates to create new (M-G) Pareto solution candidates that are different from 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 newly created (M-G) Pareto solution candidates to the simulator.

[0016] The crossover processing unit 4a acquires any two Pareto solution candidates from the G Pareto solution candidates. The crossover processing unit 4a performs crossover processing to swap 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 mutation processing to change 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 an evaluation value of each Pareto solution candidate in the DEA. The simulator outputs the evaluation value of each Pareto solution candidate in the DEA to the evaluation value acquisition unit 1. As a result, the evaluation value acquisition unit 1 performs an evaluation value acquisition process, the distance calculation unit 2 performs a distance calculation process, the Pareto solution candidate selection unit 3 performs a Pareto solution candidate selection process, and the Pareto solution candidate creation unit 4 performs a Pareto solution candidate creation process, all of which are repeated.

[0018] 1, it is assumed that each of the components of the Pareto solution search device, that is, 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, 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 as a program in the memory of a computer. A computer refers to hardware that executes a program, and includes, 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).

[0020] 3 is a hardware configuration diagram of a computer when the Pareto solution search device is realized by software, firmware, etc. When the Pareto solution search device is realized by software, firmware, etc., a memory 21 stores programs for causing the computer to execute the processing procedures of the evaluation value acquisition unit 1, distance calculation unit 2, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4. A processor 22 of the computer then executes the programs stored in the memory 21.

[0021] 2 shows an example in which each of the components of the Pareto solution search device is realized by dedicated hardware, while Fig. 3 shows an example in which the Pareto solution search device is realized by software, firmware, etc. However, this is merely an example, and some of the components in the Pareto solution search device may be realized by dedicated hardware, and the remaining components may be realized by software, firmware, etc.

[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 the processing procedure of the Pareto solution search device. When the Pareto solution search device is applied to a pumping plan for a sewage treatment plant as shown in FIG. 5, for example, three goals (1) to (3) are set as multi-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, rainwater, etc. flows into an inlet conduit and then into a pump well. The pump pumps the water accumulated in the pump well into a water treatment tank. The water accumulated in the water treatment tank is then discharged into a river or the sea.

[0023] ・Goal (1) The goal is to avoid the risk of flooding so that sewage treatment plants are not flooded by rainwater, etc. ・Goal (2) The goal is to reduce the cost of power consumption so that sewage treatment plants consume less power. ・Goal (3) The goal is to regulate the water quality of rivers, etc., when rainwater, etc. is discharged from sewage treatment plants into rivers or the sea.

[0024] When three goals (1) to (3) are set as multiple goals, the goal function of the genetic algorithm is, for example, the goal function f regarding avoidance of flood risk, as shown in the following formulas (1) to (3): １ and the target function f for reducing the cost of power consumption ２ and the target function f for water quality regulation of rivers, etc. ３ The target function f １ , f ２ , f ３ The setting may be performed by the evaluation value acquisition unit 1 or by the simulator, for example.

[0025]

[0026] In equations (1) to (4), mean(x) is the mathematical symbol representing the average value of x. Max(x, y) is the mathematical symbol representing the selection of the larger of x or y. y １ (t) indicates the water level (m) of the inlet drain at time t, and y ＳＴＤindicates the water level (m) in the inlet drain under standard conditions, and WLW ＳＴＤ indicates the water level width (m) in the inlet channel under standard conditions. ２ (t) indicates the power consumption of the sewage treatment plant at time t. COD(t) indicates the chemical oxygen demand (g / L) of the river etc. at time t, TN(t) indicates the total nitrogen amount (g / L) of the river etc. at time t, and TP(t) indicates the total phosphorus amount (g / L) of the river etc. at time t. COD Ｒｖ indicates the regulated value of chemical oxygen demand (g / L), and TN Ｒｖ indicates the regulation value of total nitrogen (g / L), and TP Ｒｖ indicates the regulation value of total phosphorus (g / L). Ｇｖ (t) indicates the total amount (Kg) of chemical oxygen demand of the river etc. at time t, and TN Ｇｖ (t) indicates the total amount of nitrogen (kg) in the river at time t, and TP Ｇｖ (t) indicates the total amount of phosphorus (kg) in the river at time t. ＴｏｔａｌＧｖ (t) indicates the regulation value (Kg) of the total chemical oxygen demand, and TN ＴｏｔａｌＧｖ indicates the regulation value (kg) of the total amount of total nitrogen, and TP ＴｏｔａｌＧｖ indicates the regulated value (kg) of the total amount of total phosphorus.

[0027] The simulator calculates M (M is an integer equal to or greater than 2) Pareto solution candidates PS for a plurality of objective functions. １ ~PS Ｍ The evaluation value Ev in DEA ｍ (m=1, ..., M). A plurality of objective functions are calculated as f １ , f ２ , f ３ If so, the objective function f １ , f ２ , f ３ M Pareto solution candidates PS １ ~PS Ｍ Each evaluation value Ev ｍ The simulator calculates the Pareto solution candidates PS ｍ Evaluation value Ev of (m = 1, ..., M) ｍSince the process of calculating f is a known technique, detailed description thereof will be omitted. １ , f ２ If there are two of these, the Pareto solution candidate PS ｍ The evaluation value Ev ｍ can be obtained by the following evaluation formula, for example: However, the following evaluation formula is merely an example, and the Pareto solution candidate PS ｍ The evaluation value Ev ｍ may be obtained by other evaluation formulas. [Evaluation formula] Ev ｍ = (Wa × f １ ) + (Wb × f ２ ) Wa is the objective function f １ Wb is the weighting coefficient for the objective function f ２ is the weighting factor for the objective function f ２ than the objective function f １ Pareto solution candidate PS ｍ The evaluation value Ev ｍ When the objective function f is calculated, the weighting coefficient Wa is set to a value greater than the weighting coefficient Wb. １ than the objective function f ２ Pareto solution candidate PS ｍ The evaluation value Ev ｍ When calculating the weighting coefficient Wa, the weighting coefficient Wb is set to a smaller value.

[0028] The evaluation value acquisition unit 1 receives the Pareto solution candidates PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ (Step ST1 in FIG. 4). However, the evaluation value acquisition unit 1 acquires the Pareto solution candidates PS ｍ When the Pareto solution candidate PS ｍ In this case, the evaluation value acquisition unit 1 receives the Pareto solution candidates PS ｍ Without obtaining the Pareto solution candidate PS ｍ The evaluation value Ev ｍ Fig. 6 shows the M Pareto solution candidates PS ｍ6 is an explanatory diagram showing an example of the objective function f (m=1, . . . , M) for the sake of simplicity. １ , f ２ In FIG. 6, black circles represent Pareto solution candidates PS ｍ The horizontal axis of FIG. 6 represents the objective function f １ When the design variables are, for example, x and y, the objective function f １ The value of f １ (x, y). For example, -1≦x≦1, -1≦y≦1. The vertical axis of FIG. 6 represents the objective function f ２ When the design variables are, for example, x and y, the objective function f ２ The value of f ２ (x, y). The evaluation value acquisition unit 1 calculates the Pareto solution candidates PS ｍ to the distance calculation unit 2 and the Pareto solution candidate selection unit 3, and ｍ The evaluation value Ev ｍ is output to the Pareto solution candidate selection unit 3.

[0029] The distance calculation unit 2 receives the Pareto solution candidate PS ｍ (m=1, . . . , M). The distance calculation unit 2 obtains M Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ (m=1, . . . , M) (step ST2 in FIG. 4). The distance calculation unit 2 calculates the relative distance L ｍ is output to the Pareto solution candidate selection unit 3.

[0030] Hereinafter, the relative distance L calculated by the distance calculation unit 2 ｍ The calculation process of M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS １ By focusing on the distance, the distance calculation unit 2 calculates the Pareto solution candidate PS １ and the Pareto solution candidate PS ｍ Distance L from (m=2, ..., M) １，ｍ The Pareto solution candidate PS １and Pareto solution candidate PS ｍ Distance L １，ｍ For example, the Pareto solution candidate PS １ and Pareto solution candidate PS ｍ The Euclidean distance between the M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS ２ By focusing on the distance, the distance calculation unit 2 calculates the Pareto solution candidate PS ２ and the Pareto solution candidate PS ｍ Distance L from (m = 1, 3, ..., M) ２，ｍ The Pareto solution candidate PS ２ and Pareto solution candidate PS ｍ Distance L ２，ｍ For example, the Pareto solution candidate PS ２ and Pareto solution candidate PS ｍ The Euclidean distance between the M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS Ｍ By focusing on the distance, the distance calculation unit 2 calculates the Pareto solution candidate PS Ｍ and the Pareto solution candidate PS ｍ Distance L from (m=1, ..., M-1) Ｍ，ｍ The Pareto solution candidate PS Ｍ and Pareto solution candidate PS ｍ Distance L Ｍ，ｍ For example, the Pareto solution candidate PS Ｍ and Pareto solution candidate PS ｍ The Euclidean distance between

[0031] The first selection processing unit 3a of the Pareto solution candidate selection unit 3 receives the Pareto solution candidates PS ｍ (m=1, . . . , M), and calculates M Pareto solution candidates PS １ ~PS Ｍ The relative distance between PS ｍ (m=1, . . . , M). The first selection processing unit 3a obtains each of the Pareto solution candidates PS ｍ For (m = 1, ..., M), the crowding distance ΣL ｍThen, (M-1) distances L ｍ Specifically, the sum of M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS １ In this case, the first selection processing unit 3a calculates the congestion degree distance ΣL as shown in the following equation (5): １ Then, (M-1) distances L １，ｍ Calculate the sum of ΣL １ =L １，２ +L １，３ +...+L １，Ｍ　　　　　 (5) M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS ２ In this case, the first selection processing unit 3a calculates the congestion degree distance ΣL as shown in the following equation (6): ２ Then, (M-1) distances L ２，ｍ Calculate the sum of ΣL ２ =L ２，１ +L ２，３ +...+L ２，Ｍ　　　　　 (6) M Pareto solution candidates PS １ ~PS Ｍ For example, the Pareto solution candidate PS Ｍ In this case, the first selection processing unit 3a calculates the congestion degree distance ΣL as shown in the following equation (7): Ｍ Then, (M-1) distances L Ｍ，ｍ Calculate the sum of ΣL Ｍ =L Ｍ，１ +L Ｍ，２ +...+L Ｍ，Ｍ－１　　　 (7)

[0032] The first selection processing unit 3a selects M congestion degree distances ΣL １ ~ΣL Ｍ The first selection processing unit 3a compares the congestion degree distance ΣL １ ~ΣL Ｍ Based on the comparison results, M Pareto solution candidates PS １ ~PS ＭThe first selection processing unit 3a preferentially selects N (N is an integer between 1 and M) Pareto solution candidates having a relatively large congestion distance ΣL from the selected N Pareto solution candidates PS' (step ST3 in FIG. 4). １ ~PS' Ｎ The first selection processing unit 3a outputs N Pareto solution candidates PS' based on the congestion degree distance ΣL. １ ~PS' Ｎ By selecting [mathematical formula - see original document], the diversity of Pareto solution candidates is improved.

[0033] The second selection processing unit 3b selects the Pareto solution candidates PS ｍ Evaluation value Ev of (m = 1, ..., M) ｍ and obtains N Pareto solution candidates PS' from the first selection processing unit 3a. １ ~PS' Ｎ The second selection processing unit 3b obtains M evaluation values ​​Ev １ ~Ev Ｍ Among these, N Pareto solution candidates PS' are selected. １ ~PS' Ｎ The evaluation value Ev' corresponding to １ ~Ev' Ｎ The second selection processing unit 3b selects N Pareto solution candidates PS'. １ ~PS' Ｎ Each evaluation value Ev' in ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ (Step ST4 in FIG. 4). Specifically, the second selection processing unit 3b selects N Pareto solution candidates PS'. １ ~PS' Ｎ From among these, the evaluation value Ev' ｎ The top G Pareto solution candidates PS” with relatively high １ ~P.S.” Ｇ The second selection processing unit 3b selects the G selected Pareto solution candidates PS" １ ~P.S.” Ｇ is output to the Pareto solution candidate generating unit 4.

[0034] The Pareto solution candidate generation unit 4 receives G Pareto solution candidates PS" from the Pareto solution candidate selection unit 3. １ ~P.S.” Ｇ The Pareto solution candidate generation unit 4 obtains G Pareto solution candidates PS" １ ~P.S.” Ｇ The Pareto solution candidate creating unit 4 uses one or more Pareto solution candidates from among the G Pareto solution candidates to newly create (M - G) Pareto solution candidates that are different from the G Pareto solution candidates. The Pareto solution candidate creating unit 4 outputs the G Pareto solution candidates and the (M - G) Pareto solution candidates to the simulator.

[0035] The process of generating (MG) Pareto solution candidates by the Pareto solution candidate generating unit 4 will be specifically described below. The crossover processing unit 4a generates G Pareto solution candidates PS" １ ~P.S.” Ｇ For the sake of convenience, it is assumed here that any two Pareto solution candidates are selected from PS １ , P.S.” ２ As shown in FIG. 7, the crossover processing unit 4a selects the Pareto solution candidates PS" １ Some values ​​in and the Pareto solution candidate PS” ２ In the example of FIG. 7, a crossover process is performed in which some values ​​in the Pareto solution candidates PS" are swapped with some values ​​in the Pareto solution candidates PS" in accordance with the crossover probability. The crossover process itself is a known technique, so a detailed description thereof will be omitted. FIG. 7 is an explanatory diagram showing an example of the crossover process performed by the crossover process unit 4a. The crossover process performed by the crossover process unit 4a improves the diversity of the Pareto solution candidates. In the example of FIG. 7, the Pareto solution candidates PS" １ The fourth to sixth bits are “111” in the above equation, and the Pareto solution candidate PS ２ The "000" from the fourth bit to the sixth bit in the above code is swapped.

[0036] Here, the crossover processing unit 4a selects the Pareto solution candidates PS" １ Some values ​​in and the Pareto solution candidate PS” ２However, this is only an example, and the crossover processing unit 4a performs a crossover process in which some values ​​in the Pareto solution candidate PS" are swapped with １ Some values ​​in and the Pareto solution candidate PS” ２ In addition to the crossover process of exchanging some values ​​in ３ Some values ​​in and the Pareto solution candidate PS” ４ Hereinafter, the Pareto solution candidates after the crossover processing by the crossover processing unit 4a are referred to as PS Ｃｒ It is called.

[0037] The mutation processing unit 4b generates G Pareto solution candidates PS" １ ~P.S.” Ｇ For the sake of convenience, it is assumed here that one of the Pareto solution candidates is selected from PS ３ The mutation processing unit 4b generates the Pareto solution candidates PS" as shown in FIG. ３ A mutation process is performed in which some values ​​in are randomly changed according to the mutation probability (step ST6 in FIG. 4). The mutation process itself is a known technique, so a detailed description will be omitted. FIG. 8 is an explanatory diagram showing an example of the mutation process performed by the mutation processing unit 4b. The mutation process performed by the mutation processing unit 4b improves the diversity of the Pareto solution candidates. In the example of FIG. 8, the Pareto solution candidate PS" ３ The third bit "0" in ３ The fifth bit of "0" in the table is changed to "3". Hereinafter, the Pareto solution candidates after the mutation process by the mutation processor 4b are referred to as PS Ｍｕ It is called.

[0038] If the number of times of processing of the series of processes in the evaluation value acquisition unit 1, distance calculation unit 2, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4 has not reached H times (step ST7 in FIG. 4: NO), the Pareto solution candidate creation unit 4 calculates the number of G Pareto solution candidates PS″ selected by the Pareto solution candidate selection unit 3. １ ~P.S.” Ｇand the Pareto solution candidates PS after the crossover process Ｃｒ and the Pareto solution candidate PS after mutation processing Ｍｕ The simulator is provided with M Pareto solution candidates PS for multiple objective functions. １ ~PS Ｍ Each evaluation value Ev ｍ (m = 1, ..., M), G Pareto solution candidates PS" １ ~P.S.” Ｇ The respective evaluation values ​​in the Pareto solution candidates PS after the crossover process Ｃｒ The evaluation value of the Pareto solution candidate PS after mutation processing Ｍｕ The simulator calculates the evaluation value of M Pareto solution candidates PS １ ~PS Ｍ and M Pareto solution candidates PS １ ~PS Ｍ Each evaluation value Ev ｍ (m=1, ..., M) to the evaluation value acquisition unit 1. The evaluation value acquisition unit 1, distance calculation unit 2, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4 each perform the processes of steps ST1 to ST6 in Fig. 4. If the number of times of processing of the series of processes in the evaluation value acquisition unit 1, distance calculation unit 2, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4 reaches H times (step ST7 in Fig. 4: YES), the Pareto solution candidate creation unit 4 outputs the G Pareto solution candidates PS" selected by the Pareto solution candidate selection unit 3 as the final selection results of the Pareto solutions. １ ~P.S.” Ｇ is displayed on a display device (not shown), for example.

[0039] In the first embodiment described above, the Pareto solution search device is configured to include: an evaluation value acquisition unit 1 that acquires evaluation values ​​of M (M is an integer equal to or greater than 2) Pareto solution candidates by envelope analysis from a simulator that calculates evaluation values ​​of each Pareto solution candidate by envelope analysis for a plurality of objective functions corresponding to a multi-objective problem whose solution is to be found by a genetic algorithm using envelope analysis; and a distance calculation unit 2 that calculates relative distances between the M Pareto solution candidates. The Pareto solution search device also includes: a Pareto solution candidate selection unit 3 that selects G (G is an integer equal to or greater than 1 and less than M) Pareto solution candidates from 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; and a Pareto solution candidate creation unit 4 that uses one or more Pareto solution candidates selected by the Pareto solution candidate selection unit 3 to newly create (M-G) Pareto solution candidates different from the G Pareto solution candidates. 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 selects the congestion degree distance ΣL ｍ (m=1, . . . , M), (M−1) distances L ｍ However, this is merely an example, and the first selection processing unit 3a calculates the sum of the congestion degree distance ΣL ｍ (m=1, . . . , M), for example, (M−1) distances L ｍ In this case, the first selection processing unit 3a may calculate the average value of the congestion degree distance ΣL １ ~ΣL Ｍ Based on the comparison results, M Pareto solution candidates PS １ ~PS Ｍ Among these, N Pareto solution candidates with relatively large congestion distances ΣL are preferentially selected.

[0041] In the Pareto solution search device shown in FIG. 1, the second selection processing unit 3b selects N Pareto solution candidates PS' １ ~PS' Ｎ From among these, the evaluation value Ev' ｎThe top G Pareto solution candidates PS” with relatively high １ ~P.S.” Ｇ However, this is merely an example, and the second selection processing unit 3b may select G Pareto solution candidates PS" by, for example, a binary tournament method. １ ~P.S.” Ｇ In the binary tournament method, N Pareto solution candidates PS' may be selected. １ ~PS' Ｎ Two Pareto solution candidates PS' are randomly selected from the two Pareto solution candidates PS', and the evaluation value Ev' ｎ The binary tournament method selects the Pareto solution candidate with the highest G Pareto solution candidates PS １ ~P.S.” Ｇ This process is repeated until the following is selected.

[0042] In the second embodiment, the evaluation value Ev acquired by the evaluation value acquisition unit 1 ｍ (m=1, . . . , M), M Pareto solution candidates PS １ ~PS Ｍ Based on the results of the evaluation, each Pareto solution candidate PS is selected from the plurality of ranks Rk. ｍ A Pareto solution search device including a rank specifying unit 5 that specifies the rank Rk to which the value belongs will be described.

[0043] 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 indicate the same or corresponding parts, and detailed description thereof will be omitted. 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 indicate the same or corresponding parts, and detailed description thereof will be 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 identification unit 5, a Pareto solution candidate selection unit 3, and a Pareto solution candidate creation unit 4.

[0044] The rank specifying unit 5 is realized by, for example, a rank specifying circuit 15 shown in FIG. 10. The rank specifying unit 5 receives the Pareto solution candidate PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The rank specification unit 5 obtains the evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ The rank specification unit 5 determines the superiority or inferiority of the Pareto solution candidates PS from among the plurality of ranks Rk based on the result of the superiority or inferiority determination. ｍ (m=1, . . . , M) belongs to the rank Rk. ｍ (m=1, . . . , M) belongs to the rank Rk, which is output to the Pareto solution candidate selection unit 3.

[0045] The Pareto solution candidate selection unit 3 is realized by, for example, a 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. The first selection processing unit 3c, like the first selection processing unit 3a shown in Fig. 1, selects the Pareto solution candidates PS ｍ (m=1, . . . , M), and calculates M Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ (m=1, . . . , M). The first selection processing unit 3c obtains the relative distance L ｍ (m=1, . . . , M) and M Pareto solution candidates PS １ ~PS Ｍ Among these, N Pareto solution candidates PS' are selected. １ ~PS' Ｎ However, unlike the first selection processing unit 3a shown in FIG. 1, the first selection processing unit 3c selects the relative distance L ｍBased on (m=1, . . . , M), a Pareto solution candidate PS' is selected from among the Pareto solution candidates PS belonging to each rank Rk.

[0046] 9, it is assumed that each of the components of the Pareto solution search device, that is, the evaluation value acquisition unit 1, the distance calculation unit 2, the rank identification unit 5, the Pareto solution candidate selection unit 3, and the Pareto solution candidate creation unit 4, 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, the distance calculation circuit 12, the rank identification circuit 15, 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.

[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, firmware, or the like, a program for causing a computer to execute the processing procedures 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 is stored in memory 21 shown in Fig. 3. Then, a processor 22 shown in Fig. 3 executes the program stored in memory 21.

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

[0049] Next, the operation of the Pareto solution search device shown in Fig. 9 will be described. However, apart from the rank identification unit 5 and the first selection processing unit 3c, the Pareto solution search device is the same as that shown in Fig. 1. Therefore, here, the operation of the rank identification unit 5 and the first selection processing unit 3c will be mainly described.

[0050] The rank specifying unit 5 receives the Pareto solution candidate PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The rank specification unit 5 obtains the evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ Hereinafter, the process of determining the superiority or inferiority by the rank determination unit 5 will be specifically described. For the sake of convenience, the rank determination unit 5 determines the superiority or inferiority of the Pareto solution candidates PS ｍ and Pareto solution candidate PS ｍ＋１ An example of determining the relative merits of the two will be described.

[0051] The rank specification unit 5 identifies the Pareto solution candidates PS ｍ The evaluation value Ev ｍ and the Pareto solution candidate PS ｍ＋１ The evaluation value Ev ｍ＋１ The rank specification unit 5 compares the Pareto solution candidates PS ｍ The evaluation value Ev ｍ is the Pareto solution candidate PS ｍ＋１ The evaluation value Ev ｍ＋１ If it is higher than ｍ is the Pareto solution candidate PS ｍ＋１ The rank specification unit 5 determines that the Pareto solution candidate PS ｍ The evaluation value Ev ｍ is the Pareto solution candidate PS ｍ＋１ The evaluation value Ev ｍ＋１ If it is lower than ｍ is the Pareto solution candidate PS ｍ＋１ is judged to be inferior to

[0052] The rank specification unit 5 identifies the Pareto solution candidates PS based on the results of the superiority / inferiority judgment. ｍ(m=1, . . . , M) is calculated. The process of calculating the rank Rk by the rank specification unit 5 will now be described in detail.

[0053] In the example of FIG. 6, the Pareto solution candidates PS １ Focusing on this, the Pareto solution candidate PS １ The evaluation value Ev １ The Pareto solution candidates having the same evaluation value as ２ and Pareto solution candidate PS ３ In addition, the Pareto solution candidates PS ４ ~PS １０ The evaluation value Ev ４ ~Ev １０ is the Pareto solution candidate PS １ The evaluation value Ev １ In this case, the Pareto solution candidate PS １ , Pareto solution candidate PS ２ and Pareto solution candidate PS ３ As shown in FIG. 11, each of the １ The Pareto solution candidates PS ｍ 10 is an explanatory diagram showing the rank Rk of the Pareto solution candidates PS (m=1, . . . , M). ４ Focusing on this, the Pareto solution candidate PS ４ The evaluation value Ev ４ The Pareto solution candidates having the same evaluation value as ５ ~PS ８ In addition, the Pareto solution candidates PS ９ ~PS １０ The evaluation value Ev ９ ~Ev １０ is the Pareto solution candidate PS ４ The evaluation value Ev ４ In this case, the Pareto solution candidate PS ４ ~PS ８ Each of the ranks Rk ２ It is classified as follows.

[0054] Pareto solution candidate PS ９ Focusing on this, the Pareto solution candidate PS ９ The evaluation value Ev９ The Pareto solution candidates having the same evaluation value as １０ In addition, the Pareto solution candidate PS ９ ~PS １０ The evaluation value Ev ９ ~Ev １０ is the Pareto solution candidate PS ４ The evaluation value Ev ４ In this case, the Pareto solution candidate PS ９ ~PS １０ Each of the three is ranked Rk ３ Here, the Pareto solution candidates PS １ The evaluation value Ev １ is the Pareto solution candidate PS ２ The evaluation value Ev ２ The same evaluation value means the evaluation value Ev １ and the evaluation value Ev ２ The evaluation value Ev １ and the evaluation value Ev ２ If the difference between the Pareto solution candidates PS and the Pareto solution candidates PS is equal to or less than a certain threshold, the rank specifying unit 5 may determine the Pareto solution candidates PS to have the same evaluation value. ｍ (m=1, . . . , M) belongs to the rank Rk, which is output to the Pareto solution candidate selection unit 3.

[0055] The first selection processing unit 3c of the Pareto solution candidate selection unit 3 receives the Pareto solution candidates PS ｍ (m=1, . . . , M), and calculates M Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ (m=1, . . . , M). The first selection processing unit 3c also acquires the Pareto solution candidates PS ｍ If the number of Pareto solution candidates selected by the second selection processing unit 3b is G, the first selection processing unit 3c obtains the rank Rk of M Pareto solution candidates PS １ ~PS Ｍ The number N of Pareto solution candidates to be selected from the above is set to be greater than G and equal to or less than M.

[0056] The first selection processing unit 3c selects M Pareto solution candidates PS １ ~PS Ｍ Among them, the Pareto solution candidates PS that are classified as high ranked are ｍ Pareto solution candidates PS ｍ When selecting one or more Pareto solutions, all Pareto solution candidates PS ｍ Therefore, in the example of Fig. 11, if G = 1 to 3, N = 3 is set, if G = 4 to 8, N = 8 is set, and if G = 9 to 10, N = 10 is set.

[0057] The first selection processing unit 3c selects M Pareto solution candidates PS １ ~PS Ｍ Among these, N Pareto solution candidates PS' are selected. １ ~PS' Ｎ In the example of FIG. 11, if N=3, the first selection processing unit 3c selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ If N=8, the first selection processing unit 3c selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ and rank Rk ２ The five Pareto solution candidates PS ４ ~PS ８ For example, if N=10, the first selection processing unit 3c selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ and rank Rk ２ The five Pareto solution candidates PS ４ ~PS ８ and rank Rk ３ The two Pareto solution candidates PS ９ ~PS １０ is selected.

[0058] The second selection processing unit 3b selects the N Pareto solution candidates PS' selected by the first selection processing unit 3c. １ ~PS' Ｎ Each evaluation value Ev' in ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ In the example of FIG. 11, if G=1, the second selection processing unit 3b selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ Any one of the Pareto solution candidates PS is selected. １ ~PS ３ The evaluation value Ev １ ~Ev ３ If there is a slight difference between the evaluation values ​​Ev and Ev, the Pareto solution candidate with the highest evaluation value is selected. １ ~Ev ３ If all the ranks are the same, one Pareto solution candidate is selected. If G=2, the second selection processing unit 3b selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ In this case, any two Pareto solution candidates are selected. １ ~Ev ３ If there is a slight difference between the two Pareto solution candidates, the two with the relatively higher evaluation values ​​will be selected. １ ~Ev ３ If all the ranks are the same, two Pareto solution candidates are selected. If G=3, the second selection processing unit 3b selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ All of the following are selected.

[0059] If G=4 to 8, the second selection processing unit 3b selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３and rank Rk ２ The eight Pareto solution candidates PS ４ ~PS ８ In this case, one to five Pareto solution candidates are selected from the five Pareto solution candidates PS ４ ~PS ８ For example, one to five Pareto solution candidates with relatively high evaluation values ​​are selected from among G. If G=9 to 10, the second selection processing unit 3b selects the rank Rk １ The three Pareto solution candidates PS １ ~PS ３ and rank Rk ２ The five Pareto solution candidates PS ４ ~PS ８ and rank Rk ３ The two Pareto solution candidates PS ９ ~PS １０ In this case, one or more and two or less Pareto solution candidates are selected from the two Pareto solution candidates PS ９ ~PS １０ For example, one to two Pareto solution candidates with relatively high evaluation values ​​are selected from the G Pareto solution candidates PS″. １ ~P.S.” Ｇ is output to the Pareto solution candidate generating unit 4.

[0060] In the Pareto solution search device shown in FIG. 9, a first selection processing unit 3c selects Pareto solution candidates PS ｍ When selecting one or more Pareto solutions, all Pareto solution candidates PS ｍ Specifically, in the example of FIG. 11, if G=1 to 3, the first selection processing unit 3c sets N=3, if G=4 to 8, the first selection processing unit 3c sets N=8, and if G=9 to 10, the first selection processing unit 3c sets N=10. However, N may be any value equal to or less than M and greater than G, and is not limited to the above settings. For example, if N=5, the first selection processing unit 3c selects the rank Rk １The three Pareto solution candidates PS １ ~PS ３ and rank Rk ２ The five Pareto solution candidates PS ４ ~PS ８ In this case, two Pareto solution candidates are selected from the five Pareto solution candidates PS ４ ~PS ８ Among these, the relative distance L ｍ For example, when N=9, the first selection processing unit 3c selects the top two Pareto solution candidates with the largest rank Rk １ The three Pareto solution candidates PS １ ~PS ３ and rank Rk ２ The five Pareto solution candidates PS ４ ~PS ８ and rank Rk ３ The two Pareto solution candidates PS ９ ~PS １０ In this case, one Pareto solution candidate is selected from the two Pareto solution candidates PS ９ ~PS １０ Among these, the relative distance L ｍ The Pareto solution candidate with the larger (m=9, 10) is selected.

[0061] In the second embodiment described above, the Pareto solution search device is configured to include a rank identification unit 5 that determines the relative merits of M Pareto solution candidates based on the evaluation values ​​acquired by the evaluation value acquisition unit 1 and identifies the rank to which each Pareto solution candidate belongs among multiple ranks based on the results of the evaluation. Furthermore, a 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 relative distances so that the total number of selected Pareto solution candidates is N. Therefore, the Pareto solution search device can select a greater variety of Pareto solution candidates than the device disclosed in Patent Document 1.

[0062] Third Embodiment In the third embodiment, M Pareto solution candidates PS １ ~PSＭ This section describes a Pareto solution search device that includes 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 in Fig. 1 indicate the same or corresponding parts, and detailed description thereof will be omitted. Fig. 13 is a hardware configuration diagram showing the hardware of a Pareto solution search device according to embodiment 3. In Fig. 13, the same reference numerals as in Fig. 2 indicate the same or corresponding parts, and detailed description thereof will be 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 correcting unit 6 is realized by, for example, an evaluation value correcting circuit 16 shown in Fig. 13. The evaluation value correcting unit 6 receives the Pareto solution candidates PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The evaluation value corrector 6 obtains the Pareto solution candidates PS ｍ The evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS included in the Pareto frontier PF ＰＦｊ (j=1, . . . , J), where J is an integer between 1 and M. The evaluation value corrector 6 identifies all the Pareto solution candidates PS included in the Pareto frontier PF. ＰＦ１ ~PS ＰＦＪ The evaluation value Ev ＰＦｊ All the Pareto solution candidates PS included in the Pareto frontier PF are selected so that (j=1, . . . , J) is 1 or more. ＰＦ１ ~PS ＰＦＪ The evaluation value Ev ＰＦｊ The evaluation value correcting unit 6 corrects the Pareto solution candidates PS ＰＦ１ ~PSＰＦＪ to the distance calculation unit 7 and the Pareto solution candidate selection unit 3, and the corrected evaluation value Ev ＰＦｊ ' to the Pareto solution candidate selection unit 3.

[0065] The distance calculation unit 7 is realized by, for example, a distance calculation circuit 17 shown in Fig. 13. The distance calculation unit 7 receives the Pareto solution candidates PS ＰＦ１ ~PS ＰＦＪ The distance calculation unit 7 obtains M Pareto solution candidates PS from the evaluation value obtaining unit 1. １ ~PS Ｍ Among them, the Pareto solution candidates PS that are not included in the Pareto frontier PF ｍ The distance calculation unit 7 obtains the Pareto solution candidate PS after the evaluation value correction. ＰＦ１ ~PS ＰＦＪ and the Pareto solution candidates PS that are not included in the Pareto frontier PF ｍ M Pareto solution candidates PS including １ ~PS Ｍ The relative distance L between ｍ The distance calculation unit 7 calculates the M number of Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ is output to the Pareto solution candidate selection unit 3.

[0066] 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 3d. The second selection processing unit 3d selects the N Pareto solution candidates PS' selected by the first selection processing unit 3a. １ ~PS' Ｎ Each evaluation value Ev ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ The Pareto solution candidates PS' selected by the first selection processing unit 3a are selected from the Pareto solution candidates PS included in the Pareto frontier PF. ＰＦｊIf so, the second selection processing unit 3d selects the evaluation value Ev ｎ The evaluation value Ev after correction by the evaluation value correction unit 6 is ＰＦｊ The Pareto solution candidates PS' selected by the first selection processing unit 3a are used to select the Pareto solution candidates PS' that are not included in the Pareto frontier PF. ｍ If so, the second selection processing unit 3d selects the evaluation value Ev ｎ The evaluation value Ev acquired by the evaluation value acquisition unit 1 is ｍ is used.

[0067] 12, it is assumed that each of the components of the Pareto solution search device, namely, 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 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, or the like, a program for causing a computer to execute the processing procedures of the evaluation value acquisition unit 1, evaluation value correction unit 6, distance calculation unit 7, Pareto solution candidate selection unit 3, and Pareto solution candidate creation unit 4 is stored in a memory 21 shown in Fig. 3. Then, a processor 22 shown in Fig. 3 executes the program stored in the memory 21.

[0069] 13 shows an example in which each of the components of the Pareto solution search device is realized by dedicated hardware, while Fig. 3 shows an example in which the Pareto solution search device is realized by software, firmware, etc. However, this is merely an example, and some of the 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, other than the evaluation value corrector 6, the distance calculator 7, and the second selection processor 3d, the Pareto solution search device is the same as that shown in Fig. 1. Therefore, here, the operation of the evaluation value corrector 6, the distance calculator 7, and the second selection processor 3d will be mainly described.

[0071] The evaluation value corrector 6 receives the Pareto solution candidate PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The evaluation value corrector 6 obtains the Pareto solution candidates PS ｍ The evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS included in the Pareto frontier PF ＰＦｊ (j=1, . . . , J) are identified. Pareto solution candidates PS included in the Pareto frontier PF ＰＦｊ For example, the rank Rk １ The Pareto solution candidates PS ｍ , the evaluation value corrector 6 determines the rank Rk in the same way as the rank specifying unit 5 shown in FIG. １ The Pareto solution candidates PS ｍ may be specified.

[0072] The evaluation value corrector 6 calculates the Pareto solution candidates PS included in the Pareto frontier PF. ＰＦ１ ~PS ＰＦＪ The evaluation value Ev ＰＦｊ All the Pareto solution candidates PS included in the Pareto frontier PF are selected so that (j=1, . . . , J) is 1 or more.ＰＦ１ ~PS ＰＦＪ The evaluation value Ev ＰＦｊ Here, the Pareto solution candidates included in the Pareto frontier PF are corrected, for example, １ ~PS ３ And PS １ The evaluation value Ev １ is "1.1", PS ２ The evaluation value Ev ２ is "1.05", PS ３ The evaluation value Ev ３ Assuming that the evaluation value correcting unit 6 has a value of "0.95", the correction process by the evaluation value correcting unit 6 will be specifically described below.

[0073] The evaluation value corrector 6 calculates the Pareto solution candidate PS １ ~PS ３ Among them, the Pareto solution candidate PS with the smallest evaluation value is ３ The evaluation value Ev ３ The coefficient α is calculated so that the value becomes "1.0".

[0074]

[0075] The evaluation value corrector 6 calculates the Pareto solution candidate PS １ ~PS ３ By multiplying each of the above by a coefficient α, the Pareto solution candidates PS １ ~PS ３ Each evaluation value Ev １ ~Ev ３ Correct the Ev ＰＦ１ '=Ev １ ×α=1.1×1.053=1.158 Ev ＰＦ２ '=Ev ２ ×α=1.05×1.053=1.106 Ev ＰＦ３ '=Ev ３ ×α=0.95×1.053=1.000 (9) In equation (9), Ev １ ', Ev ２ ', Ev ３ Each of the evaluation values ​​Ev ′ is a corrected evaluation value. ＰＦ１ ', Ev ＰＦ２ ', Ev ＰＦ３' to the distance calculation unit 7 and the second selection processing unit 3d.

[0076] The distance calculation unit 7 receives the Pareto solution candidate PS after the evaluation value correction from the evaluation value correction unit 6. ＰＦ１ ~PS ＰＦＪ The distance calculation unit 7 obtains M Pareto solution candidates PS from the evaluation value obtaining unit 1. １ ~PS Ｍ Among them, the Pareto solution candidates PS that are not included in the Pareto frontier PF ｍ The distance calculation unit 7 obtains the Pareto solution candidate PS after the evaluation value correction. ＰＦ１ ~PS ＰＦＪ and the Pareto solution candidates PS that are not included in the Pareto frontier PF ｍ M Pareto solution candidates PS including １ ~PS Ｍ The relative distance L between ｍ Calculate M Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ The calculation process itself is the same as that of the distance calculation unit 2 shown in FIG. 1. The distance calculation unit 7 calculates the M number of Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ is output to the Pareto solution candidate selection unit 3.

[0077] As described in the first embodiment, the first selection processing unit 3a selects M Pareto solution candidates PS １ ~PS Ｍ Among these, N Pareto solution candidates PS' are selected. １ ~PS' Ｎ and select N Pareto solution candidates PS' １ ~PS' Ｎ is output to the second selection processing unit 3d.

[0078] The second selection processing unit 3d selects N Pareto solution candidates PS' from the first selection processing unit 3a. １ ~PS' Ｎ The second selection processing unit 3d obtains the corrected evaluation value Ev ＰＦｊ' (j=1, . . . , J), and obtains the Pareto solution candidates PS that are not included in the Pareto frontier PF from the evaluation value acquisition unit 1. ｍ The evaluation value Ev ｍ The second selection processing unit 3d obtains N Pareto solution candidates PS' １ ~PS' Ｎ Each evaluation value Ev ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ The Pareto solution candidates PS' selected by the first selection processing unit 3a are selected from the Pareto solution candidates PS included in the Pareto frontier PF. ＰＦｊ If so, the second selection processing unit 3d selects the evaluation value Ev ｎ The evaluation value Ev after correction by the evaluation value correction unit 6 is ＰＦｊ The Pareto solution candidates PS' selected by the first selection processing unit 3a are used to select the Pareto solution candidates PS' that are not included in the Pareto frontier PF. ｍ If so, the second selection processing unit 3d selects the evaluation value Ev ｎ The evaluation value Ev acquired by the evaluation value acquisition unit 1 is ｍ is used.

[0079] In the third embodiment described above, the Pareto solution search device shown in FIG. 12 is configured to include an evaluation value correction unit 6 that identifies all Pareto solution candidates included in the Pareto frontier among the M Pareto solution candidates based on the evaluation values ​​acquired by the evaluation value acquisition unit 1 and 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 greater. Furthermore, the Pareto solution candidate selection unit 3 of the Pareto solution search device shown in FIG. 12 selects G Pareto solution candidates from the M Pareto solution candidates based on the relative distance calculated by the distance calculation unit 7, the evaluation value corrected by the evaluation value correction unit 6, and the evaluation values ​​of Pareto solution candidates not included in the Pareto frontier among the M Pareto solution candidates. Therefore, like 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. Furthermore, the Pareto solution search device shown in FIG. 12 can increase the probability that Pareto solution candidates included in the Pareto frontier are selected.

[0080] Fourth Embodiment In the fourth embodiment, M Pareto solution candidates PS １ ~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 in FIG. 1 indicate the same or corresponding parts, and detailed description thereof will be omitted. FIG. 15 is a hardware configuration diagram showing the hardware of a Pareto solution search device according to embodiment 4. In FIG. 15, the same reference numerals as in FIG. 2 indicate the same or corresponding parts, and detailed description thereof will be 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, a shape correction circuit 18 shown in Fig. 15. The shape correction unit 8 receives the Pareto solution candidates PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The shape correction unit 8 obtains the Pareto solution candidates PS ｍ The evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS included in the Pareto frontier PF ＰＦｊ (j=1, . . . , J), where J is an integer between 1 and M. The shape correction unit 8 identifies the Pareto solution candidates PS ＰＦｊ The shape corrector 8 corrects the shape of the Pareto frontier PF by correcting the Pareto solution candidate PS ＰＦｊ ' to the distance calculation unit 9 and the Pareto solution candidate selection unit 3, respectively.

[0083] The distance calculation unit 9 is realized by, for example, a distance calculation circuit 19 shown in FIG. ＰＦｊ ' and M Pareto solution candidates PS １ ~PS Ｍ Among the evaluation values ​​of the Pareto solution candidates PS ｍ The distance calculation unit 9 obtains the corrected Pareto solution candidate PS ＰＦｊ ' and M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS that have not been corrected by the shape correction unit 8 ｍ M Pareto solution candidates PS including １ ~PS Ｍ The relative distance L between ｍ The distance calculation unit 9 calculates the M number of Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ is output 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 selects the N Pareto solution candidates PS' selected by the first selection processing unit 3a. １ ~PS' Ｎ Each evaluation value Ev ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ The Pareto solution candidates PS' selected by the first selection processing unit 3a are converted into the Pareto solution candidates PS corrected by the shape correction unit 8. ＰＦｊ ', the second selection processing unit 3d selects the Pareto solution candidate PS ＰＦｊ ' evaluation value Ev ＰＦｊ If the Pareto solution candidates PS′ selected by the first selection processing unit 3 a are Pareto solution candidates whose evaluation values ​​have not been corrected by the shape correction unit 8, the second selection processing unit 3 d selects the Pareto solution candidates PS′ whose evaluation values ​​have not been corrected by the shape correction unit 8. ｎ The evaluation value Ev ｎ is used.

[0085] 14, it is assumed that each of the components of the Pareto solution search device, namely, 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 realized by dedicated hardware such as that 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, firmware, or the like, a program for causing a computer to execute the processing procedures 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 is stored in a memory 21 shown in Fig. 3. Then, a processor 22 shown in Fig. 3 executes the program stored in the memory 21.

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

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

[0089] The shape correction unit 8 receives the Pareto solution candidates PS ｍ (m=1, . . . , M) and the Pareto solution candidates PS ｍ The evaluation value Ev ｍ The shape correction unit 8 obtains the Pareto solution candidates PS ｍ The evaluation value Ev ｍ Based on this, M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS included in the Pareto frontier PF ＰＦｊ (j=1, . . . , J) are identified. Pareto solution candidates PS included in the Pareto frontier PFＰＦｊ For example, the rank Rk １ The Pareto solution candidates PS ｍ , the shape correction unit 8 determines the rank Rk in the same way as the rank determination unit 5 shown in FIG. １ The Pareto solution candidates PS ｍ may be specified.

[0090] In the example of FIG. 11, the rank Rk １ The Pareto solution candidates PS ｍ PS １ ~PS ３ and PS １ ~PS ３ The shape of the Pareto frontier PF including the objective function f is a so-called convex shape. １ The value of f １ As (x, y) increases, the Pareto solution candidates PS ｍ is the objective function f １ The objective function f ２ The value of f ２ As (x, y) increases, the Pareto solution candidates PS ｍ is the objective function f ２ If the shape of the Pareto frontier PF is a convex shape, the Pareto solution candidates PS ＰＦｊ is highly likely to be the optimal solution. In addition, if the shape of the Pareto frontier PF is a straight line, the Pareto solution candidate PS ＰＦｊ On the other hand, if the shape of the Pareto frontier PF is non-convex, the Pareto solution candidate PS ＰＦｊ is unlikely to be the optimal solution. A non-convex shape is a shape that is neither convex nor linear. Therefore, if the shape of the Pareto frontier PF is non-convex, correcting the shape of the Pareto frontier PF to a linear shape will reduce the number of Pareto solution candidates PS ＰＦｊ is more likely to be the optimal solution.

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

[0092] Hereinafter, the shape correction process by the shape correction unit 8 will be specifically described. Here, an example will be described in which the shape of the Pareto frontier PF has two dimensions. For convenience of explanation, the Pareto solution candidates PS ＰＦｊ However, as shown in Figs. 16 and 17, ＰＦ１ ~PS ＰＦ１１ 16 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is non-convex. FIG. 17 is an explanatory diagram showing an example of shape correction when the shape of the Pareto frontier PF is convex. The shape correction unit 8 specifies a parameter p that satisfies the following equation (10). The process of specifying the parameter p itself is a known technique, so a detailed description will be omitted. The shape correction unit 8 specifies the Pareto solution candidate PS ＰＦ１ ~PS ＰＦ１１ By raising each of these to the pth power as shown in the following equation (11), the shape of the Pareto frontier PF is approximated to a straight line. ＰＦｊ ' is the Pareto solution candidate after correction.

[0093]

[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 corrector 8 identifies a parameter p that satisfies equation (10) and selects the Pareto solution candidates PS ＰＦ１ ~PS ＰＦ１１16 and 17 show a method of linearly approximating the shape of the Pareto frontier PF by raising each of the above values ​​to the pth power. However, 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, as long as the shape of the Pareto frontier PF can be linearly approximated. FIGS. 16 and 17 show an example in which the shape of the Pareto frontier PF has two dimensions. Therefore, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes linear. If the shape of the Pareto frontier PF has three dimensions, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes planar. If the shape of the Pareto frontier PF has four or more dimensions, the shape correction unit 8 corrects the shape of the Pareto frontier PF so that the shape of the Pareto frontier PF becomes hyperplane.

[0095] The distance calculation unit 9 calculates the Pareto solution candidate PS after correction by the shape correction unit 8. ＰＦj ' and M Pareto solution candidates PS １ ~PS Ｍ Among these, the Pareto solution candidates PS that have not been corrected by the shape correction unit 8 ｍ The distance calculation unit 9 obtains the corrected Pareto solution candidate PS ＰＦｊ ' and the Pareto solution candidates PS ｍ M Pareto solution candidates PS including １ ~PS Ｍ The relative distance L between ｍ Calculate M Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ The calculation process itself is the same as that of the distance calculation unit 2 shown in FIG. 1. The distance calculation unit 9 calculates the M number of Pareto solution candidates PS １ ~PS Ｍ The relative distance L between ｍ is output to the Pareto solution candidate selection unit 3.

[0096] As described in the first embodiment, the first selection processing unit 3a selects M Pareto solution candidates PS１ ~PS Ｍ Among these, N Pareto solution candidates PS' are selected. １ ~PS' Ｎ and select N Pareto solution candidates PS' １ ~PS' Ｎ is output to the second selection processing unit 3e.

[0097] The second selection processing unit 3e selects N Pareto solution candidates PS' from the first selection processing unit 3a. １ ~PS' Ｎ The second selection processing unit 3e acquires the corrected Pareto solution candidates PS ＰＦｊ 's DEA evaluation value Ev ＰＦｊ (j=1, . . . , J), and the Pareto solution candidates PS ｍ The evaluation value Ev in DEA ｍ The second selection processing unit 3e obtains N Pareto solution candidates PS' １ ~PS' Ｎ Each evaluation value Ev ｎ (n=1, . . . , N), N Pareto solution candidates PS' are obtained. １ ~PS' Ｎ Among them, G Pareto solution candidates PS” １ ~P.S.” Ｇ The Pareto solution candidates PS' selected by the first selection processing unit 3a are converted into the Pareto solution candidates PS corrected by the shape correction unit 8. ＰＦｊ ', the second selection processing unit 3d selects the Pareto solution candidate PS ＰＦｊ ' evaluation value Ev ＰＦｊ If the Pareto solution candidates PS′ selected by the first selection processing unit 3 a are Pareto solution candidates whose evaluation values ​​have not been corrected by the shape correction unit 8, the second selection processing unit 3 d selects the Pareto solution candidates PS′ whose evaluation values ​​have not been corrected by the shape correction unit 8. ｎ The evaluation value Ev ｎ is used.

[0098] In the fourth embodiment described above, the Pareto solution search device shown in FIG. 14 is configured to include a shape correction unit 8 that identifies Pareto solution candidates included in the Pareto frontier from among M Pareto solution candidates based on the evaluation values ​​acquired by the evaluation value acquisition unit 1 and corrects the shape of the Pareto frontier by correcting the Pareto solution candidates included in the Pareto frontier. Furthermore, a distance calculation unit 9 of the Pareto solution search device shown in FIG. 14 calculates the relative distance between M Pareto solution candidates, including the Pareto solution candidates corrected by the shape correction unit 8 and the Pareto solution candidates not corrected by the shape correction unit 8, among the M Pareto solution candidates. Therefore, like 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. Furthermore, 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] In addition, the present disclosure allows for free combination of the respective embodiments, modification of any of the components of the respective embodiments, or omission of any of the components of the respective embodiments.

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

[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 identification 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 identification circuit, 16 Evaluation value correction circuit, 17 Distance calculation circuit, 18 Shape correction circuit, 19 Distance calculation circuit, 21 Memory, 22 Processor.

Claims

1. A Pareto solution search device comprising: an evaluation value acquisition unit that acquires an evaluation value of each Pareto solution candidate using the envelope analysis method from a simulator that calculates evaluation values ​​using the envelope analysis method for M (M is an integer equal to or greater than 2) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is found by a genetic algorithm using the envelope analysis method; a distance calculation unit that calculates a relative distance between the M Pareto solution candidates; a Pareto solution candidate selection unit that selects G (G is an integer equal to or greater than 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; and a Pareto solution candidate creation unit that uses one or more Pareto solution candidates out 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.

2. The Pareto solution search device of claim 1, characterized in that the G Pareto solution candidates selected by the Pareto solution candidate selection unit and the (M-G) Pareto solution candidates created by the Pareto solution candidate creation unit are provided to the simulator, and the evaluation value acquisition unit performs an evaluation value acquisition process, the distance calculation unit performs a distance calculation process, the Pareto solution candidate selection unit performs a Pareto solution candidate selection process, and the Pareto solution candidate creation unit performs a Pareto solution candidate creation process.

3. The Pareto solution search device described in claim 1, characterized in that the Pareto solution candidate selection unit comprises: a first selection processing unit that selects N (N 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 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 based on the evaluation values ​​of each of the N Pareto solution candidates selected by the first selection processing unit.

4. A Pareto solution search device as described in claim 3, characterized in that it is equipped with a rank identification unit that judges the superiority or inferiority of the M Pareto solution candidates based on the evaluation value acquired by the evaluation value acquisition unit, and identifies the rank to which each Pareto solution candidate belongs among multiple ranks based on the result of the superiority or inferiority judgment, and the first selection processing unit selects Pareto solution candidates from 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.

5. The Pareto solution search device of claim 1, further comprising an evaluation value correction unit that identifies all of the M Pareto solution candidates included in a Pareto frontier based on the evaluation value acquired by the evaluation value acquisition unit, and corrects the evaluation values ​​of all the Pareto solution candidates included in the Pareto frontier so that the evaluation values ​​of all the Pareto solution candidates included in the Pareto frontier are 1 or greater; and the Pareto solution candidate selection unit selects the G Pareto solution candidates from 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 value of the Pareto solution candidates not included in the Pareto frontier among the M Pareto solution candidates.

6. A Pareto solution search device as described in claim 1, further comprising a shape correction unit that identifies Pareto solution candidates included in a Pareto frontier among the M Pareto solution candidates based on the evaluation value acquired by the evaluation value acquisition unit, and corrects a shape of the Pareto frontier by correcting any of the Pareto solution candidates included in the Pareto frontier, and the distance calculation unit calculates a relative distance between M Pareto solution candidates including the Pareto solution candidates after correction by the shape correction unit and Pareto solution candidates among the M Pareto solution candidates that have not been corrected by the shape correction unit.

7. The Pareto solution search device according to claim 1, characterized in that the Pareto solution candidate creation unit comprises: a crossover processing unit that acquires any two Pareto solution candidates from the G Pareto solution candidates selected by the Pareto solution candidate selection unit, and swaps some values ​​in one of the two Pareto solution candidates with some values ​​in the other Pareto solution candidate; and a mutation processing unit that acquires any one of the G Pareto solution candidates selected by the Pareto solution candidate selection unit, and changes some values ​​in the acquired Pareto solution candidate.

8. A Pareto solution search method, in which an evaluation value acquisition unit acquires an evaluation value of each Pareto solution candidate using the envelope analysis method from a simulator that calculates evaluation values ​​using the envelope analysis method for M (M is an integer equal to or greater than 2) Pareto solution candidates in a plurality of objective functions corresponding to a multi-objective problem whose solution is found by a genetic algorithm using the envelope analysis method, a distance calculation unit calculates a relative distance between the M Pareto solution candidates, a Pareto solution candidate selection unit selects G (G is an integer equal to or greater than 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, and a Pareto solution candidate creation unit uses one or more Pareto solution candidates out 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.

Images