Pareto solution search device and Pareto solution search method

Abstract

The Pareto solution search device is configured to be provided with: an evaluation value acquisition unit (1) that acquires, from a simulator, an evaluation value for each Pareto solution candidate in an envelope analysis method, the simulator calculates evaluation values in an 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 solved by a genetic algorithm using the envelope analysis method; and a distance calculation unit (2) that calculates the relative distance between the M Pareto solution candidates. Furthermore, the Pareto solution search device is provided with: a Pareto solution candidate selection unit (3) that 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 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 generation unit (4) that regenerates (M-G) Pareto solution candidates different from the G Pareto solution candidates, using any one or more Pareto solution candidates among the G Pareto solution candidates selected by the Pareto solution candidate selection unit (3).

Description

Technical Field

[0001] This disclosure relates to Pareto solution search apparatus and Pareto solution search method. Background Technology

[0002] There exists a device for executing a genetic algorithm to find solutions to a multi-objective problem, which repeatedly updates M (M is an integer greater than 2) Pareto solution candidates from multiple objective functions corresponding to the multi-objective problem. Pareto solution candidates are candidates for solutions that approximate the ideal solution in the multi-objective problem.

[0003] As a Pareto solution search apparatus, for example, Patent Document 1 discloses an apparatus for performing a multi-objective optimization method including a selection step and a modification step. The selection step obtains evaluation values ​​for M Pareto solution candidates from a simulator that calculates evaluation values ​​for M Pareto solution candidates among multiple objective functions. Furthermore, this selection step performs a selection process that chooses G (G is an integer greater than or equal to 1 and less than M) Pareto solution candidates with relatively high evaluation values ​​from the M Pareto solution candidates. The modification step performs a generation process that uses one or more of the G Pareto solution candidates selected in the selection step to regenerate (MG) Pareto solution candidates that are different from the G Pareto solution candidates. This modification step provides the G Pareto solution candidates selected in the selection step and the newly generated (MG) Pareto solution candidates to the simulator. The simulator calculates the evaluation values ​​for each Pareto solution candidate provided in the modification step. The selection process of the selection step and the generation process of the modification step are repeated multiple times.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Patent Application Publication No. 8-36560 Summary of the Invention

[0007] The problem that the invention aims to solve

[0008] In the multi-objective optimization method performed by the device disclosed in Patent Document 1, by repeatedly performing selection processing in the selection step and generation processing in the change step, the G Pareto solution candidates finally selected in the selection step are limited to Pareto solution candidates with relatively high evaluation values. As a result, there is a problem that the final G Pareto solution candidates sometimes lack diversity.

[0009] This disclosure was made to solve the above-mentioned problems, and its purpose is to provide a Pareto solution search device that can select a variety of Pareto solution candidates compared with the device disclosed in Patent Document 1.

[0010] Methods for solving problems

[0011] The Pareto solution search apparatus disclosed herein includes: an evaluation value acquisition unit that acquires evaluation values ​​of each Pareto solution candidate in envelope analysis from a simulator, wherein the simulator calculates the evaluation values ​​of M (M is an integer greater than or equal to 2) Pareto solution candidates from multiple objective functions corresponding to a multi-objective problem solved using a genetic algorithm employing envelope analysis; and a distance calculation unit that calculates the relative distances between the M Pareto solution candidates. Furthermore, the Pareto solution search apparatus includes: 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 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 generation unit that regenerates (MG) Pareto solution candidates that are different from the G Pareto solution candidates using one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit.

[0012] Invention Effects

[0013] According to this disclosure, compared with the device disclosed in Patent Document 1, it is possible to select a variety of Pareto solution candidates. Attached Figure Description

[0014] Figure 1 This is a structural diagram showing the Pareto solution search device of Embodiment 1.

[0015] Figure 2 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Implementation Method 1.

[0016] Figure 3 This is a hardware structure diagram of a computer that implements a Pareto solution search device through software or firmware.

[0017] Figure 4 This is a flowchart illustrating the Pareto solution search method, which is a processing device for Pareto solution search.

[0018] Figure 5 This is an explanatory diagram showing an example of a pumping system in a sewage treatment plant.

[0019] Figure 6 PS represents the M Pareto solution candidates in a multi-objective problem. m An illustration of an example of (m=1, ..., M).

[0020] Figure 7 This is an explanatory diagram showing an example of the cross-processing of the cross-processing unit 4a.

[0021] Figure 8 This is an explanatory diagram showing an example of mutation processing in mutation processing unit 4b.

[0022] Figure 9 This is a structural diagram showing the Pareto solution search device of Embodiment 2.

[0023] Figure 10 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Embodiment 2.

[0024] Figure 11 This indicates that the Pareto solution candidate PS m A diagram illustrating the levels Rk (m=1, ..., M).

[0025] Figure 12 This is a structural diagram showing the Pareto solution search device of Embodiment 3.

[0026] Figure 13 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Embodiment 3.

[0027] Figure 14 This is a structural diagram showing the Pareto solution search device of embodiment 4.

[0028] Figure 15 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Embodiment 4.

[0029] Figure 16 This is an explanatory diagram illustrating a shape correction example when the shape of the Pareto front (PF) is non-convex.

[0030] Figure 17 This is an explanatory diagram illustrating a shape correction example when the shape of the Pareto front (PF) is convex. Detailed Implementation

[0031] Hereinafter, in order to illustrate this disclosure in more detail, the manner in which this disclosure is carried out will be described with reference to the accompanying drawings.

[0032] Implementation method 1.

[0033] Figure 1 This is a configuration diagram showing the Pareto solution search device of Embodiment 1.

[0034] Figure 2 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Implementation Method 1.

[0035] Figure 1 The Pareto solution search device shown is a device for executing a genetic algorithm using the Data Envelopment Analysis (DEA) method, 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 generation unit 4.

[0036] Several methods are known to be included in DEA. Figure 1 The Pareto solution search apparatus shown is used to execute methods included in DEA, such as genetic algorithms using super CCR or genetic algorithms using CCR. However, Figure 1 The genetic algorithm used in the Pareto solution search device shown is not limited to super CCR or CCR.

[0037] Evaluation value is obtained through, for example, by... Figure 2 The evaluation value is obtained by circuit 11 as shown.

[0038] Evaluation value acquisition unit 1 obtains the evaluation values ​​of each Pareto solution candidate in DEA from the simulator. The simulator calculates the evaluation values ​​of M (M is an integer greater than 2) Pareto solution candidates in DEA from multiple objective functions corresponding to the multi-objective problem solved by the genetic algorithm of DEA.

[0039] 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 the DEA to the Pareto solution candidate selection unit 3.

[0040] Distance calculation unit 2, for example, via Figure 2 The distance calculation circuit 12 shown is implemented.

[0041] The distance calculation unit 2 obtains M Pareto solution candidates from the evaluation value acquisition unit 1.

[0042] The distance calculation unit 2 calculates the relative distances between the M Pareto solution candidates.

[0043] The distance calculation unit 2 outputs the relative distances between the M Pareto solution candidates to the Pareto solution candidate selection unit 3.

[0044] Pareto solution candidate selection part 3, for example, through Figure 2 The Pareto solution candidate selection circuit 13 shown is implemented.

[0045] The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3b.

[0046] The Pareto solution candidate selection unit 3 obtains each Pareto solution candidate and its evaluation value in DEA from the evaluation value acquisition unit 1, and obtains the relative distance between the M Pareto solution candidates from the distance calculation unit 2.

[0047] 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 based on the relative distance between the M Pareto solution candidates and the evaluation value of each Pareto solution candidate in the DEA.

[0048] The Pareto solution candidate selection unit 3 outputs the selected G Pareto solution candidates to the Pareto solution candidate generation unit 4.

[0049] 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 obtained by the evaluation value acquisition unit 1 based on the relative distance calculated by the distance calculation unit 2.

[0050] The second selection processing unit 3b selects the evaluation values ​​of N Pareto solution candidates selected by the first selection processing unit 3a from the evaluation values ​​of the M Pareto solution candidates output by the evaluation value acquisition unit 1.

[0051] 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 the N Pareto solution candidates based on the evaluation values ​​of each candidate. M ≧ N > G ≧ 1.

[0052] Pareto solution candidate generation part 4, for example, through Figure 2 The Pareto solution candidate generation circuit 14 shown is implemented.

[0053] The Pareto solution candidate generation unit 4 has a crossover processing unit 4a and a mutation processing unit 4b.

[0054] The Pareto solution candidate generation unit 4 obtains G Pareto solution candidates from the Pareto solution candidate selection unit 3.

[0055] The Pareto solution candidate generation unit 4 uses any one or more of the G Pareto solution candidates to regenerate (MG) Pareto solution candidates that are different from the G Pareto solution candidates.

[0056] The Pareto solution candidate generation unit 4 outputs the G Pareto solution candidates selected by the Pareto solution candidate selection unit 3 and the newly generated (MG) Pareto solution candidates to the simulator.

[0057] The cross-processing unit 4a selects any two Pareto solution candidates from the G Pareto solution candidates.

[0058] The cross-processing unit 4a performs cross-processing to swap a portion of the values ​​of one Pareto solution candidate with a portion of the values ​​of the other Pareto solution candidate.

[0059] The mutation processing unit 4b obtains any Pareto solution candidate from the G Pareto solution candidates.

[0060] The mutation processing unit 4b performs mutation processing on a portion of the values ​​of the obtained Pareto solution candidates.

[0061] The simulator obtains G Pareto solution candidates selected by the Pareto solution candidate selection unit 3 and (MG) Pareto solution candidates generated by the Pareto solution candidate generation unit 4, and calculates the evaluation value of each Pareto solution candidate in DEA.

[0062] The simulator outputs the evaluation values ​​of each Pareto solution candidate in the DEA to the evaluation value acquisition unit 1.

[0063] As a result, the evaluation value acquisition process of the evaluation value acquisition unit 1, the distance calculation process of the distance calculation unit 2, the Pareto solution candidate selection process of the Pareto solution candidate selection unit 3, and the Pareto solution candidate generation process of the Pareto solution candidate generation unit 4 are repeatedly performed.

[0064] exist Figure 1 In this context, it is assumed that the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate generation unit 4, which are components of the Pareto solution search device, are respectively processed by... Figure 2 The dedicated hardware implementation shown is assumed to be implemented through an evaluation value acquisition circuit 11, a distance calculation circuit 12, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate generation circuit 14.

[0065] The evaluation value acquisition circuit 11, the distance calculation circuit 12, the Pareto solution candidate selection circuit 13, and the Pareto solution candidate generation circuit 14 are respectively equivalent to 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.

[0066] The components of a Pareto solution search device are not limited to being implemented through dedicated hardware; a Pareto solution search device can also be implemented through software, firmware, or a combination of software and firmware.

[0067] Software or firmware is stored as a program in a computer's memory. A computer refers to the hardware that executes programs, such as CPU (Central Processing Unit), GPU (Graphics Processing Unit), central processing unit, processing unit, arithmetic unit, microprocessor, microcomputer, processor, or DSP (Digital Signal Processor).

[0068] Figure 3This is a hardware structure diagram of a computer that implements a Pareto solution search device through software or firmware.

[0069] When the Pareto solution search device is implemented via software or firmware, the program for instructing the computer to execute the processing procedures of the evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate generation unit 4 is stored in the memory 21. Furthermore, the computer's processor 22 executes the program stored in the memory 21.

[0070] In addition, Figure 2 The example shown illustrates how the components of a Pareto solution search apparatus are implemented using dedicated hardware. Figure 3 The example shown is an instance where a Pareto solution search device is implemented using software or firmware. However, this is just one example; it is also possible that some components of a Pareto solution search device are implemented using dedicated hardware, while the remaining components are implemented using software or firmware.

[0071] Next, regarding Figure 1 The operation of the Pareto solution search device shown is explained.

[0072] Figure 4 This is a flowchart illustrating the Pareto solution search method, which is a processing device for Pareto solution search.

[0073] In the application of the Pareto solution search device Figure 5 In the case of the sewage treatment plant pumping plan, etc., as shown, as multiple objectives, for example, three objectives (1) to (3) are set as shown below.

[0074] Figure 5 This is an illustration of an example of a pumping system in a wastewater treatment plant. However, the three objectives (1) to (3) are just one example, and other objectives may also be set.

[0075] exist Figure 5 In the pumping system shown, rainwater flows into an inflow channel and then into a pump well. The pump draws the water accumulated in the pump well into a water treatment tank. The water stored in the water treatment tank is then discharged into a river or ocean.

[0076] • Objective (1)

[0077] The goal is to avoid the risk of flooding by ensuring that sewage treatment plants are not flooded by rainwater, etc.

[0078] • Objective (2)

[0079] The goal is to reduce the cost of electricity consumption by making wastewater treatment plants consume less electricity.

[0080] • Objective (3)

[0081] The target is to set water quality limits for rivers and other water bodies that are discharged from sewage treatment plants into rivers or oceans along with rainwater.

[0082] When three objectives (1) to (3) are set as multiple objectives, the objective functions of the genetic algorithm are set as follows: for example, as shown in the following equations (1) to (3), objective function f1 related to avoiding flood risk, objective function f2 related to reducing the cost of electricity consumption, and objective function f3 related to water quality restrictions of rivers, etc.

[0083] The objective functions f1, f2, and f3 can be set by the evaluation value acquisition unit 1, or by the simulator.

[0084]

[0085] 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 choosing the larger of x and y.

[0086] y1(t) represents the water level (m) flowing into the canal at time t. STD WLW represents the water level (m) under standard conditions in the inflow channel. STD This indicates the water level range (m) under standard conditions when flowing into the channel.

[0087] y2(t) represents the electricity consumed by the wastewater treatment plant at time t.

[0088] COD(t) represents the chemical oxygen demand (g / L) of rivers, etc. at time t, TN(t) represents the total nitrogen content (g / L) of rivers, etc. at time t, and TP(t) represents the total phosphorus content (g / L) of rivers, etc. at time t.

[0089] COD Rv TN represents the limit value for chemical oxygen demand (g / L). Rv TP represents the limit value for total nitrogen (g / L). Rv This indicates the limit value (g / L) for total phosphorus.

[0090] COD Gv (t) represents the total chemical oxygen demand (COD) of rivers, etc., at time t (in kg), TN Gv (t) represents the total amount of nitrogen in the river, etc. at time t (kg), TP Gv (t) represents the total amount of phosphorus in the river, etc. at time t (kg).

[0091] COD TotalGv (t) represents the limit value (kg) of the total chemical oxygen demand (TN). TotalGvTP represents the limit value (kg) of total nitrogen. TotalGv The limit value (Kg) for the total amount of phosphorus.

[0092] The simulator calculates M (M is an integer greater than 2) Pareto solution candidates PS1~PS from multiple objective functions. M The evaluation value Ev in DEA m (m=1, ..., M).

[0093] If there are multiple objective functions f1, f2, and f3, then calculate the M Pareto candidate solutions PS1~PS1 from the objective functions f1, f2, and f3. M Each evaluation value Ev m .

[0094] Simulator calculates Pareto solution candidate PS m The evaluation value Ev of (m=1,…,M) m The processing itself is a well-known technique, so detailed explanation is omitted. Furthermore, if there are multiple objective functions f1 and f2, then, for example, the Pareto candidate solution PS can be obtained through the following evaluation formula. m Evaluation value Ev m However, the following evaluation formula is just one example of a Pareto solution candidate PS. m Evaluation value Ev m It can also be obtained through other evaluation methods.

[0095] [Evaluation style]

[0096] Ev m = (Wa × f1) + (Wb × f2)

[0097] Wa is the weight coefficient for objective function f1, and Wb is the weight coefficient for objective function f2.

[0098] In calculating the Pareto candidate solution PS of objective function f1, more emphasis is placed on objective function f1 compared to objective function f2. m Evaluation value Ev m At that time, the weighting coefficient Wa was set to a value larger than the weighting coefficient Wb. On the other hand, when calculating the Pareto candidate solution PS that places greater emphasis on objective function f2 compared to objective function f1... m Evaluation value Ev m At that time, the weight coefficient Wa was set to a value smaller than the weight coefficient Wb.

[0099] Evaluation value acquisition part 1 obtains Pareto solution candidate PS from the simulator m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m ( Figure 4Step ST1). However, after setting the Pareto solution candidate PS m At that time, the evaluation value obtained by Part 1 will be the Pareto solution candidate PS. m Send to the simulator. In this case, the evaluation value acquisition section 1 does not obtain Pareto solution candidate PS from the simulator. m Only Pareto solution candidate PS was obtained m Evaluation value Ev m .

[0100] Figure 6 PS represents the M Pareto solution candidates in a multi-objective problem. m An illustration of an example of (m=1, ..., M).

[0101] exist Figure 6 To simplify the explanation, examples are shown where the objective functions are f1 and f2 and M=10.

[0102] exist Figure 6 In the middle, black ○ represents a Pareto solution candidate PS. m .

[0103] Figure 6 The horizontal axis represents the value of the objective function f1 (x, y) as the design variables of the objective function f1 change according to the design variables x and y. For example, -1≦x≦1, -1≦y≦1.

[0104] Figure 6 The vertical axis represents the value of the objective function f2 (x, y) as the design variables of the objective function f2 change according to the design variables x and y.

[0105] The evaluation value obtained by the first part will be the Pareto solution candidate PS. m The outputs are respectively sent to the distance calculation unit 2 and the Pareto solution candidate selection unit 3, and the Pareto solution candidate PS are selected. m Evaluation value Ev m Output to Pareto solution candidate selection section 3.

[0106] Distance calculation unit 2 obtains Pareto solution candidate PS from evaluation value acquisition unit 1. m (m=1, ..., M).

[0107] Distance calculation unit 2 calculates M Pareto solution candidates PS1~PS2 M The relative distance L m (m=1, ...,M) Figure 4 Step ST2).

[0108] Distance calculation unit 2 calculates the relative distance L m Output to Pareto solution candidate selection section 3.

[0109] The relative distance L of the distance calculation unit 2 will be explained in detail below. m The calculation and processing.

[0110] If we focus on M Pareto solution candidates PS1~PS M For example, in the Pareto solution candidate PS1, the distance calculation unit 2 calculates the distance between Pareto solution candidate PS1 and Pareto solution candidate PS. m The distance L between (m=2, ..., M) 1,m As Pareto solution candidate PS1 and Pareto solution candidate PS m The distance L between 1,m For example, calculating Pareto candidate solution PS1 and Pareto candidate solution PS m The Euclidean distance between them.

[0111] If we focus on the M Pareto solution candidates PS1~PS M For example, in the Pareto solution candidate PS2, the distance calculation unit 2 calculates the Pareto solution candidate PS2 and the Pareto solution candidate PS. m The distance L between (m=1, 3, ..., M) 2,m As Pareto solution candidate PS2 and Pareto solution candidate PS m The distance L between 2,m For example, calculating Pareto candidate solution PS2 and Pareto candidate solution PS m The Euclidean distance between them.

[0112] If we focus on M Pareto solution candidates PS1~PS M For example, the Pareto solution candidate PS M Then, the distance calculation unit 2 calculates the Pareto solution candidate PS. M With Pareto solution candidate PS m The distance L between (m=1, ..., M-1) M,m PS as a Pareto solution candidate M With Pareto solution candidate PS m The distance L between M,m For example, calculating Pareto candidate PS M With Pareto solution candidate PS m The Euclidean distance between them.

[0113] The first selection processing unit 3a of the Pareto solution candidate selection unit 3 obtains the Pareto solution candidate PS from the evaluation value acquisition unit 1. m (m=1,…,M), obtain M Pareto solution candidates PS1~PS from distance calculation unit 2. M Relative distance between PS m (m=1, ..., M).

[0114] The first selection processing unit 3a selects each Pareto solution candidate PS. m (m=1,…,M), calculate (M-1) distances L m The sum of these values ​​is used as the crowding distance ΣL m .

[0115] Specifically, if we focus on M Pareto solution candidates PS1~PS M For example, in the Pareto solution candidate PS1, the first selection processing unit 3a calculates (M-1) distances L as shown in the following equation (5). 1,m The sum of these values ​​is used as the crowding distance ΣL1.

[0116] ΣL1=L 1,2 +L 1,3 +…+L 1,M (5)

[0117] If we focus on M Pareto solution candidates PS1~PS M For example, in the Pareto solution candidate PS2, the first selection processing unit 3a calculates (M-1) distances L as shown in the following equation (6). 2,m The sum of these values ​​is used as the crowding distance ΣL2.

[0118] ΣL2=L 2,1 +L 2,3 +…+L 2,M (6)

[0119] If we focus on M Pareto solution candidates PS1~PS M For example, the Pareto solution candidate PS M Then, the first selection processing unit 3a calculates (M-1) distances L as shown in the following equation (7). M,m The sum of these values ​​is used as the crowding distance ΣL M .

[0120] ΣL M =L M,1 +L M,2 +…+L M,M-1 (7)

[0121] The first selection processing unit 3a compares the M congestion distances ΣL1~ΣL. M .

[0122] First selection processing unit 3a is based on congestion distance ΣL1~ΣL M The comparison results show that from M Pareto solution candidates PS1~PS M In the selection process, N (where N is an integer greater than 1 and less than M) Pareto solution candidates with relatively large crowding distance ΣL are chosen first. Figure 4 Step ST3).

[0123] The first selection processing unit 3a selects N Pareto solution candidates PS'1~PS' N The output is sent to the second selection processing unit 3b.

[0124] The first selection processing unit 3a selects N Pareto solution candidates PS'1~PS' based on the congestion distance ΣL. N This increases the diversity of Pareto solution candidates.

[0125] The second selection processing unit 3b obtains Pareto solution candidates PS from the evaluation value acquisition unit 1. m The evaluation value Ev of (m=1,…,M) m N Pareto solution candidates PS'1~PS' are obtained from the first selection processing unit 3a. N .

[0126] The second selection processing unit 3b selects from M evaluation values ​​Ev1 to Ev M Select from N Pareto solution candidates PS'1~PS' N The corresponding evaluation values ​​are Ev'1~Ev' N .

[0127] The second selection processing unit 3b is based on N Pareto solution candidates PS'1~PS' N Each evaluation value Ev' n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G ( Figure 4 Step ST4).

[0128] Specifically, the second selection processing unit 3b selects from N Pareto solution candidates PS'1~PS' N Select the evaluation value Ev' n The relatively high number of upper G Pareto solution candidates PS"1~PS" G .

[0129] The second selection processing unit 3b selects the G Pareto solution candidates PS1~PS2. G Output to Pareto solution candidate generator 4.

[0130] Pareto solution candidate generation unit 4 obtains G Pareto solution candidates PS1~PS1 from Pareto solution candidate selection unit 3. G .

[0131] Pareto solution candidate generator 4 uses G Pareto solution candidates PS1~PS1 GGiven any one or more Pareto solution candidates, regenerate (MG) Pareto solution candidates that are different from the G Pareto solution candidates.

[0132] The Pareto solution candidate generation unit 4 outputs G Pareto solution candidates and (MG) Pareto solution candidates to the simulator.

[0133] The following describes in detail the generation process of (MG) Pareto solution candidates in Pareto solution candidate generation unit 4.

[0134] Cross-processing unit 4a extracts G Pareto solution candidates PS1~PS1 from G Pareto solutions. G Obtain any two Pareto solution candidates.

[0135] For ease of explanation, let any two Pareto solution candidates be PS”1 and PS”2.

[0136] like Figure 7 As shown, the cross-processing unit 4a performs cross-processing by swapping a portion of the values ​​of Pareto solution candidate PS”1 and a portion of the values ​​of Pareto solution candidate PS”2 according to the cross-processing probability. Figure 4 Step ST5). Cross-processing is a well-known technique, so detailed explanation is omitted.

[0137] Figure 7 This is an explanatory diagram showing an example of the cross-processing of the cross-processing unit 4a.

[0138] Cross-processing is performed by cross-processing unit 4a, which increases the diversity of Pareto solution candidates.

[0139] exist Figure 7 In the example, bits 4 to 6 of Pareto solution candidate PS”1, “111”, and bits 4 to 6 of Pareto solution candidate PS”2, “000”, are swapped.

[0140] Here, the cross-processing unit 4a performs cross-processing to swap a portion of the values ​​of Pareto solution candidate PS”1 and a portion of the values ​​of Pareto solution candidate PS”2. However, this is just one example. In addition to performing cross-processing to swap a portion of the values ​​of Pareto solution candidate PS”1 and a portion of the values ​​of Pareto solution candidate PS”2, the cross-processing unit 4a may also perform cross-processing to swap a portion of the values ​​of Pareto solution candidate PS”3 and a portion of the values ​​of Pareto solution candidate PS”4.

[0141] Hereinafter, the Pareto solution candidate after cross-processing in cross-processing unit 4a will be referred to as PS. Cr .

[0142] Mutation processing unit 4b selects G Pareto solution candidates PS1~PS1 from G Pareto solutions. G We can obtain any Pareto solution candidate from the given information.

[0143] Here, for ease of explanation, let any Pareto solution candidate be PS”3.

[0144] like Figure 8 As shown, the mutation processing unit 4b performs mutation processing that randomly changes a portion of the values ​​of the Pareto solution candidate PS”3 according to the mutation probability. Figure 4 Step ST6). Mutation treatment itself is a well-known technique, so detailed explanation is omitted.

[0145] Figure 8 This is an explanatory diagram showing an example of mutation processing in mutation processing unit 4b.

[0146] By implementing mutation processing through mutation processing unit 4b, the diversity of Pareto solution candidates is improved.

[0147] exist Figure 8 In the example, the 3rd bit of the Pareto solution candidate PS”3 is changed from “0” to “2”, and the 5th bit of the Pareto solution candidate PS”3 is changed from “0” to “3”.

[0148] Hereinafter, the Pareto solution candidate after mutation processing in mutation processing unit 4b will be referred to as PS. Mu .

[0149] If the number of processing steps in the series of processes—including evaluation value acquisition unit 1, distance calculation unit 2, Pareto solution candidate selection unit 3, and Pareto solution candidate generation unit 4—does not reach H times ( Figure 4 Step ST7: (If "No"), then the Pareto solution candidate generation unit 4 will select the G Pareto solution candidates PS1~PS1 from the Pareto solution candidate selection unit 3. G Candidate PS of Pareto solution after cross-processing Cr Candidate PS of Pareto solution after mutation treatment Mu Provided to the simulator. H is an integer greater than or equal to 1.

[0150] The simulator calculates G Pareto solution candidates PS1~PS2. G The various evaluation values ​​and the candidate Pareto solutions PS after cross-processing Cr Evaluation values ​​and candidate Pareto solutions after mutation treatment Mu The evaluation value is used as one of the M Pareto solution candidates PS1~PS in multiple objective functions. M Each evaluation value Ev m (m=1, ..., M).

[0151] The simulator will generate M Pareto solution candidates PS1~PS M And M Pareto solution candidates PS1~PS M Each evaluation value Ev m(m=1, ..., M) is output to the evaluation value acquisition unit 1.

[0152] The evaluation value acquisition unit 1, the distance calculation unit 2, the Pareto solution candidate selection unit 3, and the Pareto solution candidate generation unit 4 are implemented respectively. Figure 4 The processing of steps ST1 to ST6.

[0153] If the number of processing steps in the series of steps 1 (evaluation value acquisition unit), 2 (distance calculation unit), 3 (Pareto solution candidate selection unit), and 4 (Pareto solution candidate generation unit) reaches H times ( Figure 4 Step ST7: If "yes", then the Pareto solution candidate generation unit 4 will select the G Pareto solution candidates PS1~PS1 from the Pareto solution candidate selection unit 3. G The final selection result of the Pareto solution is displayed on, for example, a display device not shown.

[0154] In Embodiment 1 described above, the Pareto solution search device is configured to include: an evaluation value acquisition unit 1, which acquires the evaluation values ​​of each Pareto solution candidate in the envelope analysis method from a simulator, and the simulator calculates the evaluation values ​​of M (M is an integer greater than or equal to 2) Pareto solution candidates from multiple objective functions corresponding to a multi-objective problem solved using a genetic algorithm of the envelope analysis method; and a distance calculation unit 2, which calculates the relative distances between the M Pareto solution candidates. Furthermore, the Pareto solution search device includes: a Pareto solution candidate selection unit 3, which 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 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 generation unit 4, which regenerates (MG) Pareto solution candidates that are different from the G Pareto solution candidates using one or more of the G Pareto solution candidates selected by the Pareto solution candidate selection unit 3. Therefore, compared with the device disclosed in Patent Document 1, the Pareto solution search device is able to select a variety of Pareto solution candidates.

[0155] exist Figure 1 In the Pareto solution search apparatus shown, the first selection processing unit 3a calculates (M-1) distances L. m The sum of these values ​​is used as the crowding distance ΣL m (m=1, ..., M). However, this is just one example; the first selection processing unit 3a can also calculate (M-1) distances L. m The average value is used as the crowding distance ΣL m (m=1, ..., M). In this case, the first selection processing unit 3a is also based on the congestion distance ΣL1~ΣL M The comparison results show that from M Pareto solution candidates PS1~PS MIn the selection process, the N Pareto solution candidates with relatively large crowding distance ΣL are given priority.

[0156] exist Figure 1 In the Pareto solution search device shown, the second selection processing unit 3b selects from N Pareto solution candidates PS'1~PS' N Select the evaluation value Ev' n The relatively high number of upper G Pareto solution candidates PS"1~PS" G However, this is just one example; the second selection processing unit 3b can also select G Pareto solution candidates PS1~PS1 through binary competition. G .

[0157] The binary competition method is processed as follows: From N Pareto solution candidates PS'1~PS' N Two Pareto solution candidates PS' are randomly selected, and the evaluation value Ev' of the two Pareto solution candidates PS' is selected. n The high number of Pareto solution candidates is determined. This process is repeated using a binary competition method until G Pareto solution candidates PS"1~PS" are selected. G until.

[0158] Implementation method 2.

[0159] In Embodiment 2, a Pareto solution search device equipped with a level determination unit 5 will be described. This level determination unit 5 is based on the evaluation value Ev obtained by the evaluation value acquisition unit 1. m (m=1,…,M) Determine M Pareto solution candidates PS1~PS M Based on the ranking results, candidate Pareto solutions PS are determined in multiple levels of Rk. m The level it belongs to is Rk.

[0160] Figure 9 This is a structural diagram showing the Pareto solution search device according to Embodiment 2. Figure 9 In, with Figure 1 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0161] Figure 10 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Embodiment 2. Figure 10 In, with Figure 2 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0162] Figure 9 The Pareto solution search device shown 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 determination unit 5, a Pareto solution candidate selection unit 3, and a Pareto solution candidate generation unit 4.

[0163] Level determination section 5, for example, through Figure 10 The grade determination circuit 15 shown is implemented.

[0164] The rating determination section 5 obtains Pareto solution candidate PS from the evaluation value obtained from section 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0165] The rating determination section 5 is based on the evaluation value Ev. m Determine M Pareto solution candidates PS1~PS M The advantages and disadvantages.

[0166] Based on the results of the superiority / inferiority assessment, the ranking determination unit 5 identifies Pareto solution candidate PS among multiple ranks Rk. m The level Rk to which (m=1, ..., M) belongs.

[0167] The grading determination department 5 will determine the Pareto candidate PS. m The level Rk of (m=1, ..., M) is output to the Pareto solution candidate selection part 3.

[0168] Pareto solution candidate selection part 3, for example, through Figure 10 The Pareto solution candidate selection circuit 13 shown is implemented.

[0169] The Pareto solution candidate selection unit 3 includes a first selection processing unit 3c and a second selection processing unit 3b.

[0170] First selection processing unit 3c and Figure 1 Similarly, the first selection processing unit 3a shown obtains Pareto solution candidate PS from the evaluation value acquisition unit 1. m (m=1,…,M), obtain M Pareto solution candidates PS1~PS from distance calculation unit 2. M The relative distance L m (m=1, ..., M).

[0171] First selection processing unit 3c and Figure 1 Similarly, the first selection processing unit 3a shown is based on the relative distance L. m (m=1,…,M), from the M Pareto solution candidates PS1~PS1 obtained by the evaluation value acquisition part 1. M Select N Pareto solution candidates PS'1~PS' N .

[0172] However, the first selection processing unit 3c and Figure 1 Unlike the first selection processing unit 3a shown, this unit uses a Pareto solution candidate PS' with a total of N selections, based on the relative distance L.m (m=1,…,M), select Pareto solution candidate PS' from the Pareto solution candidate PS belonging to each level Rk.

[0173] exist Figure 9 In this context, it is assumed that the evaluation value acquisition unit 1, distance calculation unit 2, level determination unit 5, Pareto solution candidate selection unit 3, and Pareto solution candidate generation unit 4, which are components of the Pareto solution search device, are respectively processed by... Figure 10 The dedicated hardware implementation shown is as follows. That is, it is assumed that the Pareto solution search device is implemented through an evaluation value acquisition circuit 11, a distance calculation circuit 12, a grade determination circuit 15, a Pareto solution candidate selection circuit 13, and a Pareto solution candidate generation circuit 14.

[0174] The evaluation value acquisition circuit 11, the distance calculation circuit 12, the grade determination circuit 15, the Pareto solution candidate selection circuit 13, and the Pareto solution candidate generation circuit 14 are respectively equivalent to a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0175] The components of a Pareto solution search device are not limited to being implemented through dedicated hardware; a Pareto solution search device can also be implemented through software, firmware, or a combination of software and firmware.

[0176] When the Pareto solution search device is implemented through software or firmware, the program for enabling the computer to execute the processing procedures of the evaluation value acquisition unit 1, distance calculation unit 2, grade determination unit 5, Pareto solution candidate selection unit 3, and Pareto solution candidate generation unit 4 is stored in... Figure 3 The memory 21 shown. And, Figure 3 The processor 22 shown executes the program stored in the memory 21.

[0177] In addition, Figure 10 The example shown illustrates how the components of a Pareto solution search apparatus are implemented using dedicated hardware. Figure 3 The example shown is an instance where the Pareto solution search apparatus is implemented by software or firmware. However, this is just one example; it is also possible that some components of the Pareto solution search apparatus are implemented by dedicated hardware, while the remaining components are implemented by software or firmware.

[0178] Next, regarding Figure 9 The operation of the Pareto solution search device shown will be explained. However, apart from the level determination unit 5 and the first selection processing unit 3c, the operation is similar to... Figure 1 The Pareto solution search device shown is the same. Therefore, the operation of the level determination unit 5 and the first selection processing unit 3c will be explained here.

[0179] The rating determination section 5 obtains Pareto solution candidate PS from the evaluation value obtained from section 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0180] The rating determination section 5 is based on the evaluation value Ev. m Determine M Pareto solution candidates PS1~PS M The advantages and disadvantages.

[0181] The following details the process for determining the quality of grade 5.

[0182] Here, for ease of explanation, the description of the classification section 5 determining the Pareto solution candidate PS is provided. m And Pareto solution candidate PS m+1 Examples of their advantages and disadvantages.

[0183] The ranking determination section 5 compares Pareto solutions for candidate PS. m Evaluation value Ev m And Pareto solution candidate PS m+1 Evaluation value Ev m+1 .

[0184] If the Pareto solution is a candidate PS m Evaluation value Ev m Higher than Pareto solution candidate PS m+1 Evaluation value Ev m+1 Then, the grading determination department 5 determines it to be a Pareto solution candidate PS. m Outperforming Pareto solution candidate PS m+1 .

[0185] If the Pareto solution is a candidate PS m Evaluation value Ev m Candidate PS below Pareto solution m+1 Evaluation value Ev m+1 Then, the grading determination department 5 determines it to be a Pareto solution candidate PS. m Inferior to Pareto solution candidate PS m+1 .

[0186] Based on the results of the superiority / inferiority assessment, the ranking determination department 5 calculates the Pareto solution candidate PS. m The level Rk of (m=1, ..., M).

[0187] The following is a detailed explanation of the calculation and processing of level Rk in level determination section 5.

[0188] exist Figure 6In the example, let's assume that when focusing on Pareto solution candidate PS1, the two Pareto solution candidates with the same evaluation value Ev1 as Pareto solution candidate PS1 are Pareto solution candidate PS2 and Pareto solution candidate PS3. Additionally, let's assume Pareto solution candidates PS4~PS... 10 Evaluation value Ev4~Ev 10 It is lower than the evaluation value Ev1 of the Pareto solution candidate PS1.

[0189] In this case, the Pareto solution candidates PS1, PS2, and PS3 are respectively as follows: Figure 11 The class shown is classified as level Rk1, which is the highest level.

[0190] Figure 11 This indicates that the Pareto solution candidate PS m A diagram illustrating the levels Rk (m=1, ..., M).

[0191] Suppose that, when considering Pareto solution candidate PS4, the four Pareto solution candidates PS5 through PS8 have the same evaluation value Ev4 as PS4. Additionally, suppose that Pareto solution candidates PS9 through PS... 10 Evaluation value Ev9~Ev 10 It is lower than the evaluation value Ev4 of the Pareto solution candidate PS4.

[0192] In this case, Pareto solution candidates PS4~PS8 are classified as level Rk2, which is the second highest level.

[0193] Suppose that, when considering Pareto solution candidate PS9, a Pareto solution candidate with the same evaluation value Ev9 as Pareto solution candidate PS9 is a Pareto solution candidate PS9. 10 This one. Additionally, let's assume Pareto solution candidates PS9~PS 10 Evaluation value Ev9~Ev 10 It is lower than the evaluation value Ev4 of the Pareto solution candidate PS4.

[0194] In this case, the Pareto solution candidate is PS9~PS 10 They are classified as level Rk3, which is the third highest level.

[0195] Here, we assume 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 is not limited to the evaluation value Ev1 and evaluation value Ev2 being strictly consistent. For example, if the difference between the evaluation value Ev1 and evaluation value Ev2 is below a certain threshold, then they can also be regarded as the same evaluation value.

[0196] The grading determination department 5 will determine the Pareto candidate PS. mThe level Rk of (m=1, ..., M) is output to the Pareto solution candidate selection part 3.

[0197] The first selection processing unit 3c of the Pareto solution candidate selection unit 3 obtains the Pareto solution candidate PS from the evaluation value acquisition unit 1. m (m=1,…,M), obtain M Pareto solution candidates PS1~PS from distance calculation unit 2. M The relative distance L m (m=1, ..., M).

[0198] In addition, the first selection processing unit 3c obtains Pareto solution candidate PS from the level determination unit 5. m The level is Rk.

[0199] If the number of Pareto solution candidates selected by the second selection processing unit 3b is G, then the first selection processing unit 3c will select from the M Pareto solution candidates PS1~PS2. M The number of Pareto solution candidates N selected is set to be greater than G and less than M.

[0200] The first selection processing unit 3c selects M Pareto solution candidates PS1~PS2. M In the middle, priority is given to selecting Pareto solution candidates PS that are classified as high-level. m And select one or more Pareto solution candidate PS that are classified into a certain level m When selecting all Pareto solution candidate PSs classified into a certain level, m .

[0201] Therefore, in Figure 11 In the example, if it is any power of G from 1 to 3, then N is set to 3; if it is any power of G from 4 to 8, then N is set to 8; and if it is any power of G from 9 to 10, then N is set to 10.

[0202] The first selection processing unit 3c selects M Pareto solution candidates PS1~PS2. M Select N Pareto solution candidates PS'1~PS' N .

[0203] exist Figure 11 In the example, if N=3, then the first selection processing unit 3c selects three Pareto solution candidates PS1~PS3 that are classified as level Rk1.

[0204] If N=8, then the first selection processing unit 3c selects three Pareto solution candidates PS1~PS3 classified as level Rk1 and five Pareto solution candidates PS4~PS8 classified as level Rk2.

[0205] For example, if N=10, then the first selection processing unit 3c selects three Pareto solution candidates PS1~PS3 classified as level Rk1, five Pareto solution candidates PS4~PS8 classified as level Rk2, and two Pareto solution candidates PS9~PS8 classified as level Rk3. 10 .

[0206] The second selection processing unit 3b is based on the N Pareto solution candidates PS'1~PS' selected by the first selection processing unit 3c. N Each evaluation value Ev' n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G .

[0207] exist Figure 11 In the example, if G=1, then the second selection processing unit 3b selects any one of the three Pareto solution candidates PS1~PS3 classified as level Rk1. If there are several differences in the evaluation values ​​Ev1~Ev3 of the three Pareto solution candidates PS1~PS3, the Pareto solution candidate with the highest evaluation value is selected. If all evaluation values ​​Ev1~Ev3 are the same, then any Pareto solution candidate is selected.

[0208] If G=2, then the second selection processing unit 3b selects any two Pareto solution candidates from the three Pareto solution candidates PS1~PS3 classified as level Rk1. In this case, if there are some differences in the evaluation values ​​Ev1~Ev3, then the two Pareto solution candidates with the relatively higher evaluation values ​​are also selected. If all values ​​Ev1~Ev3 are the same, then two arbitrary Pareto solution candidates are selected.

[0209] If G=3, then the second selection processing unit 3b selects all three Pareto solution candidates PS1~PS3 that are classified as level Rk1.

[0210] If G is any of the values ​​from 4 to 8, then the second selection processing unit 3b selects one to five Pareto solution candidates from the three Pareto solution candidates PS1 to PS3 classified as level Rk1 and the eight Pareto solution candidates PS4 to PS8 classified as level Rk2. In this case, for example, one to five Pareto solution candidates with relatively high evaluation values ​​are selected from the five Pareto solution candidates PS4 to PS8.

[0211] If G is any square from 9 to 10, then the second selection processing unit 3b selects three Pareto solution candidates PS1~PS3 classified as level Rk1, five Pareto solution candidates PS4~PS8 classified as level Rk2, and two Pareto solution candidates PS9~PS8 classified as level Rk3. 10 One or more but no more than two Pareto solution candidates. In this case, for example, also from two Pareto solution candidates PS9~PS 10 Choose one or more but no more than two Pareto solution candidates with relatively high evaluation values.

[0212] The second selection processing unit 3b selects the G Pareto solution candidates PS1~PS2. G Output to Pareto solution candidate generator 4.

[0213] exist Figure 9 In the Pareto solution search apparatus shown, the first selection processing unit 3c selects one or more Pareto solution candidates PS that are classified into a certain level. m When selecting all Pareto solution candidate PSs classified into a certain level, m Specifically, in Figure 11 In the example, if G is any of the numbers 1 to 3, the first selection processing unit 3c sets N to 3; if G is any of the numbers 4 to 8, the first selection processing unit 3c sets N to 8; and if G is any of the numbers 9 to 10, the first selection processing unit 3c sets N to 10. However, N only needs to be less than M and greater than G, and is not limited to the settings described above.

[0214] For example, when N=5, the first selection processing unit 3c selects two Pareto solution candidates from the three Pareto solution candidates PS1~PS3 classified as level Rk1 and the five Pareto solution candidates PS4~PS8 classified as level Rk2. In this case, the relative distance L is selected from the five Pareto solution candidates PS4~PS8. m (m=4,…,8) The two largest Pareto solution candidates are the uppermost two.

[0215] For example, when N=9, the first selection processing unit 3c selects three Pareto solution candidates PS1~PS3 classified as level Rk1, five Pareto solution candidates PS4~PS8 classified as level Rk2, and two Pareto solution candidates PS9~PS8 classified as level Rk3. 10 One Pareto solution candidate. In this case, from two Pareto solution candidates PS9~PS 10 Select relative distance L m Candidate Pareto solutions with m=9 or 10.

[0216] In Embodiment 2 described above, the Pareto solution search device is configured to include a level determination unit 5. This level determination unit 5 determines the merits of M Pareto solution candidates based on evaluation values ​​obtained by the evaluation value acquisition unit 1, and determines the level to which each Pareto solution candidate belongs from multiple levels based on the merits determination results. Furthermore, the first selection processing unit 3c of the Pareto solution search device selects Pareto solution candidates from those belonging to each level based on relative distance, with a total of N Pareto solution candidate selections. Therefore, compared to the device disclosed in Patent Document 1, the Pareto solution search device can select a greater diversity of Pareto solution candidates.

[0217] Implementation method 3.

[0218] In embodiment 3, a Pareto solution search device equipped with an evaluation value correction unit 6 will be described. This evaluation value correction unit 6 adjusts the M Pareto solution candidates PS1~PS2 to make them more compatible. M The evaluation values ​​of all Pareto solution candidates included in the Pareto front are corrected by ensuring that the evaluation value of all Pareto solution candidates included in the Pareto front is greater than or equal to 1.

[0219] Figure 12 This is a structural diagram showing the Pareto solution search device according to Embodiment 3. Figure 12 In, with Figure 1 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0220] Figure 13 This is a hardware structure diagram showing the hardware of the Pareto solution search device in Embodiment 3. Figure 13 In, with Figure 2 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0221] Figure 12 The Pareto solution search device shown 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 generation unit 4.

[0222] Evaluation value correction unit 6, for example, through Figure 13 The evaluation value correction circuit 16 shown is implemented.

[0223] Evaluation value correction unit 6 obtains Pareto solution candidate PS from evaluation value acquisition unit 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0224] Evaluation value correction unit 6 is based on Pareto solution candidate PS m Evaluation value Evm Determine M Pareto solution candidates PS1~PS M The Pareto front PF contains Pareto solution candidate PS PFj (j=1, ..., J). J is an integer greater than 1 and less than M.

[0225] Evaluation value correction unit 6 ensures that the Pareto front PF includes all Pareto solution candidates PS. PF1 ~PS PFJ Evaluation value Ev PFj In a manner where (j=1, ..., J) are greater than or equal to 1, all Pareto solution candidate PSs included in the Pareto front PF are corrected. PF1 ~PS PFJ Evaluation value Ev PFj .

[0226] Evaluation value correction unit 6 corrects the evaluation values ​​for the Pareto solution candidate PS. PF1 ~PS PFJ The corrected evaluation value Ev is output to the distance calculation unit 7 and the Pareto solution candidate selection unit 3 respectively. PFj Output to Pareto solution candidate selection section 3.

[0227] Distance calculation unit 7, for example, via Figure 13 The distance calculation circuit 17 shown is implemented.

[0228] Distance calculation unit 7 obtains the Pareto solution candidate PS after evaluation value correction from evaluation value correction unit 6. PF1 ~PS PFJ .

[0229] Distance calculation unit 7 obtains M Pareto solution candidates PS1~PS1 from evaluation value acquisition unit 1. M Candidate PS of Pareto solutions not included in the Pareto front PF m .

[0230] Distance calculation unit 7 calculates the Pareto solution candidate PS after evaluation value correction. PF1 ~PS PFJ Pareto solution candidate PS not included in the Pareto front (PF) m M Pareto solution candidates PS1~PS M The relative distance L m .

[0231] The distance calculation unit 7 will select M Pareto solution candidates PS1~PS2. M The relative distance L m Output to Pareto solution candidate selection section 3.

[0232] Pareto solution candidate selection part 3, for example, through Figure 13The Pareto solution candidate selection circuit 13 shown is implemented.

[0233] The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3d.

[0234] The second selection processing unit 3d is based on the N Pareto solution candidates PS'1~PS' selected by the first selection processing unit 3a. N Each evaluation value Ev n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G .

[0235] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is a Pareto solution candidate PS included in the Pareto front PF PFj Then the second selection processing unit 3d uses the evaluation value Ev corrected by the evaluation value correction unit 6. PFj 'As an evaluation value Ev n .

[0236] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is a Pareto solution candidate PS not included in the Pareto front PF m Then the second selection processing unit 3d uses the evaluation value Ev obtained by the evaluation value acquisition unit 1. m As an evaluation value Ev n .

[0237] exist Figure 12 In this context, it is assumed that 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 generation unit 4, which are components of the Pareto solution search device, are respectively processed by... Figure 13 The dedicated hardware implementation shown is as follows. That is, it is assumed that the Pareto solution search device is implemented through 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 generation circuit 14.

[0238] 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 generation circuit 14 are respectively equivalent to, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0239] The components of a Pareto solution search device are not limited to being implemented through dedicated hardware; a Pareto solution search device can also be implemented through software, firmware, or a combination of software and firmware.

[0240] When the Pareto solution search device is implemented by software or firmware, the program for enabling the computer to execute the processing procedures 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 generation unit 4 is stored in... Figure 3 The memory 21 shown. And, Figure 3 The processor 22 shown executes the program stored in the memory 21.

[0241] In addition, Figure 13 The example shown illustrates how the components of a Pareto solution search apparatus are implemented using dedicated hardware. Figure 3 The example shown is an instance where the Pareto solution search apparatus is implemented by software or firmware. However, this is just one example; it is also possible that some components of the Pareto solution search apparatus are implemented by dedicated hardware, while the remaining components are implemented by software or firmware.

[0242] Next, regarding Figure 12 The operation of the Pareto solution search device shown will be explained. However, apart from the evaluation value correction unit 6, the distance calculation unit 7, and the second selection processing unit 3d, the operation is similar to... Figure 1 The Pareto solution search device shown is the same. Therefore, here, the operation of the evaluation value correction unit 6, the distance calculation unit 7, and the second selection processing unit 3d will be mainly explained.

[0243] Evaluation value correction unit 6 obtains Pareto solution candidate PS from evaluation value acquisition unit 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0244] Evaluation value correction unit 6 is based on Pareto solution candidate PS m Evaluation value Ev m Determine M Pareto solution candidates PS1~PS M The Pareto front (PF) in the Pareto equation contains Pareto solution candidate PS. PFj (j=1, ..., J).

[0245] Suppose that the Pareto front (PF) contains candidate Pareto solutions (PS). PFj For example, PS is a Pareto solution candidate belonging to level Rk1. m The evaluation value correction unit 6 can also be used with Figure 9 The grade determination unit 5 shown similarly determines the Pareto solution candidate PS belonging to grade Rk1. m .

[0246] Evaluation value correction unit 6 ensures that the Pareto front PF includes all Pareto solution candidates PS. PF1 ~PS PFJ Evaluation value EvPFj In a manner where (j=1, ..., J) are greater than or equal to 1, all Pareto solution candidate PSs included in the Pareto front PF are corrected. PF1 ~PS PFJ Evaluation value Ev PFj .

[0247] Here, let the Pareto front (PF) include Pareto solution candidates such as PS1 to PS3, with the evaluation value Ev1 of PS1 being "1.1", the evaluation value Ev2 of PS2 being "1.05", and the evaluation value Ev3 of PS3 being "0.95". The correction process of the evaluation value correction unit 6 will be explained in detail below.

[0248] As shown in Equation (8) below, the evaluation value correction unit 6 calculates the coefficient α of the evaluation value Ev3 of the Pareto solution candidate PS3 with the smallest evaluation value among the Pareto solution candidates PS1~PS3, which is “1.0”.

[0249]

[0250] The evaluation value correction unit 6, as shown in the following equation (9), corrects the evaluation values ​​Ev1 to Ev3 of the Pareto solution candidates PS1 to PS3 by multiplying them by the coefficient α.

[0251] Ev PF1 =Ev1×α=1.1×1.053=1.158

[0252] Ev PF2 =Ev²×α=1.05×1.05³=1.106

[0253] Ev PF3 =Ev3×α=0.95×1.053=1.000 (9)

[0255] In equation (9), Ev1', Ev2', and Ev3' are the corrected evaluation values, respectively.

[0256] Evaluation value correction unit 6 corrects the evaluation value Ev PF1 '、Ev PF2 '、Ev PF3 The data is output to the distance calculation unit 7 and the second selection processing unit 3d, respectively.

[0257] Distance calculation unit 7 obtains the Pareto solution candidate PS after evaluation value correction from evaluation value correction unit 6. PF1 ~PS PFJ .

[0258] Distance calculation unit 7 obtains M Pareto solution candidates PS1~PS1 from evaluation value acquisition unit 1. MCandidate PS of Pareto solutions not included in the Pareto front PF m .

[0259] Distance calculation unit 7 calculates the Pareto solution candidate PS after evaluation value correction. PF1 ~PS PFJ Pareto solution candidate PS not included in the Pareto front (PF) m M Pareto solution candidates PS1~PS M The relative distance L m M Pareto solution candidates PS1~PS M The relative distance L m The computational processing itself and Figure 1 The distance calculation unit 2 shown is the same.

[0260] The distance calculation unit 7 will select M Pareto solution candidates PS1~PS2. M The relative distance L m Output to Pareto solution candidate selection section 3.

[0261] As described in Embodiment 1, the first selection processing unit 3a selects from M Pareto solution candidates PS1~PS2 M Select N Pareto solution candidates PS'1~PS' N N Pareto solution candidates PS'1~PS' N Output to the second selection processing unit 3d.

[0262] The second selection processing unit 3d obtains N Pareto solution candidates PS'1~PS' from the first selection processing unit 3a. N .

[0263] The second selection processing unit 3d obtains the corrected evaluation value Ev from the evaluation value correction unit 6. PFj (j=1,…,J), obtain Pareto solution candidate PS not included in the Pareto front PF from the evaluation value acquisition part 1. m Evaluation value Ev m .

[0264] The second selection processing unit (3D) is based on N Pareto solution candidates PS'1~PS'. N Each evaluation value Ev n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G .

[0265] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is a Pareto solution candidate PS included in the Pareto front PF PFjThen the second selection processing unit 3d uses the evaluation value Ev corrected by the evaluation value correction unit 6. PFj 'As an evaluation value Ev n .

[0266] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is a Pareto solution candidate PS not included in the Pareto front PF m Then the second selection processing unit 3d uses the evaluation value Ev obtained by the evaluation value acquisition unit 1. m As an evaluation value Ev n .

[0267] In the above implementation method 3, Figure 12 The Pareto solution search device shown is configured to include an evaluation value correction unit 6. This unit 6, based on the evaluation values ​​obtained by the evaluation value acquisition unit 1, determines all Pareto solution candidates included in the Pareto front from among the M Pareto solution candidates, and corrects the evaluation values ​​of all Pareto solution candidates included in the Pareto front in such a way that the evaluation value of all Pareto solution candidates included in the Pareto front is 1 or higher. Furthermore, Figure 12 The Pareto solution candidate selection unit 3 of the Pareto solution search device shown 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 front among the M Pareto solution candidates. Therefore, Figure 12 The Pareto solution search device shown is Figure 1 Similarly, the Pareto solution search device shown, compared to the device disclosed in Patent Document 1, is able to select a greater variety of Pareto solution candidates. Furthermore, Figure 12 The Pareto solution search apparatus shown can increase the probability of selecting Pareto solution candidates contained in the Pareto front.

[0268] Implementation method 4.

[0269] In Embodiment 4, a Pareto solution search device equipped with a shape correction unit 8 will be described. This shape correction unit 8 corrects M Pareto solution candidates PS1 to PS2. M The Pareto solution candidates included in the Pareto front are used to correct the shape of the Pareto front.

[0270] Figure 14 This is a structural diagram showing the Pareto solution search device of Embodiment 4. Figure 14 In, with Figure 1 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0271] Figure 15 This is a hardware structure diagram illustrating the Pareto solution search device of Embodiment 4. Figure 15 In, with Figure 2 The same symbols represent the same or equivalent parts, so detailed explanations are omitted.

[0272] Figure 14 The Pareto solution search device shown 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 generation unit 4.

[0273] Shape correction unit 8, for example, through Figure 15 The shape correction circuit 18 shown is implemented.

[0274] Shape correction unit 8 obtains Pareto solution candidate PS from evaluation value acquisition unit 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0275] Shape correction unit 8 is based on Pareto solution candidate PS m Evaluation value Ev m Determine M Pareto solution candidates PS1~PS M The Pareto front (PF) in the Pareto equation contains Pareto solution candidate PS. PFj (j=1, ..., J). J is an integer greater than 1 and less than M.

[0276] The shape correction unit 8 corrects the Pareto solution candidate PS contained in the Pareto front PF. PFj Correct the shape of the Pareto front (PF).

[0277] The shape correction unit 8 will correct the Pareto solution candidate PS PFj The results are output to the distance calculation unit 9 and the Pareto solution candidate selection unit 3, respectively.

[0278] Distance calculation unit 9, for example, via Figure 15 The distance calculation circuit 19 shown is implemented.

[0279] Distance calculation unit 9 obtains the Pareto solution candidate PS after correction by shape correction unit 8. PFj 'and M Pareto solution candidates PS1~PS M The Pareto solution candidate PS in the evaluation values ​​that were not corrected by the shape correction unit 8 m .

[0280] Distance calculation unit 9 calculates candidate PS solutions including corrected Pareto solutions. PFj 'and M Pareto solution candidates PS1~PS M The Pareto solution candidate PS not corrected by the shape correction unit 8 mM Pareto solution candidates PS1~PS M The relative distance L m .

[0281] The distance calculation unit 9 will select M Pareto solution candidates PS1~PS2. M The relative distance L m Output to Pareto solution candidate selection section 3.

[0282] Pareto solution candidate selection part 3, for example, through Figure 13 The Pareto solution candidate selection circuit 13 shown is implemented.

[0283] The Pareto solution candidate selection unit 3 includes a first selection processing unit 3a and a second selection processing unit 3e.

[0284] The second selection processing unit 3e is based on the N Pareto solution candidates PS'1~PS' selected by the first selection processing unit 3a. N Each evaluation value Ev n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G .

[0285] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is the Pareto solution candidate PS corrected by the shape correction unit 8 PFj Then the second selection processing unit 3d uses the Pareto solution candidate PS corrected by the shape correction unit 8. PFj 'Ev' rating PFj .

[0286] 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, then the second selection processing unit 3d uses the Pareto solution candidate PS whose evaluation value has not been corrected by the shape correction unit 8. n Evaluation value Ev n .

[0287] exist Figure 14 In this context, it is assumed that the evaluation value acquisition unit 1, shape correction unit 8, distance calculation unit 9, Pareto solution candidate selection unit 3, and Pareto solution candidate generation unit 4, which are components of the Pareto solution search device, are respectively processed by... Figure 15 The dedicated hardware implementation shown is as follows. That is, it is assumed that the Pareto solution search device is implemented through 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 generation circuit 14.

[0288] 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 generation circuit 14 are respectively equivalent to a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0289] The components of a Pareto solution search device are not limited to being implemented through dedicated hardware; a Pareto solution search device can also be implemented through software, firmware, or a combination of software and firmware.

[0290] When the Pareto solution search device is implemented through software or firmware, the program for enabling the 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 generation unit 4 is stored in... Figure 3 The memory 21 shown. And, Figure 3 The processor 22 shown executes the program stored in the memory 21.

[0291] In addition, Figure 15 The example shown illustrates how the components of a Pareto solution search apparatus are implemented using dedicated hardware. Figure 3 The example shown is an instance where the Pareto solution search apparatus is implemented by software or firmware. However, this is just one example; it is also possible that some components of the Pareto solution search apparatus are implemented by dedicated hardware, while the remaining components are implemented by software or firmware.

[0292] Next, regarding Figure 14 The operation of the Pareto solution search device shown will be explained. However, apart from the shape correction unit 8, the distance calculation unit 9, and the second selection processing unit 3e, the operation is similar to... Figure 1 The Pareto solution search device shown is the same. Therefore, the operation of the shape correction unit 8, the distance calculation unit 9, and the second selection processing unit 3e will be mainly explained here.

[0293] Shape correction unit 8 obtains Pareto solution candidate PS from evaluation value acquisition unit 1. m (m=1,…,M) and Pareto solution candidate PS m Evaluation value Ev m .

[0294] Shape correction unit 8 is based on Pareto solution candidate PS m Evaluation value Ev m From M Pareto solution candidates PS1~PS M The candidate Pareto solutions PS included in the Pareto front PF are determined in the middle. PFj (j=1, ..., J).

[0295] Pareto solution candidate PS included in the Pareto front PF PFj For example, PS is a Pareto solution candidate belonging to level Rk1. m The shape correction unit 8 can be connected with Figure 9 The grade determination unit 5 shown similarly determines the Pareto solution candidate PS belonging to grade Rk1. m .

[0296] exist Figure 11 In the example, the Pareto solution candidate PS belonging to level Rk1 m For PS1 to PS3, the shape of the Pareto front (PF) of PS1 to PS3 is a so-called convex shape.

[0297] A convex shape is defined as follows: as the value of the objective function f1(x, y) increases, the Pareto candidate solution PS... m As the x-axis of the objective function f1 gradually approaches the x-axis, and the value of the objective function f2 (x, y) increases, the Pareto candidate solution PS... m It gradually approaches the y-axis of the objective function f2.

[0298] If the shape of the Pareto front (PF) is convex, then the Pareto front (PF) contains candidate Pareto solutions (PS). PFj It is highly likely to be the optimal solution.

[0299] Additionally, if the shape of the Pareto front (PF) is a straight line, then the Pareto front (PF) contains Pareto solution candidate PS. PFj It is highly likely to be the optimal solution.

[0300] On the other hand, if the shape of the Pareto front PF is non-convex, then the Pareto front PF contains Pareto solution candidate PS. PFj The probability of finding the optimal solution is low. A non-convex shape is a shape that is neither convex nor a straight line.

[0301] Therefore, when the shape of the Pareto front (PF) is non-convex, if the shape of the Pareto front (PF) is corrected to a straight line, then the Pareto front (PF) contains a number of Pareto solution candidate PS. PFj The probability of it being the optimal solution increases.

[0302] The shape correction unit 8 corrects the Pareto solution candidate PS contained in the Pareto front PF. PFj To correct the shape of the Pareto front (PF).

[0303] The following is a detailed explanation of the shape correction process of the shape correction unit 8.

[0304] Here, we illustrate an example where the shape of the Pareto front (PF) is two-dimensional. For ease of explanation, let's assume that the Pareto front (PF) contains Pareto solution candidate PS.PFj like Figure 16 and Figure 17 The image shown is PS PF1 ~PS PF11 .

[0305] Figure 16 This is an explanatory diagram illustrating a shape correction example when the shape of the Pareto front (PF) is non-convex.

[0306] Figure 17 This is an explanatory diagram illustrating a shape correction example when the shape of the Pareto front (PF) is convex.

[0307] The shape correction unit 8 determines the parameter p that satisfies the following equation (10). The process of determining the parameter p is itself a well-known technique, so detailed explanation is omitted.

[0308] The shape correction unit 8 corrects each Pareto solution candidate PS PF1 ~PS PF11 As shown in equation (11) below, the shape of the Pareto front PF is approximated by a straight line by taking the p-th square root. PFj ' is a candidate Pareto solution after correction.

[0309]

[0310] exist Figure 16 In the example, the shape of the Pareto front (PF) is corrected from a non-convex shape to a linear shape.

[0311] exist Figure 17 In the example, the shape of the Pareto front (PF) is corrected from a convex shape to a straight shape.

[0312] Here, the following method is shown: the shape correction unit 8 determines the parameter p that satisfies equation (10) and performs Pareto solution on each candidate PS. PF1 ~PS PF11 The shape of the Pareto front PF is approximated by a straight line by taking the p-th square root. However, it is sufficient to approximate the shape of the Pareto front PF by a straight line. Of course, other methods besides the above method can also be used, and the shape correction unit 8 can approximate the shape of the Pareto front PF by a straight line.

[0313] exist Figure 16 and Figure 17The example shown illustrates a Pareto front (PF) with a two-dimensional shape. Therefore, the shape correction unit 8 corrects the shape of the PF to make it a straight line. When the shape of the PF has a three-dimensional shape, the shape correction unit 8 corrects it to make it planar. When the shape of the PF has a four-dimensional or higher shape, the shape correction unit 8 corrects it to make it a hyperplane.

[0314] Distance calculation unit 9 obtains the Pareto solution candidate PS after correction by shape correction unit 8. PFj 'and M Pareto solution candidates PS1~PS M The Pareto solution candidate PS not corrected by the shape correction unit 8 m .

[0315] Distance calculation unit 9 calculates candidate PS solutions including corrected Pareto solutions. PFj 'and Pareto solution candidate PS not corrected by shape correction unit 8 m M Pareto solution candidates PS1~PS M The relative distance L m M Pareto solution candidates PS1~PS M The relative distance L m The computational processing itself and Figure 1 The distance calculation unit 2 shown is the same.

[0316] The distance calculation unit 9 will select M Pareto solution candidates PS1~PS2. M The relative distance L m Output to Pareto solution candidate selection section 3.

[0317] As described in Embodiment 1, the first selection processing unit 3a selects from M Pareto solution candidates PS1~PS2 M Select N Pareto solution candidates PS'1~PS' N N Pareto solution candidates PS'1~PS' N The output is sent to the second selection processing unit 3e.

[0318] The second selection processing unit 3e obtains N Pareto solution candidates PS'1~PS' from the first selection processing unit 3a. N .

[0319] The second selection processing unit 3e obtains the corrected Pareto solution candidate PS from the shape correction unit 8. PFj 'Ev rating in DEA' PFj (j=1,…,J), obtain Pareto solution candidate PS from the evaluation value of Part 1. mThe evaluation value Ev in DEA m .

[0320] The second selection processing unit 3e is based on N Pareto solution candidates PS'1~PS' N Each evaluation value Ev n (n=1,…,N), from N Pareto solution candidates PS'1~PS' N Select G Pareto solution candidates PS1~PS2 G .

[0321] If the Pareto solution candidate PS' selected by the first selection processing unit 3a is the Pareto solution candidate PS corrected by the shape correction unit 8 PFj Then the second selection processing unit 3d uses the Pareto solution candidate PS corrected by the shape correction unit 8. PFj 'Ev' rating PFj .

[0322] 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, then the second selection processing unit 3d uses the Pareto solution candidate PS that has not been corrected by the shape correction unit 8. n Evaluation value Ev n .

[0323] In the above implementation method 4, Figure 14 The Pareto solution search device shown is configured to include a shape correction unit 8. This shape correction unit 8 determines Pareto solution candidates included in the Pareto front from among M Pareto solution candidates based on evaluation values ​​obtained by the evaluation value acquisition unit 1. By correcting the Pareto solution candidates included in the Pareto front, the shape of the Pareto front is corrected. Furthermore, Figure 14 The distance calculation unit 9 of the Pareto solution search device shown calculates the relative distances between the M Pareto solution candidates, including those corrected by the shape correction unit 8 and those not corrected by the shape correction unit 8. Therefore, Figure 14 The Pareto solution search device shown is Figure 1 Similarly, the Pareto solution search device shown, compared to the device disclosed in Patent Document 1, is able to select a greater variety of Pareto solution candidates. Furthermore, Figure 14 The Pareto solution search device shown can increase the probability of selecting Pareto solution candidates as the optimal solution.

[0324] Furthermore, this disclosure allows for free combination of various embodiments, modification of any constituent elements of various embodiments, or omission of any constituent elements in various embodiments.

[0325] Industrial availability

[0326] This disclosure is applicable to Pareto solution search apparatus and Pareto solution search method.

[0327] Label Explanation

[0328] 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 generation unit; 4a: Cross-processing unit; 4b: Mutation processing unit; 5: Grade 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 generation circuit; 15: Grade 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. A Pareto solution search device, comprising: an evaluator that calculates evaluation values of M (M is an integer of 2 or more) Pareto solution candidates in an envelope analysis method, the M Pareto solution candidates being candidates of M Pareto solutions in a plurality of objective functions corresponding to a multi-objective problem solved by a genetic algorithm using the envelope analysis method; a distance calculator that calculates relative distances between the M Pareto solution candidates; a Pareto solution candidate selector that selects G (G is an integer of 1 or more and less than M) Pareto solution candidates from the M Pareto solution candidates on the basis of the relative distances calculated by the distance calculator and the evaluation values obtained by the evaluation value obtainer; and a Pareto solution candidate generator that regenerates (M-G) Pareto solution candidates different from the G Pareto solution candidates selected by the Pareto solution candidate selector using any one or more of the G Pareto solution candidates. an evaluation value acquisition section that acquires an evaluation value of each of the Pareto solution candidates in the envelope analysis method from the simulator, wherein 2. The Pareto solution search device according to claim 1, wherein the G Pareto solution candidates selected by the Pareto solution candidate selector and the (M-G) Pareto solution candidates generated by the Pareto solution candidate generator are provided to the evaluator, and the evaluation value obtainer performs the evaluation value obtaining process, the distance calculator performs the distance calculating process, the Pareto solution candidate selector performs the Pareto solution candidate selecting process, and the Pareto solution candidate generator performs the Pareto solution candidate generating process are repeatedly performed.

3. The Pareto solution search device according to claim 1, wherein the Pareto solution candidate selector includes: a first selection processor that selects N (N is an integer of 1 or more and less than M) Pareto solution candidates from the M Pareto solution candidates on the basis of the relative distances calculated by the distance calculator; and a second selection processor that selects G (G is an integer of 1 or more and less than N) Pareto solution candidates from the N Pareto solution candidates on the basis of the evaluation values of the N Pareto solution candidates selected by the first selection processor.

4. The Pareto solution search device according to claim 3, wherein the Pareto solution search device includes a level determiner that determines the superiority or inferiority of the M Pareto solution candidates on the basis of the evaluation values obtained by the evaluation value obtainer, and determines a level to which each of the Pareto solution candidates belongs among a plurality of levels on the basis of a result of the determination of the superiority or inferiority, and the first selection processor selects the Pareto solution candidates from the Pareto solution candidates belonging to each of the levels on the basis of the relative distances in such a manner that the number of the selected Pareto solution candidates is N in total.

5. The Pareto solution search device according to claim 1, wherein the Pareto solution search device includes an evaluation value corrector that determines all of the Pareto solution candidates included in a Pareto front among the M Pareto solution candidates on the basis of the evaluation values obtained by the evaluation value obtainer, and corrects the evaluation values of all of the Pareto solution candidates included in the Pareto front in such a manner that the evaluation values of all of the Pareto solution candidates included in the Pareto front are 1 or more. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ The Pareto solution candidate selection section selects the G Pareto solution candidates from the M Pareto solution candidates on the basis of the relative distances calculated by the distance calculation section, the evaluation values corrected by the evaluation value correction section, and the evaluation values of the Pareto solution candidates not included in the Pareto front among the M Pareto solution candidates.

6. The Pareto solution search device according to claim 1, wherein The Pareto solution search device includes a shape correction section that determines the Pareto solution candidates included in the Pareto front among the M Pareto solution candidates on the basis of the evaluation values acquired by the evaluation value acquisition section, and corrects the shape of the Pareto front by correcting an arbitrary Pareto solution candidate included in the Pareto front, The distance calculation section calculates the relative distances among the M Pareto solution candidates including the Pareto solution candidates corrected by the shape correction section and the Pareto solution candidates not corrected by the shape correction section among the M Pareto solution candidates.

7. The Pareto solution search device according to claim 1, wherein The Pareto solution candidate generation section includes: a crossover processing section that acquires an arbitrary two of the G Pareto solution candidates selected by the Pareto solution candidate selection section, and exchanges a part of the values of one of the two Pareto solution candidates and a part of the values of the other of the two Pareto solution candidates; and a mutation processing section that acquires an arbitrary Pareto solution candidate from the G Pareto solution candidates selected by the Pareto solution candidate selection section, and changes a part of the values of the acquired Pareto solution candidate.

8. A Pareto solution search method, wherein an evaluation value acquisition section acquires evaluation values of respective Pareto solution candidates in an envelope analysis method from a simulator that calculates the evaluation values of M (M is an integer of two or more) Pareto solution candidates in the envelope analysis method, the M Pareto solution candidates corresponding to a plurality of objective functions of a multi-objective problem solved by a genetic algorithm using the envelope analysis method, a distance calculation section calculates relative distances among the M Pareto solution candidates, a Pareto solution candidate selection section selects G (G is an integer of one or more and less than M) Pareto solution candidates from the M Pareto solution candidates on the basis of the relative distances calculated by the distance calculation section and the evaluation values acquired by the evaluation value acquisition section, a Pareto solution candidate generation section newly generates (M-G) Pareto solution candidates different from the G Pareto solution candidates selected by the Pareto solution candidate selection section using an arbitrary one or more of the G Pareto solution candidates. ​

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