Computer-readable recording medium storing operation program, operation method, and information processing apparatus

Abstract

The invention discloses a computer-readable recording medium, an operation method, and an information processing apparatus. The computer-readable recording medium stores an operation program for causing a computer to execute: in a case where an operation process is repeatedly executed, the operation process includes: creating an Isin model based on a learning data set; searching a first set number of first recommendation points for the Isin model; searching a second set number and a second recommendation point for the learning data group through a genetic algorithm; and adding the first recommendation point and the first evaluation value of the first recommendation point as well as the second recommendation point and the second evaluation value of the second recommendation point as learning data to a learning data group, and representing each learning data segment in the learning data group as a target variable obtained through linear weighting sum of a plurality of target functions, and the weight of the linear weighted sum is changed each time the operation processing is performed.

Description

Technical Field

[0001] The embodiments discussed herein relate to operating procedures, operating methods, and information processing devices. Background Art

[0002] Techniques for performing optimization by performing sampling on binary variables have been disclosed.

[0003] Japanese Laid-Open Patent Publication No. 2022-190752, Japanese Laid-Open Patent Publication No. 2021-33544, and Japanese Laid-Open Patent Publication No. 2022-45870 are disclosed as related arts. Summary of the invention

[0004] question

[0005] For example, since the sampling technique of the Ising model using the quadratic unconstrained binary optimization (QUBO) format is a method of sequentially sampling recommended points on the model, there is a possibility that the sampling area is limited. Therefore, as a result, there is a possibility that the number of samplings increases.

[0006] In one aspect, an object of the present disclosure is to provide an operation program, an operation method, and an information processing device that can reduce the number of samplings.

[0007] According to one aspect of the embodiment, a computer-readable recording medium stores an operation program for causing a computer to perform the following processing: when the operation processing is repeatedly performed, the operation processing includes: creating an Ising model based on a learning data group; searching a first set number of first recommended points for the Ising model; searching a second set number of second recommended points for the learning data group through a genetic algorithm; and adding the first recommended point and the first evaluation value of the first recommended point and the second evaluation value of the second recommended point as learning data to the learning data group, representing each learning data segment in the learning data group as a target variable obtained by a linear weighted sum of multiple objective functions, and changing the weight of the linear weighted sum each time the operation processing is performed.

[0008] [Effects of the invention]

[0009] The number of sampling can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a diagram illustrating the search for a solution in QUBO format;

[0011] Figure 2 is a graph showing evaluation values ​​for movies viewed by many users;

[0012] Figure 3is a flow chart showing the execution process in the sampling technique using a model in the QUBO format;

[0013] Figure 4A is a block diagram illustrating the overall configuration of an information processing device, and Figure 4B is a block diagram illustrating a hardware configuration of an information processing device;

[0014] Figure 5 is a flowchart showing an example of the operation of an information processing device;

[0015] Figure 6 is a flowchart showing the details of step S11;

[0016] Figure 7 is a diagram illustrating the matrix X;

[0017] Figure 8 is a flowchart showing the details of step S13;

[0018] Fig.9A and Fig. 9B is a diagram illustrating NSGAII;

[0019] Fig. 10A is a diagram illustrating the crossover, and Fig. 10B is a diagram illustrating the variation;

[0020] Fig.11A is a diagram illustrating the optimization problem of magnetic shielding. Fig. 11B is a diagram illustrating the arrangement of Gaussian basis functions, and Fig. 11C is a diagram illustrating magnetic flux lines generated from a coil;

[0021] Fig.12 is a diagram illustrating positive and negative arrangements;

[0022] Fig.13 is a diagram showing the distribution of shape function y;

[0023] Fig.14 is a diagram showing simulation results; and

[0024] Fig.15 is a graph used to describe a hypervolume (HV). DETAILED DESCRIPTION

[0025] As a technique for searching for a good solution with a high evaluation value from a large number of combinations, sequences, etc., a sampling technique of a binary variable is used. As a sampling technique of a binary variable, there are a sampling technique of randomly performing sampling, a sampling technique of an Ising model using a QUBO format, and the like.

[0026] The sampling technique of randomly performing sampling can easily perform sampling, but has disadvantages in that sampling efficiency is poor and the number of times of sampling is increased in order to obtain a good solution with high accuracy.

[0027] For example, as a sampling technique for a model using the QUBO format, there is a factorization machine with quantum annealing (FMQA) and the like. FMQA is a method that combines quantum annealing (QA) and a factorization machine (FM) (a machine learning method). In the FMQA method, a FM model in the QUBO format is created based on learning data; a good solution is obtained through QA; the evaluation value of the good solution is analyzed by a solver; the result is added to the learning data; and sampling is performed interactively. In addition, as a sampling technique for a model using the QUBO format, there is the FMDA technique. FMDA is obtained by replacing the QA part of FMQA with a digital annealer (DA).

[0028] The QUBO format is a quadratic unconstrained binary optimization format that is not subject to quadratic constraints and can achieve binary optimization. For example, the QUBO format can be expressed as follows: i =0 or 1 (i=1,...,N). ij For x i With x j The coupling coefficient between i For x i The first term on the right side is a quadratic term and represents the interaction. The second term on the right side is a linear term and represents the bias effect. The third term on the right side is a constant term. Figure 1 As illustrated, in the QUBO format, a good solution x for minimizing E(x) representing energy is searched according to the following formula.

[0029]

[0030] As an example of a sampling technique using a model in the QUBO format, an overview of FMDA will be described. Figure 2 The evaluation values ​​for movies watched by many users are shown. These evaluation values ​​are n-dimensional vectors. First, a QUBO format model for representing interactions is created based on these evaluation values. The QUBO format model can be expressed as the following formula.

[0031]

[0032] In the above formula, w0, w i 、v i and v j is the coefficient to be learned. This machine learning model is a strong adversarial model for sparse data sets. Since this model is in QUBO format, a QUBO format model can be automatically generated by learning FM.

[0033] Figure 3 is a flow chart showing the execution process in the sampling technique of the model using the QUBO format. Figure 3 As illustrated, first, a learning data set is generated by randomly generating learning data segments (initial points) (step S1). The number of learning data segments to be generated is determined by the user's setting.

[0034] Next, the evaluation value of the initial point is calculated by using the solver (step S2). The evaluation value is an indicator for determining whether the initial point or the recommended point to be described later is good. Through the steps described above, an initial learning data set is generated in which the initial point and the evaluation value form a set.

[0035] Next, a model in QUBO format is created by generating FM according to the learning data set (step S3). Since FM is in QUBO format, the generation of FM is equivalent to the generation of a model in QUBO format. As long as a model in QUBO format can be generated, any other machine learning model can be used.

[0036] Next, optimization of the created QUBO format model is performed by using DA, and a good solution having an optimal evaluation value (DA recommended point) is generated (step S4).

[0037] Next, the evaluation value of the DA recommendation point is calculated by using the solver (step S5 ).

[0038] Next, the evaluation results (recommendation points and evaluation value sets) are added to the learning data group as learning data (step S6).

[0039] Next, it is determined whether the number of iterations reaches the upper limit (step S7). When it is determined as "No" in step S7, the process is performed again from step S3. Therefore, steps S3 to S6 are repeated until the end condition is met. When it is determined as "Yes" in step S7, the execution of the flowchart ends. As the end condition, a condition such as the case where the amount of change of the objective function is less than a threshold value within a certain period of time can be used.

[0040] Through the above process, the learning data set is updated and the optimal solution can be obtained.

[0041] Although FMDA has Figure 3 However, the DA part of FMDA can be replaced with QA, and any other method can be used as long as it is an Ising machine capable of solving QUBO. In addition to using an Ising machine dedicated to solving QUBO, the Ising model can be solved by using software.

[0042] Since the sampling technique of the model using the QUBO format is a method of sequentially sampling the recommendation points on the model, there is a possibility that the sampling area may be limited. In the sampling technique of the model using the QUBO format, the sampling performance depends on the learning data set used for model generation. Since FM is a quadratic model, there is a possibility that the problem may not be fully expressed. In the case of using multiple recommendation methods, it is difficult to adjust the number of recommendations. As can be seen from the above, the number of samplings is increased in order to improve the accuracy of searching for the optimal solution.

[0043] Therefore, in the following embodiments, examples in which the number of samplings can be reduced will be described.

[0044] [First embodiment]

[0045] Figure 4A is a block diagram illustrating the overall configuration of the information processing device 100. Figure 4A As illustrated, the information processing apparatus 100 includes a storage unit 10 , an initial point generation unit 20 , an evaluation unit 30 , an FMDA execution unit 40 , a GA execution unit 50 , a learning data update unit 60 , an output unit 70 , and the like.

[0046] Figure 4B is a block diagram illustrating the hardware configuration of the information processing device 100. Figure 4B As illustrated, the information processing apparatus 100 includes a central processing unit (CPU) 101 , a random access memory (RAM) 102 , a storage device 103 , an input device 104 , a display device 105 , and the like.

[0047] CPU 101 is a central processing unit. CPU 101 includes one or more cores. RAM 102 is a volatile memory that temporarily stores programs executed by CPU 101, data processed by CPU 101, etc. Storage device 103 is a non-volatile storage device. As storage device 103, for example, read-only memory (ROM), solid-state drive (SSD) such as flash memory, hard disk driven by hard disk drive, etc. can be used. Storage device 103 stores operation programs. Input device 104 is an input device such as a keyboard or a mouse. Display device 105 is a display device such as a liquid crystal display (LCD). By executing the operation program by the CPU, storage unit 10, initial point generation unit 20, evaluation unit 30, FMDA execution unit 40, GA execution unit 50, learning data update unit 60, output unit 70, etc. are realized. Hardware such as dedicated circuits may be used as the storage unit 10 , the initial point generation unit 20 , the evaluation unit 30 , the FMDA execution unit 40 , the GA execution unit 50 , the learning data update unit 60 , the output unit 70 , and the like.

[0048] Figure 51 is a flowchart showing an example of the operation of the information processing device 100. Figure 5 As illustrated, the initial point generation unit 20 generates a learning data set by generating an initial point of the learning data (step S11). The number of learning data segments to be generated is determined by the user's settings. In this embodiment, initial points are widely generated in the analysis space. For example, a D optimal design is used. The D optimal design is a design that can most effectively estimate the effect for a certain number of trials and a specific model. For example, it is a design generated by an iterative search algorithm and minimizes the covariance of parameter estimates for a specific model.

[0049] Next, the evaluation unit 30 calculates the evaluation value of the initial point by using the solver (step S12 ). The initial learning data set in which the initial point obtained in step S11 and the evaluation value calculated in step S12 are set is stored in the storage unit 10 .

[0050] Next, the FMDA execution unit 40 generates DA recommendation points, and the GA execution unit 50 generates GA recommendation points (step S13 ).

[0051] Next, the evaluation unit 30 calculates the evaluation value of the recommendation point generated in step S13 by using the solver (step S14 ).

[0052] Next, the learning data updating unit 60 adds the evaluation results (recommendation points and evaluation value sets) to the learning data group as learning data (step S15 ).

[0053] Next, the FMDA execution unit 40 determines whether the number of iterations reaches an upper limit (step S16). The number of executions of step S16 can be set to the number of iterations. The upper limit of the number of iterations is preset by the user.

[0054] When it is determined as "NO" in step S16, the process is executed again from step S3. When it is determined as "YES" in step S16, the execution of the flowchart ends.

[0055] Figure 6 It is shown Figure 5 Flowchart of details of step S11 in FIG. The initial point generation unit 20 randomly creates a matrix X having a value of 0 or 1 for (initial point, number of variables) (step S21). As an example, Figure 7 The upper part of is a diagram illustrating a randomly created matrix X when (initial point, number of variables) = (10, 10).

[0056] Next, the initial point generation unit 20 calculates the determinant D=|X T X|(Step S22). Tis the transposed matrix of matrix X.

[0057] Next, the initial point generation unit 20 saves the current D and X as D 最佳 and X 最佳 (Step S23). In this flowchart, the X created in step S21 is saved as X 最佳 , and the D created in step S22 is saved as D 最佳 .

[0058] Next, the initial point generation unit 20 re-and randomly creates a matrix X having a value of 0 or 1 for the same (initial point, number of variables) as in step S21 (step S24 ).

[0059] Next, the initial point generation unit 20 calculates the determinant D=|X T X|(Step S25).

[0060] Next, the initial point generation unit 20 determines whether D>D 最佳 (Step S26 ) When “NO” is determined in step S26 , the process is executed again from step S24 .

[0061] When the determination is “yes” in step S26, the initial point generation unit 20 saves the current D and X as D 最佳 and X 最佳 In this flowchart, the X finally created in step S24 is saved as X 最佳 , the D finally created in step S25 is saved as D 最佳 .

[0062] Next, the initial point generation unit 20 determines whether the number of searches has reached the upper limit (step S28). As the number of searches, the number of executions of step S28, etc., can be used. For example, the number of searches is 10000, etc. When it is determined to be "No" in step S28, the process is performed again from step S24.

[0063] When the determination is “Yes” in step S28, the initial point generation unit 20 sets the current X 最佳 The initial point is set (step S29). Thereafter, the execution of the flowchart ends.

[0064] By executing Figure 6 Processing, search the matrix X, so that the determinant D = |X T X| increases. Therefore, when Figure 6 At the end of the process of , a matrix X is obtained with a large D. This means that the initial points are generated in a wide range in the analysis space.

[0065] exist Figure 7 In the upper matrix X, the mean of the row counts is 4.50, and the deviation of the counts is 1.28. The mean of the column counts is 4.50, and the deviation of the counts is 1.28. It can be seen that there is variation in bit generation across trials (rows) and variables (columns), and that the distribution is biased. The value of the determinant D is 36.

[0066] Figure 7 The lower part is done by executing Figure 6 The matrix X is obtained by processing. Figure 7 In the lower matrix X, the mean of the row totals is 5.30, and the deviation of the totals is 0.90. The mean of the column totals is 5.30, and the deviation of the totals is 0.64. The value of the determinant D is 2916. Figure 7 In the lower matrix X of , it can be seen that the larger the value of the determinant D is, the smaller the variation of bit generation in the trials (rows) and variables (columns) is, and the sampling can be performed more widely.

[0067] Figure 8 It is shown Figure 5 Flow chart of the details of step S13 in FIG. Figure 8 As illustrated, the FMDA execution unit 40 determines the size of the weight of the objective function (step S31). For each iteration, the weight determination method is random or similar. Therefore, each time step S31 is executed, the weight is changed.

[0068] Next, the FMDA execution unit 40 calculates the objective function value by linear weighted sum (step S32). In the flowchart, the FMDA execution unit 40 adds multiple objective functions by linear weighted sum, and converts multiple objective functions into one objective function. For example, when the first objective function F1=y1 and the second objective function F2=y2, the converted objective function E=αF1+(1-α)F2. α is a weight and satisfies 0<α<1. Each time step S31 is iterated, the value of α changes. Alternatively, an interaction term can be introduced such as in E=αF1+βF2+γF1F2. In this case, α, β and γ are weights, and when β=(1-α) and γ=0, E=αF1+(1-α)F2.

[0069] Next, the learning data updating unit 60 determines whether the total number of learning data pieces in the learning data group exceeds the upper limit number (step S33). The upper limit number of the number of learning data pieces is set in advance by the user.

[0070] When it is determined as "yes" in step S33, the learning data update unit 60 selects the upper limit number of learning data segments in descending order of the evaluation value of the objective function value by linear weighting, and deletes data other than the selected learning data (step S34). Alternatively, the learning data update unit 60 may select learning data having an evaluation value equal to or greater than a predetermined value, and delete learning data other than the selected learning data.

[0071] When “NO” is determined in step S33 , the learning data updating unit 60 sets all the learning data pieces as learning data (step S35 ).

[0072] After the execution of step S34 or step S35, the FMDA execution unit 40 generates a model in the QUBO format by generating FM based on the learning data set stored in the storage unit 10 (step S36). Since FM has the QUBO format, the generation of FM is equivalent to the generation of a model in the QUBO format. As long as a model in the QUBO format can be generated, any other machine learning model can be used.

[0073] Next, the FMDA execution unit 40 calculates the coefficient of determination R of the FM model for the learning data set. 2 (Step S37). Determine the coefficient R 2 is an indicator of model accuracy and indicates that when the coefficient of determination is closer to 1, the accuracy of searching for a good solution with a high evaluation value is higher. 2 It can be calculated by the following formula.

[0074]

[0075] In the formula, y i is the actual measured size. The following formula is the predicted value.

[0076]

[0077] The following formula is the average value of the actual measured size.

[0078]

[0079] Next, the FMDA execution unit 40 determines the determination coefficient R 2 Whether it exceeds the threshold value δ (step S38). The threshold value δ is preset by the user. An example of the threshold value δ will be described. For example, when step S38 is performed for the first time, the threshold value δ is set to about 0.8. Preferably, when the DA recommendation works effectively, the value of the threshold value δ is small, and when the DA recommendation does not work effectively, the value of the threshold value δ is large. For example, whether the DA recommendation works effectively can be determined based on whether the determination rate of "yes" in step S38 is equal to or greater than the threshold value.

[0080] When it is determined as "yes" in step S38, the FMDA execution unit 40 generates as many DA recommendation points as the number of DA set recommendations through QUBO optimization performed by DA (step S39). The number of DA set recommendations is preset by the user. The DA recommendation point is a good solution (recommendation point) with the best evaluation value. Alternatively, the DA recommendation point is a good solution (recommendation point) with an evaluation value equal to or greater than a threshold. Alternatively, the DA recommendation point is a good solution (recommendation point) with an evaluation value up to a predetermined ranking from the top.

[0081] Thereafter, the GA execution unit 50 sets the GA recommended number as the GA set recommended number (step S40 ).

[0082] When it is determined as "No" in step S38, the GA execution unit 50 sets the number of GA recommendations to (the number of GA set recommendations + the number of DA set recommendations) (step S41). The number of GA set recommendations is preset by the user. The number of GA recommendations does not necessarily have to be (the number of GA set recommendations + the number of DA set recommendations), but can be a number greater than the number of GA recommendations.

[0083] After the execution of step S40 or after the execution of step S41, the GA execution unit 50 selects the same number of parent individuals as the number recommended by the GA from all the learning data groups stored in the storage unit 10 by using a multi-objective GA method. The method of selecting the parent individuals is not particularly limited as long as the method is a multi-objective GA method. For example, a non-dominated sorting genetic algorithm II (NSGAII) can be used. In NSGAII, individuals are selected from a diversity perspective based on convergence based on non-dominated rank and crowding distance. For example, individuals are selected in rank order (rank 1→rank 2→...), and individuals are selected in ascending order of crowding within the same rank. For example, as Fig.9A As illustrated, in the optimization of minimizing the first objective function f1(x) and the second objective function f2(x), the rank is determined in order from the solution that is not dominated to rank 1 according to the convergence (dominance relation). Fig. 9B As shown in the example, (a+b) calculated as the Manhattan distance between adjacent individuals is set as the crowding distance. It is ensured that both ends are infinite.

[0084] Next, the GA execution unit 50 generates as many child individuals (GA recommended points) as the number recommended by the GA from the parent individuals through crossover and mutation (step S43 ). Fig. 10A For example, some genes (crossover points) of parent individual A and some genes (crossover points) of parent individual B are randomly determined and replaced with each other, and child individual A and child individual B are obtained. Fig. 10Bis a diagram illustrating a mutation. For example, a randomly selected gene is replaced by an allele. The crossover probability and mutation probability are preset by the user. After this, the execution of the flowchart ends.

[0085] The output unit 70 outputs Figure 5 For example, the output result is displayed by the display device 105. For example, the output unit 70 may output the content of the learning data group, and may output the learning data having a high evaluation value in the learning data group as a good solution.

[0086] According to the present embodiment, the number of DA set recommendations and the number of GA set recommendations are determined according to the accuracy of the FM model generated from the learning data set. Therefore, high accuracy for obtaining a good solution and a reduction in the number of samplings can be achieved at the same time.

[0087] For example, in the case where the accuracy of the FM model generated from the learning data group is low, there is a possibility that the accuracy of searching for a good solution in DA is low. Therefore, without performing DA recommendation, the number of GA recommendations is increased. By using GA, the learning data can be regarded as a population and recommendation points can be generated by using GA processing. Therefore, areas where the evaluation value is likely to be good can be sampled over a wide range. In this case, since DA recommendation with low accuracy is not performed, a good solution with high accuracy can be obtained with a smaller number of sampling times.

[0088] For example, in the case where the accuracy of the FM model generated from the learning data set is high, a good solution can be generated in the FM model as a recommended point through DA. In this case, the area with a high evaluation value can be actively sampled. Therefore, the number of samplings used to obtain a good solution can be reduced.

[0089] As can be seen from the above, according to this embodiment, high accuracy for obtaining a good solution and a reduction in the number of sampling times can be achieved simultaneously.

[0090] In this embodiment, multiple objective functions are added by linear weighted sum. During the solution search stage by FMDA and GA, the weight of the linear weighted sum is dynamically changed. By doing so, multiple objective functions can be optimized while reducing the number of samplings.

[0091] In step S42, as many parent individuals as the number of GA recommendations are selected from all learning data groups by using a multi-objective GA method. Therefore, since all learning data segments are regarded as a population, GA recommendation points can be generated by using a multi-objective GA process (selection, crossover and mutation of multiple-purpose GA).

[0092] By using the D optimal design in step S11, initial points can be generated in a wide range in the analysis space. Therefore, the search miss of the optimal solution can be reduced.

[0093] When the number of data segments in the learning data group exceeds the upper limit number, the accuracy of the model used for sampling can be improved by updating the learning data group according to the evaluation value of each learning data segment included in the learning data group.

[0094] (Simulation results)

[0095] Hereinafter, a description will be given of simulation results obtained by setting a virtual problem and executing the operation process according to the above-described embodiment. Fig.11A 2 is a diagram illustrating the optimization problem of magnetic shielding. Fig.11A The figure is a magnetic shielding analysis model that illustrates the design area of ​​the coil and magnetic body and the target area. The target area is the area where the influence of magnetic flux is to be reduced. The design area of ​​the magnetic body is the area for arranging the magnetic body. Fig. 11B is a diagram illustrating the arrangement of Gaussian basis functions. Fig. 11B As shown in the example, 96 magnetic bodies can be arranged in the design area of ​​the magnetic body. Fig. 11C is a diagram illustrating magnetic flux lines generated from a coil.

[0096] Fig.12 The table in is a diagram illustrating positive arrangement and negative arrangement. S1 to S96 indicate 96 positive arrangement positions. "0" in S1 to S96 indicates that a magnetic body is not arranged, and "1" indicates that a magnetic body is arranged. Z1 to Z96 indicate 96 negative arrangement positions. "0" in Z1 to Z96 indicates that a magnetic body is not arranged, and "1" indicates that a magnetic body is arranged.

[0097] The layout problem can be expressed as a shape function y, as follows: i 、z i ∈{0,1} and w i ∈{-1,0,1}. In this way, the optimization problem of magnetic shielding is regarded as an arrangement problem of positive and negative Gaussian basis functions.

[0098]

[0099] The distribution of shape function y is as follows Fig.13 According to this result, if Fig.13 As shown in the lower figure, the material information can be determined based on the size of the shape function y. Fig.13 In the lower graph of , when the shape function y is equal to or greater than 0, matter exists, and when the shape function y is less than 0, matter does not exist.

[0100] The goal of magnetic shield shape optimization is to reduce the average magnetic flux density in the target area to and the magnetic body area S mag Minimize. For example, the objective is to minimize the following first objective function F1 and second objective function F2. Converted objective function E = αF1 + (1-α)F2.

[0101]

[0102] For this optimization problem, sampling has been performed by two methods, the method according to the comparative example and the method of the above-mentioned embodiment. In the comparative example, the learning data is represented by a single objective function rather than a linear weighted sum of multiple objective functions. Although the D optimal design is not implemented in the method of the above-mentioned embodiment, the other method is the method of the above-mentioned embodiment. As a general setting, the number of initial points is 192, the number of iterations is 384, and the number of DA set recommendations is 1. The number of GA set recommendations is 3, the crossover probability is 0.9, the mutation probability is 0.1, the threshold δ is 0.99, and the upper limit number of learning data segments is 400. In the comparative example, α=0.5 is fixed. In the method of the above-mentioned embodiment, the size of α changes randomly between 0 and 1 at each iteration.

[0103] Fig.14 is a graph showing the results. Fig.14 In the embodiment, the Pareto solution of the result list obtained by the search is extracted and visualized. In the comparative example, the solution of the optimization result is concentrated in a part, and a sparse Pareto solution is obtained. In contrast, in the present embodiment, the Pareto solution is expanded, and a solution that is good in a multi-objective viewpoint is obtained. In the comparative example, the hypervolume is 0.788, while in the present embodiment, the hypervolume is 0.860. As described above, a better solution is obtained by the method of the above embodiment.

[0104] The hyper volume (HV) will be described. Fig.15 is a graph for describing HV. HV is a performance indicator of the Pareto solution. For example, HV represents the area or volume of a region in the objective function space formed by a certain reference point and a set of solutions obtained by the algorithm. As an example, the reference point is (0,0), and the value obtained by normalizing each objective function can be used. In the case where the number of objective functions is 2, Fig.15 The region shown in is HV. When this HV becomes larger, the solution is expanded, and thus it can be determined that a good result is obtained.

[0105] Although the D-optimal design is not achieved in the simulation of the method for the above-described embodiment, since initial points can be generated in a wide range in the analysis space by achieving the D-optimal design, the Pareto solution is further expanded.

[0106] In the above example, the number recommended by the DA set is an example of the first set number, the DA recommended point is an example of the first recommended point, the number recommended by the GA set is an example of the second set number, and the GA recommended point is an example of the second recommended point. The FMDA execution unit 40 and the GA execution unit are examples of execution units that perform the following processing: each learning data segment in the learning data group is represented as a target variable obtained by the linear weighted sum of multiple objective functions, and each time the operation processing is performed, the weight of the linear weighted sum is changed. The initial point generation unit 20 is an example of an initial point generation unit that repeatedly randomly creates a matrix X in which the number of variables and initial points is represented by a value of 0 or 1 and calculates D=|X for the matrix X. T X| to search for a matrix X that satisfies a predetermined condition, and generates an initial point for each learning data segment in the learning data group using each value represented by the searched matrix X. The learning data updating unit 60 is an example of an updating unit that updates the learning data group according to the evaluation value of each learning data segment when the number of learning data segments in the learning data group exceeds an upper limit.

[0107] Although the embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to such specific embodiments, and various modifications and alterations may be made within the scope of the gist of the present disclosure described in the claims.

Claims

1. A computer-readable recording medium storing an operation program for causing a computer to execute the following processing: In the case of repeatedly performing an operation process, the operation process includes: Creating an Ising model based on the learning data set; searching a first set of first number of recommended points for the Ising model; searching for a second set of second recommended points for the learning data set by a genetic algorithm; and adding the first recommended point and the first evaluation value of the first recommended point and the second recommended point and the second evaluation value of the second recommended point as learning data to the learning data set, Each learning data segment in the learning data group is represented as a target variable obtained by a linear weighted sum of a plurality of target functions, and a weight of the linear weighted sum is changed each time the operation process is performed.

2. The computer-readable recording medium according to claim 1, wherein The computer is caused to execute the following processing: By repeatedly randomly creating a matrix X in which several initial points and variables are represented by values ​​0 or 1 and calculating D=|X for the matrix X T X| to search for the matrix X that satisfies a predetermined condition, and set each value represented by the searched matrix X as an initial point of each learning data segment in the learning data group.

3. The computer-readable recording medium according to claim 1, wherein: In the case where the genetic algorithm is applied to the learning data set, all learning data segments included in the learning data set are targeted.

4. The computer-readable recording medium according to claim 1, wherein: The computer is caused to execute the following processing: The first set number and the second set number are determined according to the accuracy of the Ising model.

5. The computer-readable recording medium according to claim 4, wherein: The computer is caused to execute the following processing: When the accuracy of the Ising model is less than a threshold, the second recommended point is searched for by increasing the number of the second sets without searching for the first recommended point.

6. The computer-readable recording medium according to claim 4, wherein: The computer is caused to execute the following processing: In a case where the accuracy of the Ising model is less than a threshold, the second recommended point is searched for by setting a sum of the first set number and the second set number to the second set number without searching for the first recommended point.

7. The computer-readable recording medium according to claim 4, wherein: The computer is caused to execute the following processing: In a case where the accuracy of the Ising model is equal to or greater than a threshold value, the first recommended point and the second recommended point are searched without changing the first set number and the second set number.

8. The computer-readable recording medium according to claim 1, wherein: An upper limit is set for the number of learning data segments in the learning data set, and The computer is caused to execute the following processing: In a case where the number of learning data pieces in the learning data set exceeds the upper limit, the learning data set is updated according to the evaluation value of each learning data piece.

9. The computer-readable recording medium according to claim 8, wherein: The computer is caused to execute the following processing: In a case where the number of learning data pieces in the learning data group exceeds the upper limit, the other learning data pieces are deleted while retaining the upper limit number of learning data pieces in the learning data group in descending order of evaluation value.

10. An operating method, comprising: In the case of repeatedly performing the operation process, the operation process includes: creating an Ising model based on a learning data set; searching a first set number of first recommended points for the Ising model; searching a second set number of second recommended points for the learning data set by a genetic algorithm; and adding the first recommended point and the first evaluation value of the first recommended point and the second recommended point and the second evaluation value of the second recommended point as learning data to the learning data set, Each learning data segment in the learning data group is represented as a target variable obtained by a linear weighted sum of a plurality of target functions, and a weight of the linear weighted sum is changed each time the operation process is performed.

11. The operating method according to claim 10, further comprising: By repeatedly randomly creating a matrix X in which several initial points and variables are represented by values ​​0 or 1 and calculating D=|X for the matrix X T X| to search for the matrix X that satisfies a predetermined condition, and set each value represented by the searched matrix X as an initial point of each learning data segment in the learning data group.

12. The operating method according to claim 10, wherein: In the case where the genetic algorithm is applied to the learning data set, all learning data segments included in the learning data set are targeted.

13. The operating method according to claim 10, further comprising: The first set number and the second set number are determined according to the accuracy of the Ising model.

14. The operating method according to claim 13, further comprising: When the accuracy of the Ising model is less than a threshold, the second recommended point is searched for by increasing the number of the second sets without searching for the first recommended point.

15. The operating method according to claim 13, further comprising: In a case where the accuracy of the Ising model is less than a threshold, the second recommended point is searched for by setting a sum of the first set number and the second set number to the second set number without searching for the first recommended point.

16. The operating method according to claim 13, further comprising: In a case where the accuracy of the Ising model is equal to or greater than a threshold value, the first recommended point and the second recommended point are searched without changing the first set number and the second set number.

17. The operating method according to claim 10, wherein: An upper limit is set for the number of learning data segments in the learning data set, and The operation method also includes: In a case where the number of learning data pieces in the learning data set exceeds the upper limit, the learning data set is updated according to the evaluation value of each learning data piece.

18. The operating method according to claim 17, further comprising: In a case where the number of learning data pieces in the learning data group exceeds the upper limit, the other learning data pieces are deleted while retaining the upper limit number of learning data pieces in the learning data group in descending order of evaluation value.

19. An information processing device, comprising: An execution unit, the execution unit being configured to: In the case of repeatedly performing the operation process, the operation process includes: creating an Ising model based on a learning data set; searching a first set number of first recommended points for the Ising model; searching a second set number of second recommended points for the learning data set by a genetic algorithm; and adding the first recommended point and the first evaluation value of the first recommended point and the second recommended point and the second evaluation value of the second recommended point as learning data to the learning data set, Each learning data segment in the learning data group is represented as a target variable obtained by a linear weighted sum of a plurality of target functions, and a weight of the linear weighted sum is changed each time the operation process is performed.

20. The information processing device according to claim 19, further comprising: An initial point generation unit, wherein the initial point generation unit is configured to: By repeatedly randomly creating a matrix X in which several initial points and variables are represented by values ​​0 or 1 and calculating D=|X for the matrix X T X| to search for the matrix X that satisfies a predetermined condition, and set each value represented by the searched matrix X as an initial point of each learning data segment in the learning data group.

21. The information processing device according to claim 19, wherein: In the case where the genetic algorithm is applied to the learning data set, all learning data segments included in the learning data set are targeted.

22. The information processing device according to claim 19, wherein: The execution unit determines the first set number and the second set number according to the accuracy of the Ising model.

23. The information processing device according to claim 22, wherein: The execution unit searches for the second recommended point by increasing the number of the second sets without searching for the first recommended point when the accuracy of the Ising model is less than a threshold.

24. The information processing device according to claim 22, wherein: The execution unit searches for the second recommended point by setting a sum of the first set number and the second set number as the second set number without searching for the first recommended point if the accuracy of the Ising model is less than a threshold value.

25. The information processing device according to claim 22, wherein: The execution unit searches for the first recommended point and the second recommended point without changing the first set number and the second set number, if the accuracy of the Ising model is equal to or greater than a threshold value.

26. The information processing device according to claim 19, wherein: An upper limit is specified for the number of learning data segments in the learning data set, and The information processing apparatus further includes an updating unit configured to update the learning data group according to an evaluation value of each learning data segment, if the number of learning data segments in the learning data group exceeds the upper limit.

27. The information processing device according to claim 26, wherein: The execution unit deletes other learning data segments while retaining the upper limit number of learning data segments in the learning data group in descending order of evaluation values, if the number of learning data segments in the learning data group exceeds the upper limit.

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