Information processing device, information processing method, and program

Abstract

Efficiently calculate the Pareto solution for multi-objective optimization problems. [Solution] The information processing device according to the embodiment calculates a Pareto solution to a multi-objective optimization problem, each optimizing multiple objective functions that each contain multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions. The information processing device includes a processing unit. Each of the multiple evaluation devices outputs an evaluation value that evaluates the objective function value. The processing unit generates multiple candidate information sets, each containing a candidate set of setting values ​​that is identical to one or more of the set of setting values, based on dataset information containing one or more set of setting values. The processing unit selects one of the multiple candidate information sets as recommended candidate information. The processing unit generates a recommended set of setting values ​​based on the candidate set of setting values ​​included in the recommended candidate information. The processing unit supplies the recommended set of setting values ​​to one of the multiple evaluation devices to generate an evaluation value.

Description

Technical Field

[0001] Embodiments of the present invention relate to an information processing apparatus, an information processing method, and a program.

Background Art

[0002] In various fields, optimization processing based on simulation is utilized to improve the set values set in a system. For example, the set values set in a manufacturing system for manufacturing a product can be calculated by optimization processing based on simulation. In this case, the optimal set values are calculated by optimization processing that maximizes or minimizes an objective function for evaluating the manufacturing system.

[0003] Also, in the real world, there are many problems in which the optimal solution is not determined by a single evaluation value but by considering multiple evaluation values. Such an optimization problem using multiple evaluation values is called a multi-objective optimization problem. In a multi-objective optimization problem, a solution is called a Pareto solution. When determining multiple set values so as to improve one of the multiple evaluation values, there is often a trade-off relationship in which other evaluation values deteriorate. Therefore, when solving a multi-objective optimization problem, multiple Pareto solutions with different balances of multiple evaluation values are calculated. The user selects one Pareto solution from among the multiple Pareto solutions obtained by solving the multi-objective optimization problem, considering the trade-off relationship, and determines the selected Pareto solution as the optimal solution.

[0004] Also, there are cases where optimization processing based on simulation is applied to a multi-objective optimization problem. As a method for solving a multi-objective optimization problem, a multi-objective Bayesian optimization method is known.

[0005] Conventional multi-objective Bayesian optimization methods calculate multiple evaluation values ​​simultaneously. Therefore, in conventional multi-objective Bayesian optimization methods, if, for example, the contribution of evaluation values ​​calculated by some of the multiple simulators is small, or if the contribution becomes small, the simulator with the small contribution will continue to run. Consequently, conventional multi-objective Bayesian optimization methods suffer from poor overall operational efficiency, leading to increased computational costs and simulation time. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2022-118610 [Overview of the project] [Problems that the invention aims to solve]

[0007] The problem that this invention aims to solve is to efficiently calculate the Pareto solution of a multi-objective optimization problem using multiple evaluation devices. [Means for solving the problem]

[0008] The information processing device according to the embodiment calculates a Pareto solution to a multi-objective optimization problem, each optimizing a plurality of objective functions, each containing a plurality of decision variables, using a plurality of evaluation devices corresponding to the plurality of objective functions. The information processing device includes a processing unit. Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setting values ​​into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The processing unit generates a plurality of candidate information sets, each containing a candidate setting value set that is identical to one or more of the plurality of setting value sets, based on a dataset information containing one or more setting value sets. The processing unit selects one of the plurality of candidate information sets as recommended candidate information. The processing unit generates a recommended setting value set based on the candidate setting value set included in the recommended candidate information. The processing unit supplies the recommended setting value set to one of the plurality of evaluation devices to generate the evaluation value. [Brief explanation of the drawing]

[0009] [Figure 1] A diagram illustrating the configuration of an information processing system according to the embodiment. [Figure 2] A diagram illustrating the relationship between evaluation values ​​and Pareto solutions. [Figure 3] A diagram showing an example of evaluation device information represented in graph format. [Figure 4] A diagram showing an example of evaluation device information presented in tabular format. [Figure 5] A diagram showing an example of dataset information. [Figure 6] A diagram showing an example of candidate list information. [Figure 7] A diagram showing an example of a recommended set of settings. [Figure 8] A diagram showing the functional configuration of the processing unit along with the memory unit. [Figure 9] A diagram showing an example of the confidence region of a Pareto front. [Figure 10] A flowchart illustrating the process of solving a multi-objective optimization problem. [Figure 11]A diagram showing an example of the hardware configuration of an information processing device according to the embodiment. [Modes for carrying out the invention]

[0010] Embodiments of this invention will be described in detail below with reference to the attached drawings.

[0011] Figure 1 is a diagram showing the configuration of the information processing system 10 according to the embodiment.

[0012] The information processing system 10 solves a multi-objective optimization problem. That is, the information processing system 10 outputs one or more Pareto solutions that optimize multiple objective functions in a multi-objective optimization problem.

[0013] Each of the multiple objective functions is a function containing multiple decision variables. Each of the multiple decision variables corresponds one-to-one with each of the multiple setting values. Each of the multiple decision variables is a variable representing a corresponding setting value among the multiple setting values.

[0014] Each of the multiple settings is a separate value. Each of the multiple settings can be a continuous value, a discrete value, or a logical value (categorical variable). In other words, there are no particular limitations on the types of each of the multiple settings.

[0015] Each of the multiple settings represents, for example, a value set in the target system. If the target system is a production system that manufactures products such as semiconductors, each of the multiple settings is, for example, a value set in the production system such as processing time, dimensions, resistance, voltage, and charge. Alternatively, each of the multiple settings may be a physical value set in the target system such as temperature and pressure, or it may represent a value related to the operating conditions of the target system such as processing time and processing conditions. Furthermore, the target system may be an information processing system such as a machine learning system. In this case, each of the multiple settings may be a hyperparameter used in the machine learning system.

[0016] Each of the multiple objective functions is a function that expresses, for example, the operational results, intermediate states, or constraints of the target system using multiple decision variables. Each of the multiple objective functions is a function that expresses, for example, productivity, yield, reliability, and manufacturing time in a production system using multiple decision variables. Alternatively, each of the multiple objective functions may be a function that expresses, for example, the energy consumption at a given time, the energy constraints at a given time, the number of transports, the inspection interval, the amount of greenhouse gas emissions, and the trading revenue in a power plant using multiple decision variables.

[0017] The information processing system 10 calculates and outputs one or more Pareto solutions that optimize these multiple objective functions. In the optimization process for a multi-objective optimization problem, if the objective function value of the first objective function is set to the best value (e.g., maximum or minimum), the objective function value of the second objective function may no longer be the best value (e.g., maximum or minimum). Conversely, if the objective function value of the second objective function is set to the best value, the objective function value of the first objective function may no longer be the best value. Therefore, the user determines one of the one or more Pareto solutions output from the information processing system 10, considering the trade-off relationships between the evaluation values ​​of each of the multiple objective functions. The user then sets multiple setting values ​​represented by the determined Pareto solution in the target system. This allows the user to set multiple setting values ​​in the target system while considering trade-offs such as operational results, intermediate states, or constraints in the target system.

[0018] The information processing system 10 comprises a plurality of evaluation devices 20 (20-1 to 20-N) and an information processing device 30. N is an integer greater than or equal to 1.

[0019] Each of the multiple evaluation devices 20 corresponds to one or more of the multiple objective functions. Furthermore, each of the multiple objective functions corresponds to at least one of the evaluation devices 20.

[0020] Each of the multiple evaluation devices 20 outputs an evaluation value that evaluates the objective function value obtained by substituting multiple setpoints into multiple decision variables included in the corresponding objective function among the multiple objective functions.

[0021] For example, the first evaluation device 20-1 among the multiple evaluation devices 20 corresponds to the first objective function among the multiple objective functions. The first evaluation device 20-1 outputs a first evaluation value that evaluates the objective function value of the first objective function when multiple setting values ​​are given to the first objective function. Also, for example, the second evaluation device 20-2 among the multiple evaluation devices 20 corresponds to the second objective function among the multiple objective functions. The second evaluation device 20-2 outputs a second evaluation value that evaluates the objective function value of the second objective function when multiple setting values ​​are given to the second objective function. Also, for example, the Nth evaluation device 20-N among the multiple evaluation devices 20 corresponds to the Nth objective function among the multiple objective functions. The Nth evaluation device 20-N outputs an Nth evaluation value that evaluates the objective function value of the Nth objective function when multiple setting values ​​are given to the Nth objective function.

[0022] Each of the multiple evaluation devices 20 is provided with a set of recommended settings from the information processing device 30. The set of recommended settings includes multiple settings corresponding to multiple decision variables.

[0023] Furthermore, each of the multiple evaluation devices 20 may be provided with a set of recommended settings that includes multiple settings corresponding to one or more decision variables, excluding the decision variables that are not used in the calculation of the corresponding objective function. For example, if the first objective function corresponding to the first evaluation device 20-1 is represented by a function that does not include the first decision variable among the multiple decision variables, the set of recommended settings provided to the first evaluation device 20-1 may include one or more settings, excluding the setting corresponding to the first decision variable.

[0024] Furthermore, the recommended setting set may include evaluation values ​​output from any of the evaluation devices 20, instead of some or all of the multiple setting values.

[0025] For example, suppose the second evaluation device 20-2 outputs a second evaluation value that depends on the first evaluation value output by the first evaluation device 20-1. That is, suppose the second objective function corresponding to the second evaluation device 20-2 has some terms that are identical to the first objective function. In this case, the recommended setting value set given to the second evaluation device 20-2 may include the first evaluation value output by the first evaluation device 20-1 instead of setting values ​​corresponding to the decision variables that are included only in the terms of the first objective function among the multiple decision variables. As a result, the second evaluation device 20-2 can use the first evaluation value as the result of calculations on a function identical to the first objective function, thus reducing the amount of computation.

[0026] Each of the multiple evaluation devices 20 is a simulator that performs a simulation through information processing based on a pre-configured simulation model. One of the multiple evaluation devices 20 may be implemented by the information processing device 30. The simulation may include experiments. For example, at least one of the multiple evaluation devices 20 may be an experimental device that performs physical experiments. The experimental device may, for example, have multiple recommended settings included in a recommended setting set configured via a network or manually configured by a user, perform experiments, and output evaluation values.

[0027] The information processing device 30 comprises a storage unit 40 and a processing unit 50.

[0028] The storage unit 40 is composed of any commonly used storage medium, such as flash memory, memory cards, RAM (Random Access Memory), HDD (Hard Disk Drive), and optical discs.

[0029] The storage unit 40 stores data used in the processing of the information processing device 30. The storage unit 40 stores at least evaluation device information and dataset information. The storage unit 40 may also store other information. For example, the storage unit 40 may store the processing results of each component of the information processing device 30.

[0030] The processing unit 50 acquires evaluation device information, for example, input by the user, at the start of the multi-objective optimization problem solving process. The processing unit 50 stores the evaluation device information input at the start of the multi-objective optimization problem solving process in the storage unit 40. The processing unit 50 may also acquire updated evaluation device information during the multi-objective optimization problem solving process and overwrite the evaluation device information stored in the storage unit 40 with the updated evaluation device information.

[0031] Furthermore, the processing unit 50 stores initial dataset information in the storage unit 40 at the start of the problem-solving process. The processing unit 50 also repeatedly updates the dataset information stored in the storage unit 40 during the problem-solving process.

[0032] Furthermore, during the problem-solving process, the processing unit 50 generates a set of recommended settings based on the evaluation device information and the dataset information, and selects one of the multiple evaluation devices 20 to which the set of recommended settings will be supplied. When a set of recommended settings is generated, the processing unit 50 provides the generated set of recommended settings to the selected evaluation device 20. The evaluation device 20 that receives the set of recommended settings generates an evaluation value based on the received set of recommended settings. When an evaluation value is generated by any of the multiple evaluation devices 20, the processing unit 50 acquires the generated evaluation value. When an evaluation value is acquired, the processing unit 50 registers the acquired evaluation value in the dataset information and updates the dataset information. When the dataset information is updated, the processing unit 50 generates a new set of recommended settings based on the evaluation device information and the updated dataset information. During the problem-solving process, the processing unit 50 repeatedly performs the above steps of generating a set of recommended settings, supplying the set of recommended settings, acquiring an evaluation value, and updating the dataset information.

[0033] Then, when the processing unit 50 reaches a predetermined termination condition, it stops the iterative processing and generates and outputs one or more Pareto solutions based on the dataset information. Further details of the processing unit 50 will be explained with reference to Figure 8.

[0034] Note that the components shown in Figure 1 are for generating a recommended setting set and calculating and outputting one or more Pareto solutions, and other components are omitted. Also, each component may be subdivided or combined. For example, the storage unit 40 may be divided into multiple storage devices (e.g., multiple storage media) depending on the files to be stored. Also, components other than the storage unit 40 may be considered as one unit. Furthermore, the processing results of each component may be sent to the component that performs the next processing, or stored in the storage unit 40. In the latter case, the component that performs the next processing accesses the storage unit 40 to obtain the processing results. Alternatively, for example, the processing unit 50 may output the recommended setting set and information of the selected evaluation device 20 to the evaluation device 20. The evaluation device 20 may change the settings of the evaluation device 20 and the simulation model based on the information of the selected evaluation device 20, generate evaluation values ​​based on the recommended setting set, and output them to the processing unit 50.

[0035] Figure 2 is a diagram illustrating the relationship between evaluation values ​​and Pareto solutions.

[0036] The horizontal axis in Figure 2 represents the first evaluation value, which assesses the first objective function (f1(x)) among multiple objective functions. The vertical axis in Figure 2 represents the second evaluation value, which assesses the second objective function (f2(x)) among multiple objective functions. In the example in Figure 2, a larger first evaluation value, i.e., a value to the right of the graph, indicates a better outcome. In the example in Figure 2, a larger second evaluation value, i.e., a value higher up on the graph, indicates a better outcome.

[0037] In a multi-objective optimization problem, a feasible solution is a solution that satisfies all of the objective functions. In a multi-objective optimization problem, each of the one or more Pareto solutions is a non-inferior solution in the solution set that includes multiple feasible solutions. A non-inferior solution is one in the solution set that includes multiple feasible solutions where no other solution has a superior objective function value for each of the objective functions. Each of the one or more ideal Pareto solutions is a non-inferior solution in the solution set that includes all feasible solutions. However, the information processing device 30 according to this embodiment may output not only ideal Pareto solutions but also approximate Pareto solutions. That is, the information processing device 30 outputs one or more non-inferior solutions from the solution set that includes a portion of the feasible solutions as one or more Pareto solutions.

[0038] For example, in the example in Figure 2, each of the black circles represents one of the feasible solutions. Also, each of the black circles A, B, C, and D represents a Pareto solution calculated by the information processing device 30. That is, each of the black circles A, B, C, and D represents a non-inferior solution from the set of multiple feasible solutions that satisfy multiple objective functions calculated by the information processing device 30.

[0039] Furthermore, the hyperplane representing the boundary of a feasible solution formed by connecting multiple Pareto solutions is called the Pareto front. The region containing the set of feasible solutions bounded by the Pareto front, as shown by the shaded area in Figure 2, is called the hypervolume.

[0040] In this embodiment, the number of multiple decision variables is M, where M is an integer greater than or equal to 2. Also in this embodiment, the number of multiple objective functions is N, where N is an integer greater than or equal to 2. In such a case, a multi-objective minimization problem, which is an example of a multi-objective optimization problem, can be expressed as shown in equation (1).

number

[0041] Furthermore, in this embodiment, multiple Pareto solutions can be expressed, for example, as shown in equation (2) below. Note that H is an integer greater than or equal to 2.

number

[0042] Figure 3 shows an example of evaluation device information presented in graph format. Figure 4 shows an example of evaluation device information presented in tabular format.

[0043] Each of the multiple evaluation devices 20 receives at least one input value. Each of the at least one input values ​​is either one of a set value or one of an evaluation value. For example, each of the at least one input values ​​input to the first evaluation device 20-1 among the multiple evaluation devices 20 is either one of a set value or an evaluation value output from any other evaluation device 20 different from the first evaluation device 20-1 among the multiple evaluation devices 20.

[0044] The evaluation device information represents information that identifies at least one input value for each of the multiple evaluation devices 20, and information that identifies which of the multiple objective functions the evaluation value of will be output. For example, the evaluation device information for the first evaluation device 20-1 includes information that identifies at least one input value input to the first evaluation device 20-1, and information that identifies which of the multiple objective functions the first evaluation device 20-1 will output the evaluation value of.

[0045] The evaluation device information shown in Figures 3 and 4 represents the information for the first evaluation device 20-1, the second evaluation device 20-2, and the third evaluation device 20-3 when solving a multi-objective optimization problem involving three objective functions (f1(x), f2(x), f3(x)). Furthermore, the evaluation device information shown in Figures 3 and 4 indicates that each of the three objective functions (f1(x), f2(x), f3(x)) is represented by four decision variables (x1, x2, x3, x4).

[0046] In Figures 3 and 4, the first evaluation device 20-1 is represented as S1, the second evaluation device 20-2 as S2, and the third evaluation device 20-3 as S3. The evaluation device information shown in Figures 3 and 4 indicates that the first evaluation device 20-1 (S1) outputs a first evaluation value (y1) which evaluates the objective function value of the first objective function (f1(x)). The evaluation device information shown in Figures 3 and 4 indicates that the second evaluation device 20-2 (S2) outputs a second evaluation value (y2) which evaluates the objective function value of the second objective function (f2(x)). The evaluation device information shown in Figures 3 and 4 indicates that the third evaluation device 20-3 (S3) outputs a third evaluation value (y3) which evaluates the objective function value of the third objective function (f3(x)).

[0047] The evaluation device information shown in Figures 3 and 4 indicates that the first setting value to be substituted for the first decision variable (x1) and the second setting value to be substituted for the second decision variable (x2) are input to the first evaluation device 20-1 (S1). Furthermore, the evaluation device information shown in Figures 3 and 4 indicates that the third setting value to be substituted for the third decision variable (x3) and the first evaluation value (y1) are input to the second evaluation device 20-2 (S2). Finally, the evaluation device information shown in Figures 3 and 4 indicates that the fourth setting value to be substituted for the fourth decision variable (x4) and the first evaluation value (y1) are input to the third evaluation device 20-3 (S3).

[0048] Such evaluation device information is pre-generated by the user at the start of the multi-objective optimization problem solving process. Furthermore, this evaluation device information may be updated during the multi-objective optimization problem solving process.

[0049] The evaluation device information may be presented in graph format, as shown in Figure 3. Alternatively, the evaluation device information may be presented in tabular format, as shown in Figure 4. Furthermore, the evaluation device information may be presented in a format other than graph or tabular format.

[0050] Figure 5 shows an example of dataset information.

[0051] Dataset information includes one or more sets of setting values. For example, the dataset information shown in Figure 5 includes J sets of setting values ​​(P1, P2, P3, P4, ..., P J ) is included. J is any integer greater than or equal to 1.

[0052] Each of the one or more setting value sets represents multiple setting values ​​that are substituted for multiple decision variables. In Figure 5, each of the one or more setting value sets represents a second setting value substituted for the first decision variable (x1), a second setting value substituted for the second decision variable (x2), a third setting value substituted for the third decision variable (x3), and a fourth setting value substituted for the fourth decision variable (x4).

[0053] For example, the first set of settings (P1) shown in Figure 5 represents {x1=0.5, x2=-4.1, x3=2.2, x4=1.0}. The second set of settings (P2) shown in Figure 5 represents {x1=0.4, x2=-4.8, x3=-0.8, x4=1.5}. The third set of settings (P3) shown in Figure 5 represents {x1=-0.6, x2=3.3, x3=3.9, x4=4.6}. The fourth set of settings (P4) shown in Figure 5 represents {x1=-1.2, x2=2.8, x3=2.9, x4=0.3}. The Jth set of settings (P J ) represents {x1=0.7, x2=3.7, x3=4.3, x4=-4.3}.

[0054] The dataset information allows for the registration of registered evaluation devices among multiple evaluation devices 20 that acquire evaluation values, corresponding to each of one or more sets of setting values. For example, suppose the dataset information includes a first set of setting values ​​as one of the one or more sets of setting values, and the first evaluation device 20-1(S1) is not registered as a registered evaluation device corresponding to the first set of setting values. Subsequently, when the processing unit 50 acquires a first evaluation value (y1) obtained by providing multiple setting values ​​represented by the first set of setting values ​​to a first objective function (f1) from the first evaluation device 20-1(S1), the first evaluation device 20-1(S1) is added to the registered evaluation device, corresponding to the first set of setting values.

[0055] The dataset information shown in Figure 5 corresponds to the first set of settings (P1), and none of the evaluation devices 20 are registered as registered evaluation devices. The dataset information shown in Figure 5 corresponds to the second set of settings (P2), and the first evaluation device 20-1 (S1) and the third evaluation device 20-3 (S3) are registered as registered evaluation devices. The dataset information shown in Figure 5 corresponds to the third set of settings (P3), and the first evaluation device 20-1 (S1), the second evaluation device 20-2 (S2), and the third evaluation device 20-3 (S3) are registered as registered evaluation devices. The dataset information shown in Figure 5 corresponds to the fourth set of settings (P4), and the first evaluation device 20-1 (S1) is registered as a registered evaluation device. The dataset information shown in Figure 5 corresponds to the Jth set of settings (P J In accordance with this, none of the evaluation devices 20 are registered as registered evaluation devices.

[0056] Furthermore, the dataset information can register evaluation values ​​obtained from each of the multiple evaluation devices 20, corresponding to each of one or more sets of setting values. For example, suppose the dataset information includes a first set of setting values ​​as one of the one or more sets of setting values, and the first evaluation value (y1) corresponding to the first set of setting values ​​has not been registered. Subsequently, when the processing unit 50 obtains the first evaluation value (y1) obtained by providing the multiple setting values ​​represented by the first set of setting values ​​to the first objective function (f1) from the first evaluation device 20-1 (S1), the acquired first evaluation value (y1) is additionally registered in the dataset information, corresponding to the first set of setting values.

[0057] For example, the dataset information shown in Figure 5 corresponds to the first set of settings (P1), and no evaluation values ​​are registered. The dataset information shown in Figure 5 corresponds to the second set of settings (P2), and the first evaluation value (y1=1.6) and the third evaluation value (y3=0.8) are registered. The dataset information shown in Figure 5 corresponds to the third set of settings (P3), and the first evaluation value (y1=-2.4), the second evaluation value (y2=-2.1), and the third evaluation value (y3=-2.3) are registered. The dataset information shown in Figure 5 corresponds to the fourth set of settings (P4), and the first evaluation value (y1=-4.8) is registered. The dataset information shown in Figure 5 corresponds to the Jth set of settings (P J In response to this, none of the evaluation values ​​have been registered.

[0058] Furthermore, during the problem-solving process, at predetermined timings, one or more new sets of setting values ​​representing multiple setting values ​​are added to the dataset information. When a new set of setting values ​​is added, no registered evaluation devices or evaluation values ​​are registered in conjunction with the new set of setting values.

[0059] Furthermore, the dataset information is initialized at the start of the solution process. The initial dataset information includes an initial set of settings representing multiple settings. The initial dataset information may also include only the initial set of settings. Initial dataset information containing only the initial set of settings does not have any registered evaluation devices or evaluation values ​​registered.

[0060] In the example shown in Figure 5, the dataset information is described in tabular format, but it can be described in any format.

[0061] Figure 6 shows an example of candidate list information.

[0062] During the problem-solving process, the processing unit 50 repeatedly generates candidate list information based on evaluation device information and dataset information.

[0063] The candidate list information contains multiple candidate pieces of information. For example, the candidate list information shown in Figure 6 contains K pieces of candidate information (Q1, Q2, Q3, Q4, ..., Q K ) is included. K is any integer greater than or equal to 1.

[0064] Each of the multiple candidate information entries includes a candidate setting value set and unregistered device information representing an unregistered evaluation device.

[0065] The candidate setting value set is identical to one or more setting value sets included in the dataset information.

[0066] For example, the set of candidate settings included in the first candidate information (Q1) shown in Figure 6 is the same as the set of first settings (P1) included in the dataset information shown in Figure 5. For example, the set of candidate settings included in the second candidate information (Q2) shown in Figure 6 is the same as the set of second settings (P2) included in the dataset information shown in Figure 5. For example, the set of candidate settings included in the third candidate information (Q3) shown in Figure 6 is the same as the set of fourth settings (P4) included in the dataset information shown in Figure 5. For example, the set of fourth candidate settings included in the candidate information (Q4) shown in Figure 6 is the same as the set of fourth settings (P4) included in the dataset information shown in Figure 5. For example, the Kth candidate information (Q) shown in Figure 6 K The candidate setting set included in ) is the Jth setting set (P) included in the dataset information shown in Figure 5. J It is identical to ).

[0067] An unregistered evaluation device represented by unregistered device information is an evaluation device 20 among multiple evaluation devices 20 that is not registered in the dataset information as a registered evaluation device corresponding to a candidate setting value set.

[0068] For example, the first candidate information (Q1) shown in FIG. 6 includes a candidate set of setting values that is the same as the first set of setting values (P1) shown in FIG. 5. The first set of setting values (P1) of the dataset information shown in FIG. 5 is not registered as a registered evaluation device by the first evaluation device 20-1 (S1). Therefore, the first candidate information (Q1) shown in FIG. 6 can include unregistered device information representing the first evaluation device 20-1 (S1) as an unregistered evaluation device.

[0069] On the other hand, the second candidate information (Q2) shown in FIG. 6 includes a candidate set of setting values that is the same as the second set of setting values (P2) shown in FIG. 5. The second set of setting values (P2) of the dataset information shown in FIG. 5 is registered as a registered evaluation device by the first evaluation device 20-1 (S1). Therefore, the second candidate information (Q2) shown in FIG. 6 cannot include unregistered device information representing the first evaluation device 20-1 (S1) as an unregistered evaluation device.

[0070] For example, the first candidate information (Q1) shown in FIG. 6 includes unregistered device information representing the first evaluation device 20-1 (S1) that is not registered corresponding to the first set of setting values (P1) as an unregistered evaluation device. For example, the second candidate information (Q2) shown in FIG. 6 includes unregistered device information representing the second evaluation device 20-2 (S2) that is not registered corresponding to the second set of setting values (P2) as an unregistered evaluation device. For example, the third candidate information (Q3) shown in FIG. 6 includes unregistered device information representing the second evaluation device 20-2 (S2) that is not registered corresponding to the fourth set of setting values (P4) as an unregistered evaluation device. For example, the fourth candidate information (Q4) shown in FIG. 6 includes unregistered device information representing the third evaluation device 20-3 (S3) that is not registered corresponding to the fourth set of setting values (P4) as an unregistered evaluation device. For example, the Kth candidate information (Q K ) includes unregistered device information representing the first evaluation device 20-1 (S1) that is not registered corresponding to the Jth set of setting values (P J ) as an unregistered evaluation device.

[0071] In the example in Figure 6, the candidate list information is described in a table format, but it can be described in any format. Also, in the example in Figure 6, the candidate list information describes one unregistered evaluation device per line, but multiple unregistered evaluation devices may be described per line.

[0072] Figure 7 shows an example of a recommended setting set, along with recommended candidate information, evaluation device information, dataset information, and candidate list information.

[0073] During the problem-solving process, the processing unit 50 repeatedly generates a set of recommended settings based on evaluation device information, dataset information, and candidate list information.

[0074] The processing unit 50 selects one of the multiple candidate information items included in the candidate list information as the recommended candidate information. Then, the processing unit 50 generates a recommended setting value set based on the candidate setting value set, evaluation device information, and dataset information included in the selected recommended candidate information.

[0075] The recommended setting value set includes the candidate setting value set included in the recommended candidate information, and at least one input value from among the evaluation values ​​registered in the dataset information corresponding to the candidate setting value set, which represents an unregistered evaluation device in the evaluation device information.

[0076] For example, in the example in Figure 7, the selected recommendation candidate information consists of K candidate pieces of information (Q1, Q2, Q3, Q4, ..., Q K This is the third candidate information (Q3) among the three. The third candidate information (Q3) includes four setting values ​​(X1=-1.2, X2=2.8, X3=2.9, X4=0.3) and unregistered device information that represents the second evaluation device 20-2 (S2) as an unregistered evaluation device. In the example in Figure 7, the evaluation device information indicates that the input values ​​of the second evaluation device 20-2 (S2), which is an unregistered evaluation device, are the third setting value (X3) and the first evaluation value (y1). Also in the example in Figure 7, the third candidate information (Q3) is the same as the fourth setting value set (P4) in the dataset information.

[0077] Therefore, in the example in Figure 7, the processing unit 50 generates a recommendation setting value set that includes the third setting value (X3=2.9) included in the recommendation candidate information and the first evaluation value (y1=-4.8) which is registered in correspondence with the fourth setting value set (P4) in the dataset information. The processing unit 50 then supplies the generated recommendation setting value set (X3=2.9, y1=-4.8) to the second evaluation device 20-2 (S2), which is an unregistered evaluation device included in the recommendation candidate information. Furthermore, if there are multiple unregistered evaluation devices included in the recommendation candidate information, the processing unit 50 supplies the recommendation setting value set to each of the multiple evaluation devices 20.

[0078] Figure 8 shows the functional configuration of the processing unit 50 together with the storage unit 40.

[0079] The processing unit 50 includes an input unit 52, a candidate information generation unit 54, an estimation unit 56, a recommendation unit 58, an evaluation value acquisition unit 60, an addition unit 62, a repetition control unit 64, and an output unit 66.

[0080] The input unit 52 acquires evaluation device information generated by the user. The input unit 52 may also acquire evaluation device information from an external device. For example, the input unit 52 may acquire evaluation device information in the format shown in Figure 3 or Figure 4, or it may acquire evaluation device information expressed in other formats. Furthermore, the input unit 52 may modify the format of the acquired evaluation device information.

[0081] The input unit 52 acquires evaluation device information at the start of the multi-objective optimization problem solving process and stores it in the storage unit 40. The processing unit 50 may also acquire updated evaluation device information during the multi-objective optimization problem solving process and overwrite the evaluation device information stored in the storage unit 40 with the updated evaluation device information.

[0082] Furthermore, the input unit 52 may acquire information other than evaluation device information. For example, the input unit 52 may acquire the termination conditions for the multi-objective optimization problem solving process at the start of the multi-objective optimization problem solving process.

[0083] The candidate information generation unit 54 generates candidate list information based on the evaluation device information and the dataset information. For example, the candidate information generation unit 54 generates candidate list information that includes multiple candidate information as shown in Figure 6.

[0084] The candidate information generation unit 54 selects as a candidate setting value set any of the one or more setting value sets included in the dataset information that is not a setting value set for which all of the multiple evaluation devices 20 are registered as registered evaluation devices.

[0085] Furthermore, the candidate information generation unit 54 selects an unregistered evaluation device for the selected candidate setting value set. An unregistered evaluation device is any evaluation device 20 that is not registered as a registered evaluation device for the setting value set selected as the candidate setting value set. The candidate information generation unit 54 then generates candidate information that includes the selected candidate setting value set and unregistered device information representing the selected unregistered evaluation device.

[0086] For example, in the dataset information shown in Figure 5, the first set of settings (P1) indicates that the first evaluation device 20-1 (S1) is not registered as a registered evaluation device. Therefore, the candidate information generation unit 54 generates the first candidate information (Q1) shown in Figure 6, which includes the first set of settings (P1) as a candidate set of settings and unregistered device information representing the first evaluation device 20-1 (S1) as an unregistered evaluation device.

[0087] The candidate information generation unit 54 then generates multiple such candidate information items and includes them in the candidate list information.

[0088] Furthermore, the candidate information generation unit 54 does not select as a candidate setting value set any setting value set from among the one or more setting value sets included in the dataset information for which all of the multiple evaluation devices 20 are registered as registered evaluation devices.

[0089] For example, in the dataset information shown in Figure 5, the third set of settings (P3) includes all three evaluation devices: the first evaluation device 20-1 (S1), the second evaluation device 20-2 (S2), and the third evaluation device 20-3 (S3), all of which are registered as registered evaluation devices. Therefore, the candidate information generation unit 54 does not generate candidate information that includes the third set of settings (P3) in the dataset information shown in Figure 5 as a candidate set of settings.

[0090] Furthermore, the candidate information generation unit 54 generates candidate list information in such a way that it does not generate candidate information that includes unregistered device information, which represents non-executable devices among the multiple evaluation devices 20 as unregistered evaluation devices. Non-executable devices are evaluation devices 20 that take the evaluation value output from an unregistered evaluation device as at least one of the input values.

[0091] For example, in the dataset information shown in Figure 5, the first set of settings (P1) does not include the first evaluation device 20-1 (S1) and the second evaluation device 20-2 (S2) as registered evaluation devices. As shown in Figure 3, the second evaluation device 20-2 (S2) uses the first evaluation value (y1) output from the first evaluation device 20-1 (S1) as one of its input values. However, the first evaluation device 20-1 (S1) is an unregistered evaluation device that is not registered as a registered evaluation device for the first set of settings (P1). In other words, if the first set of settings (P1) is used as a candidate set of settings, the second evaluation device 20-2 (S2) becomes an unexecutable device. Therefore, the candidate information generation unit 54 generates candidate list information so as not to generate candidate information that includes the first set of settings (P1) as a candidate set of settings and unregistered device information that represents the second evaluation device 20-2 (S2) as an unregistered evaluation device.

[0092] The candidate information generation unit 54 provides the candidate list information generated in this manner to the recommendation unit 58.

[0093] The estimation unit 56 calculates a function (μ) representing the estimated value for each of the multiple evaluation values ​​based on the dataset information. j (n)We estimate (x) and a function that represents the uncertainty of the estimate. This function (μ j (n) By using (x), the estimation unit 56 can obtain an estimated value of the evaluation value obtained by supplying a candidate set of values ​​(x) to the unregistered evaluation device (j). In this embodiment, the estimation unit 56 uses a function that represents the uncertainty of the estimated value, which is a function that represents the estimated standard deviation of the estimated evaluation value (σ). j (n) Estimate (x). Note that n is an integer greater than or equal to 1, and j is an integer greater than or equal to 1.

[0094] For example, the estimation unit 56 calculates the j-th evaluation value (y j A function (μ) that represents an estimate of the value of ). j (n) (x) and the function (σ) representing the estimated standard deviation j (n) When estimating (x), the data shown in equation (3) is obtained from the dataset information.

number

[0095] x is a vector representing multiple decision variables. (i) y represents multiple setting values ​​included in the i-th setting value set. j (i) This represents the j-th evaluation value registered in the i-th set of settings.

[0096] For example, the estimation unit 56 uses a function (μ1) that represents the estimated value of the first evaluation value (y1) in the dataset information shown in Figure 5. (n) (x) and a function (σ1) representing the estimated standard deviation of the first evaluation value (y1). (n)When estimating (x), the estimation unit 56 retrieves each of the multiple setting value sets in which the first evaluation value (y1) is registered, and the corresponding multiple evaluation values ​​that are registered. More specifically, when the estimation unit 56 calculates an estimated value of the first evaluation value (y1) in the dataset information shown in Figure 5, it retrieves the pair of the second setting value set (P2) and the first evaluation value (y1) registered in correspondence with P2, the pair of the third setting value set (P3) and the first evaluation value (y1) registered in correspondence with P3, and the pair of the fourth setting value set (P4) and the first evaluation value (y1) registered in correspondence with P4.

[0097] For example, the estimation unit 56 uses a regression method to represent the estimated value as a function (μ) such that the sum of the squared errors between the evaluation value and the estimated value is minimized for each of the multiple evaluation values. j (n) (x)) may be estimated. The estimation unit 56 uses linear regression, Lasso regression, elastic network regression, random forest regression considering monotonicity, Gaussian process regression considering monotonicity, and neural network considering monotonicity as regression methods to estimate the function (μ) that represents the estimated value. j (n) (x) may be estimated.

[0098] Furthermore, the estimation unit 56 calculates a function (σ) representing the estimated standard deviation for each of the multiple evaluation values ​​based on the regression results. j (n) (x)) may be estimated. For example, the estimation unit 56 uses a function (σ) to represent the estimated standard deviation based on the confidence interval of Bayesian linear regression, the variance of the outputs of the multiple learned decision trees, and the variance of the output when dropout is performed probabilistically multiple times in the neural network. j (n) (x) may be estimated.

[0099] For example, when using Gaussian process regression, the function that represents the estimated value is (μ j (n) (x) is expressed by equation (4).

number

[0100] In equation (4), the i-th decision variable is x (i) Let the i-th decision variable be (x (i) ) The j-th evaluation value corresponding to y j (i) It is stated that... j The i-th element is y j (i) μ is a vector. j (0) (x) is an arbitrary function. In equation (4), the i-th multiple setting value (x) (i) ) and the h-th multiple setting value (x (h) Covariance (K) ih ) is the kernel function (k(x (i) ,x (h) It is expressed by ). The kernel function is, for example, an exponential kernel, a Matern kernel, or a linear kernel. Also, in equation (4), K is the (i,h) element K ih This is a matrix of k. i (x) = k(x, x (i) ) and k(x) is such that the i-th element is k i This is the vector of (x). T represents the transpose. In equation (4), σ j 2 m is an arbitrary constant, and I is the identity matrix. j This represents the average value of the evaluation scores.

[0101] For example, when using Gaussian process regression, the function that represents the estimation error is the square of the estimated standard deviation (σ j (n) (x) 2 ) is expressed by equation (5).

number

[0102] Furthermore, the estimation unit 56 may use the evaluation device information to estimate a function representing the estimated value and a function representing the estimated standard deviation for each of the multiple evaluation values. Each of the multiple evaluation devices 20 may not input all of the multiple setting values ​​as input values, but rather some of the multiple setting values ​​as input values. In such cases, the estimation unit 56 may use the decision variables corresponding to one or more input values ​​input to the corresponding evaluation device 20 to estimate a function representing the estimated value and a function representing the estimated standard deviation for each of the multiple evaluation values. For example, the first evaluation device 20-1 that outputs the first evaluation value (y1) in the dataset information shown in Figure 5 is indicated in the evaluation device information to input the first setting value (x1) and the second setting value (x2). In this case, the estimation unit 56 uses the first setting value (x1) and the second setting value (x2) in the setting value set to estimate a function (μ1) representing the estimated value of the first evaluation value (y1). (n) (x) and a function (σ1) representing the estimated standard deviation (n) (x)) is estimated. This allows the estimation unit 56 to estimate a function representing the estimated value and a function representing the estimated standard deviation in a short time with high accuracy.

[0103] Furthermore, each of the multiple evaluation devices 20 may input evaluation values ​​output from other evaluation devices 20 as input values. In such cases, the estimation unit 56 may estimate a function representing the estimated value and a function representing the estimated standard deviation for each of the multiple evaluation values, using a function representing the estimated value of the other evaluation values ​​and a function representing the estimated standard deviation. For example, the evaluation device information indicates that the second evaluation device 20-2, which outputs the second evaluation value (y2) in the dataset information shown in Figure 5, inputs the first evaluation value (y1). In this case, the estimation unit 56 uses a function representing the estimated value of the first evaluation value (y1) (μ1 (n) (x) and the function (σ1) representing the estimated standard deviation (n) Using (x), we express the function (μ²) that represents the estimated value of the second evaluation value (y²). (n) (x) and a function (σ²) representing the estimated standard deviation. (n) (x)) is estimated. This allows the estimation unit 56 to estimate a function representing the estimated value and a function representing the estimated standard deviation in a short time with high accuracy.

[0104] Furthermore, in this case, even if only the first evaluation value (y1) is registered in one of the setting value sets in the dataset information and the second evaluation value (y2) is not registered, the function (μ1) representing the estimated value of the first evaluation value (y1) will still be used. (n) (x) and a function (σ1) representing the estimated standard deviation (n) (x)) is updated. Therefore, even if the second evaluation value (y2) is not registered, the estimation unit 56 generates a function (μ2) that represents the estimated value of the second evaluation value (y2). (n) (x) and a function (σ²) representing the estimated standard deviation. (n) (x) can be updated. Therefore, by performing this process, the estimation unit 56 can estimate a function representing the estimated value and a function representing the estimated standard deviation.

[0105] Furthermore, the estimation unit 56 may repeat the process for the number of evaluation values ​​and estimate a function representing the estimated value and a function representing the estimated standard deviation for each of the evaluation values. That is, the estimation unit 56 estimates f(x)={f1(x),f2(x),…,f m For (x), μ1 for f1(x) (n) (x) and σ1 (n) Calculate (x), and μ2 for f2(x) (n) (x) and σ² (n) Calculate (x), ..., f m μ for (x) m (n) (x) and σ m (n) The process may be executed m times, such as calculating (x). Furthermore, the estimation unit 56 may simultaneously calculate functions representing the estimated values ​​of multiple evaluation values ​​and functions representing the estimated standard deviations using a multi-output regression method.

[0106] The estimation unit 56 provides the recommendation unit 58 with a function representing the estimated value for each of the above-mentioned evaluation values, and a function representing the uncertainty of the estimated value.

[0107] The recommendation unit 58 obtains dataset information, evaluation device information, and candidate list information. The recommendation unit 58 also obtains a function representing the estimated value for each of the multiple evaluation values, and a function representing the uncertainty of the estimated value.

[0108] The recommendation unit 58 selects one of several candidates included in the candidate list information as the recommended candidate information. Next, the recommendation unit 58 generates a recommended setting value set based on the candidate setting value set included in the recommended candidate information. Then, the recommendation unit 58 supplies the recommended setting value set to the unregistered evaluation device represented by the unregistered device information included in the recommended candidate information, causing it to generate evaluation values.

[0109] The recommendation unit 58 selects one of the candidate information items included in the candidate list information as a recommended candidate information item, based on a function representing the estimated value for each of the multiple evaluation values ​​and a function representing the uncertainty of the estimated value. For example, the recommendation unit 58 may select the recommended candidate information item using a black-box optimization method. Alternatively, for example, the recommendation unit 58 may select the recommended candidate information item using a genetic algorithm. Alternatively, for example, the recommendation unit 58 may select the recommended candidate information item using an evolutionary strategy, CMA-ES, or Bayesian optimization.

[0110] For example, the recommendation unit 58 generates an acquisition function that represents the quality of the evaluation value obtained by supplying a candidate setting value set (x) to an unregistered evaluation device for each of the multiple candidate pieces of information included in the candidate list information. That is, the recommendation unit 58 generates an acquisition function (α) that represents the quality of the evaluation value obtained by supplying a candidate setting value set (x) to an unregistered evaluation device (j) for each of the multiple candidate pieces of information included in the candidate list information. j (n)The system generates (x). For example, the recommendation unit 58 calculates a function representing the estimated value and a function representing the uncertainty of the estimated value for each of the multiple candidate information items, based on a function representing the estimated value for each of the multiple evaluation values ​​and a function representing the uncertainty of the estimated value, for the evaluation value obtained by supplying a candidate setting value set to an unregistered evaluation device. Subsequently, the recommendation unit 58 calculates an acquisition function for each of the multiple candidate information items, based on the calculated function representing the estimated value and the function representing the uncertainty of the estimated value.

[0111] For example, the recommendation unit 58 may calculate the acquisition function using EHVI (Expected HyperVolume Improvement).

[0112] Next, the recommendation unit 58, for each of the multiple candidate pieces of information included in the candidate list information, provides the unregistered evaluation device (j) and the candidate setting value set (x) to an acquisition function that represents the quality of the evaluation value obtained by supplying the candidate setting value set to the unregistered evaluation device, thereby obtaining the acquisition function value (α j (n) The recommendation unit 58 calculates (x). Then, based on the acquisition function value of each of the multiple candidate pieces of information, the recommendation unit 58 selects recommended candidate information (a combination of an unregistered evaluation device (j) and a candidate setting value set (x)) from the multiple candidate pieces of information. For example, the recommendation unit 58 selects the candidate information that has the maximum acquisition function value among the multiple candidate pieces of information as the recommended candidate information. Alternatively, for example, the recommendation unit 58 may maximize the acquisition function using any optimization method. For example, the recommendation unit 58 may maximize the acquisition function using exhaustive search, random search, grid search, gradient method, L-BFGS, DIRECT, CMA-ES, or multi-start local algorithm.

[0113] Furthermore, because the number of setting value sets included in the dataset information is small, the candidate list information may not include any candidate information. For example, immediately after starting the optimization process, the candidate list information may not include any candidate information. In such cases, the recommendation unit 58 may generate a pre-configured set of recommended setting values. Alternatively, for example, the recommendation unit 58 may set multiple setting values ​​and unregistered evaluation devices using random numbers, Latin squares, Sobol sequences, and grid points.

[0114] Each time the recommendation unit 58 supplies a recommended setting value set to an unregistered evaluation device, the evaluation value acquisition unit 60 acquires an evaluation value calculated from the unregistered evaluation device according to the recommended setting value set. Upon acquiring an evaluation value, the evaluation value acquisition unit 60 registers the unregistered evaluation device as a registered evaluation device in the dataset information, corresponding to the recommended setting value set supplied to the unregistered evaluation device from one or more setting value sets. At the same time, upon acquiring an evaluation value, the evaluation value acquisition unit 60 registers the acquired evaluation value in the dataset information, corresponding to the recommended setting value set supplied to the unregistered evaluation device from one or more setting value sets.

[0115] The additional unit 62 stores dataset information, including one or more initial sets of setting values, in the storage unit 40 at the start of the problem-solving process. For example, at the start of the problem-solving process, the additional unit 62 obtains an initial set of setting values ​​representing multiple values ​​to be substituted for multiple decision variables from an external device, or obtains an initial set of candidate values ​​from a user, and stores dataset information, including the obtained initial set of candidate values, in the storage unit 42.

[0116] For example, the additional unit 62 may generate an initial set of setting values ​​using random numbers, Latin squares, Sobol sequences, and grid points at the start of the solution-finding process, and store the dataset information, including the generated initial set of candidate values, in the storage unit 42. Alternatively, the additional unit 62 may obtain the variable range for each of the multiple decision variables and generate an initial set of setting values ​​within the obtained variable range using random numbers, Latin squares, Sobol sequences, and grid points.

[0117] Furthermore, the addition unit 62 updates the dataset information stored in the storage unit 42. For example, during the problem-solving process, the addition unit 62 generates a new set of setting values ​​representing multiple values ​​to be substituted for multiple decision variables at predetermined intervals, and adds the generated new set of setting values ​​to one or more set of setting values ​​included in the dataset information.

[0118] For example, the addition unit 62 adds a new set of settings to one or more sets of settings included in the dataset information each time a recommended set of settings is supplied to any of the evaluation devices 20. Alternatively, the addition unit 62 may add a new set of settings to one or more sets of settings included in the dataset information each time a recommended set of settings is supplied to any of the evaluation devices 20 a predetermined number of times, at predetermined intervals, or each time a predetermined condition is met.

[0119] The additional unit 62 may generate a new set of settings using, for example, random numbers, Latin squares, Sobol sequences, and grid points. Alternatively, the additional unit 62 may generate a new set of settings within the variable range for each of the multiple decision variables.

[0120] Furthermore, the additional unit 62 may generate multiple estimation functions based on the dataset information, and generate a new set of settings based on the generated multiple estimation functions. For example, the additional unit 62 may generate multiple functions (μ1) estimated by the estimation unit 56, each representing an evaluation value. (n) (x), μ2 (n) Alternatively, (x),…) can be obtained as multiple estimation functions to generate a new set of settings.

[0121] For example, the additional unit 62 calculates a non-inferior solution to a multi-objective optimization problem that optimizes multiple estimation functions using a genetic algorithm such as NSGA-II. Then, the additional unit 62 generates a new set of settings based on the calculated non-inferior solution. Alternatively, the additional unit 62 may generate a new set of settings by replacing a part of one or more set of settings included in the dataset information with a part of the calculated non-inferior solution.

[0122] The repetition control unit 64 controls the repetition of the processing unit 50 during the solution-finding process. Specifically, the repetition control unit 64 controls the repetition of the following: generation of candidate list information by the candidate information generation unit 54, generation of a function representing the estimated value and a function representing the uncertainty of the estimated value by the estimation unit 56, generation of an acquisition function by the recommendation unit 58, selection of recommended candidate information by the recommendation unit 58, supply of a set of recommended setting values ​​by the recommendation unit 58, acquisition of evaluation values ​​by the evaluation value acquisition unit 60, and registration of registered evaluation devices and evaluation values ​​to the dataset information by the evaluation value acquisition unit 60.

[0123] The repetition control unit 64 terminates the repetition process when a predetermined termination condition is reached. For example, the repetition control unit 64 determines that the termination condition has been reached when the process has been repeated a predetermined number of times or when a predetermined time has elapsed.

[0124] When the predetermined termination condition is reached, the output unit 66 selects one or more sets of setting values ​​that are non-inferior solutions for multiple objective functions from the dataset information of the state after the termination condition has been reached. The output unit 66 then outputs the selected one or more sets of setting values ​​as one or more Pareto solutions.

[0125] The output unit 66 may output one or more Pareto solutions in any data format. For example, the output unit 66 may convert or output one or more Pareto solutions as image data, display them in graph format, or output them in tabular format. In addition, the output unit 66 may output data included in the dataset information of the state after the termination condition has been reached, along with one or more Pareto solutions.

[0126] Figure 9 shows an example of the confidence region of a Pareto front.

[0127] The recommendation section 58 may calculate the acquisition function based on the confidence region of the Pareto front, for example, as follows:

[0128] First, for each of the plurality of candidate information, the recommendation unit 58 calculates a confidence region of the target objective function among the plurality of objective functions based on a function representing an estimated value with respect to an evaluation value obtained by supplying a candidate setting value set to an unregistered evaluation device and a function representing the uncertainty of the estimated value.

[0129] The confidence region is the direct product of intervals that satisfy Equation (6) for each of the plurality of evaluation values (y i ). Note that β j (n) is an arbitrary constant.

Equation

[0130] Also, the confidence region may be the direct product of intervals that satisfy Equation (7) for each of the plurality of evaluation values (y i ).

Equation

[0131] Subsequently, for each of the plurality of candidate information, the recommendation unit 58 calculates a confidence region of the Pareto front of the target objective function based on the confidence region of the target objective function with respect to the evaluation value.

[0132] The Pareto front is a hyperplane formed by the objective functions of the decision variables that are not dominated by the objective functions of any other decision variables. The recommendation unit 58 calculates, for each decision variable, a point that takes the largest value of the confidence region of the target objective function as the maximum value, and calculates a Pareto front where all of the plurality of decision variables become the maximum value. Similarly, the recommendation unit 58 calculates, for each decision variable, a point that takes the smallest value of the confidence region of the target objective function as the minimum value, and calculates a Pareto front where all of the plurality of decision variables become the minimum value. Then, the recommendation unit 58 calculates the region between the two Pareto fronts as the confidence region of the Pareto front of the target objective function.

[0133] For example, the horizontal axis in Figure 9 represents the first evaluation value, which evaluates the first objective function (f1(x)) among multiple objective functions. The vertical axis in Figure 9 represents the second evaluation value, which evaluates the second objective function (f2(x)) among multiple objective functions.

[0134] In the example in Figure 9, the confidence regions of the Pareto front of the objective function are the first region 82 hatched with diagonal lines in Figure 9, the second region 84 hatched with dots in Figure 9, and the multiple point regions 86 indicated by black circles in Figure 9. Note that when the estimated standard deviation is 0, the confidence region is represented by points.

[0135] In the first region 82, the point with the largest value in each dimension is at the upper right corner, and the point with the smallest value in each dimension is at the lower left corner. The Pareto front where all multiple decision variables reach their maximum value is represented by the first line 88, which is a solid line in the upper right corner of the first region 82. The Pareto front where all multiple decision variables reach their minimum value is represented by the second line 90, which is a dotted line that partially passes below and to the left of the first line 88. Note that the first line 88 and the second line 90 partially overlap. In the example in Figure 9, the confidence region of the Pareto front of the target objective function is the region between the first line 88 and the second line 90.

[0136] Furthermore, the recommendation section 58 may calculate, as the acquisition function, a function that represents the decrease in the confidence region of the Pareto front when the function representing the uncertainty of the estimated value with respect to the evaluation value is 0.

[0137] For example, the setting value included in the candidate setting value set is x (10) Therefore, if the unregistered evaluation device is the first evaluation device 20-1, the recommendation unit 58 will determine σ1 (n) (x( 10) Let ) = 0. Recommendation 58 is σ1 (n) (x( 10)Without changing anything other than the above, the confidence region of the Pareto front of the objective function is calculated. The recommendation unit 58 calculates the difference between the confidence regions of the Pareto fronts of the two objective functions and uses the calculated difference as the acquisition function. The recommendation unit 58 may also calculate the acquisition function per unit cost as a new acquisition function by dividing the calculated difference by the computational cost or the logarithm of the computational cost of each of the multiple evaluation devices 20. Furthermore, if there are multiple unregistered evaluation devices, the recommendation unit 58 may set the function representing the uncertainty of the estimated value for each of the multiple unregistered evaluation devices to 0.

[0138] Furthermore, recommendation section 58 may calculate the acquisition function based on the improvement in hypervolume as follows: The hypervolume is the supervolume of the region between the Pareto front and the reference point.

[0139] First, the recommendation unit 58 calculates a first hypervolume based on a set of setting values ​​in which evaluation values ​​for all of the multiple evaluation devices 20 are registered, which is one or more set of setting values ​​included in the dataset information.

[0140] Next, the recommendation unit 58 calculates a second hypervolume obtained by supplying a candidate setting value set to an unregistered evaluation device, based on a function representing the estimated value for each evaluation value obtained by supplying a candidate setting value set to an unregistered evaluation device and a function representing the uncertainty of the estimated value, for each of the multiple candidate information.

[0141] In this case, the recommendation unit 58 may assume that the estimated values ​​for each of the evaluation values ​​obtained by supplying the candidate set of values ​​(x) to the unregistered evaluation device (j) are given by equation (8) or equation (9).

number

number

[0142] Furthermore, the recommendation unit 58 may calculate a second hypervolume for each of the multiple candidate information sources based on the estimated evaluation value obtained by supplying a candidate setting value set to an unregistered evaluation device and the evaluation values ​​output from all other evaluation devices 20.

[0143] Then, the recommendation unit 58 calculates a function representing the difference between the first hypervolume and the second hypervolume for each of the multiple candidate information items, as the acquisition function.

[0144] The difference between the first hypervolume and the second hypervolume represents the amount of improvement in the hypervolume when evaluation is performed with a certain candidate information. The recommendation unit 58 can improve the hypervolume more efficiently the greater the improvement in the hypervolume. The recommendation unit 58 may also calculate a new acquisition function by dividing the difference between the first hypervolume and the second hypervolume by the computational cost of each of the multiple evaluation devices 20 or the logarithm of the computational cost. Alternatively, the recommendation unit 58 may calculate the expected improvement in the hypervolume after repeating the evaluation g times as the acquisition function and select the recommended candidate information that maximizes the acquisition function. For example, in the first iteration, the recommendation unit 58 evaluates the candidate setting value set (x) with an unregistered evaluation device (j). The system considers a strategy where, if the first evaluation value is above a threshold, a different unregistered evaluation device (k(≠j)) is evaluated using the same candidate setting value set (x) from the second evaluation onward; and if the first evaluation value is below the threshold, evaluation is performed using an arbitrary unregistered evaluation device with a different candidate setting value set (x'(≠x)) from the second evaluation onward. The recommendation unit 58 calculates the expected improvement in hypervolume at the evaluation values ​​obtained up to the gth iteration of this strategy as the acquisition function. The recommendation unit 58 finds the first unregistered evaluation device (j) and candidate setting value set (x) that maximize the acquisition function among the candidate information, and uses them as recommended candidate information.

[0145] Figure 10 is a flowchart showing the flow of the multi-objective optimization problem solving process by the information processing system 10 according to the embodiment. The information processing system 10 according to the embodiment executes the multi-objective optimization problem solving process in the flow shown in Figure 10.

[0146] First, in S11, the processing unit 50 acquires evaluation device information and stores it in the storage unit 40.

[0147] Next, in S12, the processing unit 50 initializes the dataset information. For example, the processing unit 50 stores initial dataset information, which includes one or more initial setting value sets, in the storage unit 40.

[0148] Next, in S13, the processing unit 50 generates a candidate list containing multiple candidate information based on the dataset information and evaluation device information.

[0149] Next, in S14, the processing unit 50 estimates a function representing the estimated value and a function representing the uncertainty of the estimated value for each of the multiple evaluation values ​​based on the dataset information. For example, for each of the multiple evaluation values, the processing unit 50 estimates a function representing the estimated value using a regression method such that the sum of the squared errors between the evaluation value and the estimated value is minimized. Furthermore, for each of the multiple evaluation values, the processing unit 50 estimates a function representing the estimated standard deviation based on the regression results.

[0150] Next, in S15, the processing unit 50 generates an acquisition function for each of the multiple candidate information items included in the candidate list information, which represents the quality of the evaluation value obtained from the unregistered evaluation device.

[0151] Next, in S16, the processing unit 50 calculates an acquisition function value for each of the multiple candidate information included in the candidate list information by providing an unregistered evaluation device and a candidate setting value set to the generated acquisition function. Then, based on the acquisition function value of each of the multiple candidate information included in the candidate list information, the processing unit 50 selects one recommended candidate information from among the multiple candidate information.

[0152] Next, in S17, the processing unit 50 generates a set of recommended settings based on the selected recommendation candidate information, evaluation device information, and dataset information. For example, based on the evaluation device information, the processing unit 50 identifies the type of input value to be input to the unregistered evaluation device represented by the recommendation candidate information. Then, the processing unit 50 obtains the identified type of input value from the candidate setting set included in the recommendation candidate information and one or more evaluation values ​​registered in correspondence with the candidate setting set included in the dataset information, and generates a set of recommended settings.

[0153] Next, in S18, the processing unit 50 supplies the generated recommended setting value set to the unregistered evaluation device represented in the selection candidate information.

[0154] Next, in S19, the evaluation device 20, which is an unregistered evaluation device that has acquired the recommended setting value set, calculates evaluation values ​​based on the recommended setting value set through simulation or the like.

[0155] Next, in S20, the processing unit 50 obtains evaluation values ​​calculated by simulation or the like from the evaluation device 20, which is an unregistered evaluation device.

[0156] Next, in S21, the processing unit 50 registers the acquired evaluation values ​​in the dataset information. In this case, the processing unit 50 registers the acquired evaluation values ​​in correspondence with the same set of setting values ​​as the set of recommended setting values ​​included in the selection candidate information selected in S16, which is included in the dataset information.

[0157] Next, in S22, the processing unit 50 determines whether or not a predetermined termination condition has been reached. For example, the processing unit 50 determines that the termination condition has been reached if the processes from S13 to S21 have been repeated a predetermined number of times, or if a predetermined time has elapsed. If the processing unit 50 has not reached the termination condition (No in S22), it proceeds to S23. If the processing unit 50 has reached the termination condition (Yes in S22), it proceeds to S24.

[0158] In S23, the processing unit 50 generates a new set of setting values ​​and adds the generated new set of setting values ​​to one or more set of setting values ​​included in the dataset information stored in the storage unit 40. The processing unit 50 may execute the process in S23 every time, or it may execute the process in S23 every predetermined number of times the processes from S13 to S21 are executed.

[0159] When the processing unit 50 completes S23, it returns to processing S13. Then, the processing unit 50 repeats the processes from S13 to S23 until the termination condition is reached.

[0160] In S24, the processing unit 50 selects one or more sets of settings from the dataset information that are non-inferior solutions for multiple objective functions.

[0161] Next, in S25, the processing unit 50 outputs the selected set of settings as one or more Pareto solutions.

[0162] Once processing S25 is complete, processing unit 50 terminates this flow.

[0163] The information processing system 10 described above repeatedly calculates evaluation values ​​using the evaluation device 20 that has a large contribution to the calculated Pareto solution from among the multiple evaluation devices 20. Thus, according to the information processing system 10, one or more Pareto solutions that optimize multiple objective functions in a multi-objective optimization problem can be efficiently calculated using multiple evaluation devices 20.

[0164] Figure 11 shows an example of the hardware configuration of the information processing device 30 according to the embodiment.

[0165] The information processing device 30 according to this embodiment includes a control device such as a CPU 201, storage devices such as a ROM 202 (Read Only Memory) and a RAM 203, a communication I / F 204 that connects to a network for communication, and a bus 211 that connects each part.

[0166] The program executed by the information processing device 30 according to this embodiment is provided pre-installed in a ROM 202 or the like.

[0167] The program executed by the information processing device 30 according to this embodiment may be configured to be provided as a computer program product by recording it in an installable or executable file format onto a computer-readable recording medium such as a CD-ROM (Compact Disk Read Only Memory), a flexible disk (FD), a CD-R (Compact Disk Recordable), or a DVD (Digital Versatile Disk).

[0168] The program executed on such an information processing device 30 includes, for example, processing modules including an input module, a candidate information generation module, an estimation module, a recommendation module, an evaluation value acquisition module, an addition module, a repetition control module, and an output module.

[0169] This program is loaded and executed on RAM203 by CPU201 (processor), causing the information processing device 30 to function as a processing unit 50, which includes an input unit 52, a candidate information generation unit 54, an estimation unit 56, a recommendation unit 58, an evaluation value acquisition unit 60, an addition unit 62, a repetition control unit 64, and an output unit 66. The processing unit 50 may be partially or entirely configured as hardware circuits. The RAM203 functions as a storage unit 40.

[0170] Furthermore, programs executed on a computer are provided as files in a format that can be installed on a computer or in an executable format, recorded on computer-readable recording media such as CD-ROMs, flexible disks, CD-Rs, and DVDs (Digital Versatile Disks).

[0171] Furthermore, this program may be configured to be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. Alternatively, this program may be provided or distributed via a network such as the Internet. Furthermore, the program may be provided pre-installed in ROM202 or the like.

[0172] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents.

[0173] <Note> Furthermore, this technology can also be configured as follows.

[0174] [1] An information processing device that calculates a Pareto solution to a multi-objective optimization problem, each of which optimizes multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Equipped with a processing unit, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The aforementioned processing unit, Based on dataset information containing one or more sets of setting values, multiple candidate sets of information are generated, each containing a candidate set of setting values ​​that is identical to one or more of the aforementioned sets of setting values. Select one of the aforementioned multiple candidate pieces of information as the recommended candidate piece of information. A set of recommended settings is generated based on the set of candidate settings included in the recommended candidate information. The recommended set of settings is supplied to one of the evaluation devices of the plurality of evaluation devices to generate the evaluation value. Information processing device.

[0175] [2] Each of the one or more sets of setting values ​​represents the plurality of setting values, The dataset information can be associated with each of the one or more sets of setting values, and registered evaluation devices among the multiple evaluation devices that acquire the evaluation values ​​can be registered. Each of the above-mentioned plurality of candidate information includes the candidate setting value set and unregistered device information representing an unregistered evaluation device, The unregistered evaluation device is an evaluation device among the plurality of evaluation devices that is not registered in the dataset information as a registered evaluation device corresponding to the candidate setting value set. The aforementioned processing unit, The recommended setting value set is supplied to the unregistered evaluation device, which is represented by the unregistered device information included in the recommended candidate information, to generate the evaluation value. [1] The information processing device described above.

[0176] [3] The aforementioned information processing device is For each of the above-mentioned multiple candidate information, an acquisition function is generated that represents the quality of the evaluation value obtained by supplying the candidate setting value set to the unregistered evaluation device. For each of the aforementioned multiple candidate information, the acquired function value is calculated by providing the generated acquired function with the unregistered evaluation device and the candidate setting value set. Based on the acquisition function values ​​of each of the multiple candidate pieces of information, the recommended candidate information is selected from the multiple candidate pieces of information. [2] The information processing device described above.

[0177] [4] The dataset information can register the evaluation values ​​obtained from each of the multiple evaluation devices, corresponding to each of the one or more sets of setting values. The processing unit repeatedly generates the plurality of candidate information, generates the acquisition function, selects the recommended candidate information, and supplies the recommended setting value set. The aforementioned processing unit, Each time the recommended set of settings is supplied, the evaluation value is obtained from the unregistered evaluation device. In the dataset information, the unregistered evaluation device is registered as the registered evaluation device, and the acquired evaluation values ​​are registered, corresponding to the recommended setting value set supplied from the one or more setting value sets. [3] The information processing device described above.

[0178] [5] When the processing unit reaches a predetermined termination condition, it selects one or more sets of setting values ​​from the dataset information that represent non-inferior solutions for the multiple objective functions, and outputs the selected set of one or more setting values ​​as the Pareto solution. [4] The information processing device described above.

[0179] [6] Prior to iteration, the processing unit includes an initial set of setting values ​​representing the plurality of setting values ​​in the dataset information. [5] The information processing device described above.

[0180] [7] Each of the aforementioned plurality of evaluation devices receives at least one input value, Each of the at least one input value is the evaluation value output from one of the plurality of setting values ​​or one of the plurality of evaluation devices. The processing unit acquires evaluation device information, The evaluation device information includes, for each of the plurality of evaluation devices, information identifying the at least one input value, and information identifying which of the plurality of objective functions' evaluation values ​​will be output. The aforementioned processing unit, The recommended setting value set, which includes the candidate setting value set contained in the recommended candidate information and the at least one input value from the evaluation values ​​registered in the dataset information corresponding to the candidate setting value set, that is represented for the unregistered evaluation device in the evaluation device information, is supplied to the unregistered evaluation device. An information processing device as described in any one of [3] through [6].

[0181] [8] The aforementioned processing unit, To avoid generating candidate information that includes unregistered device information representing non-executable devices among the plurality of evaluation devices as unregistered evaluation devices, the plurality of candidate information is generated. The non-executable device is an evaluation device that takes the evaluation value output from the unregistered evaluation device as one of the at least one input value. [7] The information processing device described above.

[0182] [9] The processing unit generates a new set of setting values ​​representing the plurality of setting values ​​at predetermined intervals, and adds the generated new set of setting values ​​to the one or more setting value sets included in the dataset information. An information processing device as described in any one of [3] through [8].

[0183]

[10] The aforementioned processing unit, Based on the dataset information, multiple estimated functions are generated by estimating the multiple objective functions. The new set of settings is generated based on the aforementioned multiple estimation functions. [9] The information processing device described above.

[0184]

[11] The aforementioned processing unit, A non-inferior solution to the problem of optimizing the aforementioned multiple estimation functions is generated using a genetic algorithm. Based on the aforementioned non-inferior solution, the new set of settings is generated.

[10] The information processing device described above.

[0185]

[12] The aforementioned processing unit, For each of the multiple candidate information items, a function representing the estimated value and a function representing the uncertainty of the estimated value are calculated for the evaluation value obtained by supplying the candidate setting value set to the unregistered evaluation device, and the acquisition function is calculated based on the calculated function representing the estimated value and the function representing the uncertainty of the estimated value. An information processing device as described in any one of [3] through

[11] .

[0186]

[13] The aforementioned processing unit, For each of the aforementioned multiple candidate pieces of information, Based on the function representing the estimated value and the function representing the uncertainty of the estimated value obtained by supplying the candidate set value set to the unregistered evaluation device, the confidence region of the target objective function among the multiple objective functions is calculated. Based on the confidence region of the target objective function, the confidence region of the Pareto front of the target objective function is calculated for the aforementioned evaluation value. The function representing the decrease in the confidence region of the Pareto front when the function representing the uncertainty of the estimated value relative to the evaluation value is 0 is calculated as the acquisition function.

[12] The information processing device described above.

[0187]

[14] The aforementioned processing unit, Based on the set of setting values ​​in which the evaluation values ​​for all of the multiple evaluation devices are registered, among the one or more set of setting values ​​included in the dataset information, the first hypervolume is calculated. For each of the above-mentioned multiple candidate information, a second hypervolume obtained by supplying the candidate setting value set to the unregistered evaluation device is calculated based on a function representing the estimated value for each of the evaluation values ​​obtained by supplying the candidate setting value set to the unregistered evaluation device and a function representing the uncertainty of the estimated value. For each of the multiple candidate information items, a function representing the difference between the first hypervolume and the second hypervolume is calculated as the acquisition function.

[12] The information processing device described above.

[0188]

[15] The information processing device further comprises the plurality of evaluation devices. An information processing device described in any one of [1] through

[14] .

[0189]

[16] An information processing method using an information processing device, which calculates a Pareto solution to a multi-objective optimization problem, each of which optimizes multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The information processing device generates multiple candidate information sets, each of which is identical to one or more of the aforementioned set of setting values, based on dataset information that includes one or more set of setting values. The information processing device selects one of the plurality of candidate information as recommended candidate information. The information processing device generates a set of recommended setting values ​​based on the set of candidate setting values ​​included in the recommended candidate information. The information processing device supplies the recommended setting value set to one of the multiple evaluation devices to generate the evaluation value. Information processing methods.

[0190]

[17] A program for causing a computer to function as an information processing device that calculates Pareto solutions to multi-objective optimization problems, each optimizing multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The aforementioned information processing device is Based on dataset information containing one or more sets of setting values, multiple candidate sets of information are generated, each containing a candidate set of setting values ​​that is identical to one or more of the aforementioned sets of setting values. Select one of the aforementioned multiple candidate pieces of information as the recommended candidate piece of information. A set of recommended settings is generated based on the set of candidate settings included in the recommended candidate information. The recommended set of settings is supplied to one of the evaluation devices of the plurality of evaluation devices to generate the evaluation value. program. [Explanation of symbols]

[0191] 10. Information Processing Systems 20 Evaluation device 30 Information Processing Devices 40 Storage section 42 Storage section 50 Processing Unit 52 Input section 54 Candidate information generation section 56 Estimation part 58 Recommendation Department 60 Evaluation Value Acquisition Unit 62 Additional section 64 Repetition Control Unit Output section of 66

Claims

1. An information processing device that calculates a Pareto solution to a multi-objective optimization problem, each of which optimizes multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Equipped with a processing unit, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The aforementioned processing unit, Based on dataset information containing one or more sets of setting values, multiple candidate information sets are generated, each containing a candidate set of setting values ​​that is identical to one or more of the aforementioned sets of setting values. Select one of the aforementioned multiple candidate information as the recommended candidate information. A set of recommended settings is generated based on the set of candidate settings included in the recommended candidate information. The recommended set of settings is supplied to one of the evaluation devices of the plurality of evaluation devices to generate the evaluation value. Information processing device.

2. Each of the one or more sets of setting values ​​represents the plurality of setting values, The dataset information can be associated with each of the one or more sets of setting values, and registered evaluation devices among the multiple evaluation devices that acquire the evaluation values ​​can be registered. Each of the above-mentioned plurality of candidate information includes the candidate setting value set and unregistered device information representing an unregistered evaluation device, The unregistered evaluation device is an evaluation device among the plurality of evaluation devices that is not registered in the dataset information as a registered evaluation device corresponding to the candidate setting value set. The aforementioned processing unit, The recommended setting value set is supplied to the unregistered evaluation device, which is represented by the unregistered device information included in the recommended candidate information, to generate the evaluation value. The information processing apparatus according to claim 1.

3. The aforementioned information processing device is For each of the above-mentioned multiple candidate information, an acquisition function is generated that represents the quality of the evaluation value obtained by supplying the candidate setting value set to the unregistered evaluation device. For each of the aforementioned multiple candidate information, the acquired function value is calculated by providing the generated acquired function with the unregistered evaluation device and the candidate setting value set. Based on the acquisition function values ​​of each of the multiple candidate pieces of information, the recommended candidate information is selected from the multiple candidate pieces of information. The information processing apparatus according to claim 2.

4. The dataset information can register the evaluation values ​​obtained from each of the multiple evaluation devices, corresponding to each of the one or more sets of setting values. The processing unit repeatedly generates the plurality of candidate information, generates the acquisition function, selects the recommended candidate information, and supplies the recommended setting value set. The aforementioned processing unit, Each time the recommended set of settings is supplied, the evaluation value is obtained from the unregistered evaluation device. In accordance with the supplied recommended setting value set from the one or more setting value sets mentioned above, the unregistered evaluation device is registered as a registered evaluation device in the dataset information, and the acquired evaluation values ​​are also registered. The information processing apparatus according to claim 3.

5. When the processing unit reaches a predetermined termination condition, it selects one or more sets of setting values ​​from the dataset information that represent non-inferior solutions for the multiple objective functions, and outputs the selected set of one or more setting values ​​as the Pareto solution. The information processing apparatus according to claim 4.

6. Prior to iteration, the processing unit includes an initial set of setting values ​​representing the plurality of setting values ​​in the dataset information. The information processing apparatus according to claim 5.

7. Each of the aforementioned plurality of evaluation devices receives at least one input value, Each of the at least one input value is the evaluation value output from one of the plurality of setting values ​​or one of the plurality of evaluation devices. The processing unit acquires evaluation device information, The evaluation device information includes, for each of the plurality of evaluation devices, information identifying the at least one input value, and information identifying which of the plurality of objective functions' evaluation values ​​to output. The aforementioned processing unit, The recommended setting value set, which includes the candidate setting value set contained in the recommended candidate information and the at least one input value from the evaluation values ​​registered in the dataset information corresponding to the candidate setting value set, that is represented for the unregistered evaluation device in the evaluation device information, is supplied to the unregistered evaluation device. The information processing apparatus according to claim 3.

8. The aforementioned processing unit, To avoid generating candidate information that includes unregistered device information representing non-executable devices among the plurality of evaluation devices as unregistered evaluation devices, the plurality of candidate information is generated. The non-executable device is an evaluation device that takes the evaluation value output from the unregistered evaluation device as one of the at least one input value. The information processing apparatus according to claim 7.

9. The processing unit generates a new set of setting values ​​representing the plurality of setting values ​​at predetermined intervals, and adds the generated new set of setting values ​​to the one or more setting value sets included in the dataset information. The information processing apparatus according to claim 3.

10. The aforementioned processing unit, Based on the dataset information, multiple estimated functions are generated by estimating the multiple objective functions. The new set of settings is generated based on the aforementioned multiple estimation functions. The information processing apparatus according to claim 9.

11. The aforementioned processing unit, A non-inferior solution to the problem of optimizing the aforementioned multiple estimation functions is generated using a genetic algorithm. Based on the aforementioned non-inferior solution, the new set of settings is generated. The information processing apparatus according to claim 10.

12. The aforementioned processing unit, For each of the multiple candidate information items, a function representing the estimated value and a function representing the uncertainty of the estimated value are calculated for the evaluation value obtained by supplying the candidate setting value set to the unregistered evaluation device, and the acquisition function is calculated based on the calculated function representing the estimated value and the function representing the uncertainty of the estimated value. The information processing apparatus according to claim 3.

13. The aforementioned processing unit, For each of the aforementioned multiple candidate pieces of information, Based on the function representing the estimated value and the function representing the uncertainty of the estimated value obtained by supplying the candidate set value set to the unregistered evaluation device, the confidence region of the target objective function among the multiple objective functions is calculated. Based on the confidence region of the target objective function, the confidence region of the Pareto front of the target objective function is calculated for the aforementioned evaluation value. The function representing the decrease in the confidence region of the Pareto front when the function representing the uncertainty of the estimated value relative to the evaluation value is zero is calculated as the acquisition function. The information processing apparatus according to claim 12.

14. The aforementioned processing unit, Based on the set of setting values ​​in which the evaluation values ​​for all of the multiple evaluation devices are registered, among the one or more set of setting values ​​included in the dataset information, the first hypervolume is calculated. For each of the aforementioned multiple pieces of candidate information, a second hypervolume obtained by supplying the candidate setting value set to the unregistered evaluation device is calculated based on a function representing the estimated value for each of the evaluation values ​​obtained by supplying the candidate setting value set to the unregistered evaluation device and a function representing the uncertainty of the estimated value. For each of the multiple candidate information items, a function representing the difference between the first hypervolume and the second hypervolume is calculated as the acquisition function. The information processing apparatus according to claim 12.

15. The information processing device further comprises the plurality of evaluation devices. The information processing apparatus according to claim 1.

16. An information processing method using an information processing device, which calculates a Pareto solution to a multi-objective optimization problem, each of which optimizes multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The information processing device generates a plurality of candidate information sets, each of which is identical to one or more of the aforementioned one or more set of setting values, based on dataset information that includes one or more set of setting values. The information processing device selects one of the plurality of candidate information as a recommended candidate information. The information processing device generates a set of recommended setting values ​​based on the set of candidate setting values ​​included in the recommended candidate information. The information processing device supplies the recommended setting value set to one of the multiple evaluation devices to generate the evaluation value. Information processing methods.

17. A program for causing a computer to function as an information processing device that calculates Pareto solutions to multi-objective optimization problems, each optimizing multiple objective functions containing multiple decision variables, using multiple evaluation devices corresponding to the multiple objective functions, Each of the plurality of evaluation devices outputs an evaluation value that evaluates the objective function value obtained by substituting a plurality of setpoints into the plurality of decision variables included in the corresponding objective function among the plurality of objective functions. The aforementioned information processing device is Based on dataset information containing one or more sets of setting values, multiple candidate information sets are generated, each containing a candidate set of setting values ​​that is identical to one or more of the aforementioned sets of setting values. Select one of the aforementioned multiple candidate information as the recommended candidate information. A set of recommended settings is generated based on the set of candidate settings included in the recommended candidate information. The recommended set of settings is supplied to one of the evaluation devices of the plurality of evaluation devices to generate the evaluation value. program.

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