Information processing program, information processing method, and information processing device

Abstract

To enable implementation of multi-objective optimization considering reliability of a characteristic predictive model.SOLUTION: An information processing apparatus 100 generates, as to each characteristic variable of a plurality of characteristic variables, a solution set of a combination of values for the characteristic variables and index values indicating reliability of the values for the characteristic variables by performing first multi-objective optimization. The information processing apparatus 100 specifies, as to each characteristic variable, the index values included in the combination that can become a solution when the characteristic variables are specified values from the generated solution set. The information processing apparatus 100 generates a solution set of a combination for each value of the characteristic variables by performing second multi-objective optimization using an objective function that includes penalty items based on a specified index value δ and is for retrieving each value of the characteristic variables.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an information processing program, an information processing method, and an information processing device. [Background technology]

[0002] Conventionally, there is a technology for learning a characteristic prediction model that uses learning data to model the relationship between multiple objective variables and multiple explanatory variables and outputs a predicted value of each of the multiple objective variables according to the multiple explanatory variables input. There is also a technology called multi-objective optimization that uses a characteristic prediction model to find a solution for multiple explanatory variables that optimizes the values ​​of multiple objective variables.

[0003] Prior art techniques include, for example, a technique for creating a prediction model by machine learning based on the relationship between manufacturing parameters used in manufacturing an organic EL device and the product characteristics of an organic EL device manufactured using the manufacturing parameters. In addition, there is a technique for obtaining a set of design parameters corresponding to a value range by performing an inverse image calculation of a given value range using a model formula of an objective function generated by linear regression modeling. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2021-034168 A [Patent Document 2] JP 2010-122832 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, in the conventional technology, there are cases where the solutions of multiple explanatory variables obtained by multi-objective optimization cannot be trusted. For example, a case can be considered in which multi-objective optimization is performed using a characteristic prediction model trained without using learning data related to the domain of a specific explanatory variable. In this case, the characteristic prediction model cannot accurately obtain predicted values ​​of each objective variable according to the domain of the specific explanatory variable. Therefore, the multi-objective optimization cannot appropriately optimize the values ​​of multiple objective variables, and cannot accurately obtain solutions of multiple explanatory variables.

[0006] In one aspect, the present invention aims to make it possible to perform multi-objective optimization taking into account the reliability of a property prediction model. [Means for solving the problem]

[0007] According to one embodiment, an information processing program, an information processing method, and an information processing device are proposed that perform a first multi-objective optimization using a first objective function for searching for a value of a characteristic variable predicted by a model for each of a plurality of characteristic variables, and a second objective function for searching an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value, identify, for each of the plurality of characteristic variables, an index value included in a combination from the generated solution set that is a solution when the characteristic variable is a specified value, and generate a solution set of combinations of values ​​of each of the plurality of characteristic variables by performing a second multi-objective optimization using an objective function for searching for each of the plurality of characteristic variables predicted by the model, the index value including a penalty term based on the identified index value. Effect of the Invention

[0008] According to one embodiment, it is possible to make it possible to perform multi-objective optimization taking into account the reliability of a characteristic prediction model. [Brief description of the drawings]

[0009] [Figure 1]FIG. 1 is a diagram illustrating an example of an information processing method according to an embodiment. [Diagram 2] FIG. 2 is an explanatory diagram illustrating an example of an information processing system 200. As shown in FIG. [Diagram 3] FIG. 3 is a block diagram showing an example of a hardware configuration of the information processing device 100. As shown in FIG. [Figure 4] FIG. 4 is a block diagram showing an example of a functional configuration of the information processing device 100. As shown in FIG. [Diagram 5] FIG. 5 is an explanatory diagram (part 1) showing an operation example 1 of the information processing device 100. In FIG. [Figure 6] FIG. 6 is an explanatory diagram (part 2) showing the first operation example of the information processing device 100. In FIG. [Figure 7] FIG. 7 is an explanatory diagram (part 3) showing the first operation example of the information processing device 100. In FIG. [Figure 8] FIG. 8 is an explanatory diagram (part 4) showing the first operation example of the information processing device 100. [Figure 9] FIG. 9 is an explanatory diagram (part 5) showing the first operation example of the information processing device 100. [Figure 10] FIG. 10 is an explanatory diagram (part 6) showing the first operation example of the information processing device 100. [Figure 11] FIG. 11 is an explanatory diagram (part 7) showing the first operation example of the information processing device 100. [Figure 12] FIG. 12 is an explanatory diagram (part 8) showing the first operation example of the information processing device 100. [Figure 13] FIG. 13 is an explanatory diagram (part 9) showing the first operation example of the information processing device 100. [Figure 14] FIG. 14 is an explanatory diagram (part 10) showing the first operation example of the information processing device 100. [Figure 15] FIG. 15 is an explanatory diagram (part 11) showing the first operation example of the information processing device 100. [Figure 16] FIG. 16 is an explanatory diagram (part 12) showing the first operation example of the information processing device 100. [Figure 17] FIG. 17 is an explanatory diagram (part 13) showing the first operation example of the information processing device 100. [Figure 18] FIG. 18 is an explanatory diagram (part 14) showing the first operation example of the information processing device 100. [Figure 19] FIG. 19 is an explanatory diagram (part 15) showing the first operation example of the information processing device 100. [Figure 20] FIG. 20 is an explanatory diagram (part 16) showing the first operation example of the information processing device 100. [Figure 21] FIG. 21 is an explanatory diagram (part 17) showing the first operation example of the information processing device 100. [Figure 22] FIG. 22 is an explanatory diagram (part 18) showing the first operation example of the information processing device 100. [Figure 23] FIG. 23 is an explanatory diagram (part 19) showing the first operation example of the information processing device 100. [Figure 24] FIG. 24 is a flowchart illustrating an example of a setting process procedure in the first operation example. [Diagram 25] FIG. 25 is a flowchart illustrating an example of a solution-finding process procedure in the first operational example. [Figure 26] FIG. 26 is a flowchart illustrating an example of an update process procedure in the first operation example. [Figure 27] FIG. 27 is an explanatory diagram (part 1) showing the second operation example of the information processing device 100. [Figure 28] FIG. 28 is an explanatory diagram (part 2) showing the second operation example of the information processing device 100. [Figure 29] FIG. 29 is an explanatory diagram (part 3) showing the second operation example of the information processing device 100. [Diagram 30] FIG. 30 is an explanatory diagram (part 4) showing the second operation example of the information processing device 100. [Diagram 31] FIG. 31 is an explanatory diagram (part 5) showing the second operation example of the information processing device 100. [Diagram 32] FIG. 32 is an explanatory diagram (part 6) showing the second operation example of the information processing device 100. [Diagram 33] FIG. 33 is a flowchart illustrating an example of an update process procedure in the second operation example. [Diagram 34]FIG. 34 is an explanatory diagram (part 1) showing the third operation example of the information processing device 100. [Diagram 35] FIG. 35 is an explanatory diagram (part 2) showing the third operation example of the information processing device 100. [Diagram 36] FIG. 36 is an explanatory diagram (part 3) showing the third operation example of the information processing device 100. [Figure 37] FIG. 37 is an explanatory diagram (part 4) showing the third operation example of the information processing device 100. [Figure 38] FIG. 38 is an explanatory diagram (part 5) showing the third operation example of the information processing device 100. [Figure 39] FIG. 39 is a flowchart illustrating an example of a solution-finding process procedure in the third operation example. [Diagram 40] FIG. 40 is a diagram illustrating an example of single-objective optimization. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of an information processing program, an information processing method, and an information processing device according to the present invention will be described in detail with reference to the drawings.

[0011] (An example of an information processing method according to an embodiment) 1 is an explanatory diagram showing an example of an information processing method according to an embodiment. An information processing device 100 is a computer for performing multi-objective optimization using an objective function for searching values ​​of each of a plurality of characteristic variables.

[0012] The objective function is, for example, a function for searching the value of a characteristic variable and bringing the value of the characteristic variable closer to a desired value. More specifically, the objective function is a function for optimizing the value of the characteristic variable. The optimization is, for example, minimization or maximization.

[0013] Multi-objective optimization uses, for example, a genetic algorithm. Multi-objective optimization is a technique that optimizes the values ​​of each characteristic variable, which is, for example, an objective variable, and finds multiple solutions for combinations of the values ​​of each characteristic variable. For example, solutions found by multi-objective optimization are sometimes called "Pareto solutions." There is a tendency for the number of Pareto solutions to not be limited to one. For this reason, multi-objective optimization specifically seeks a set of Pareto solutions.

[0014] The characteristic variables are, for example, objective variables of multi-objective optimization. The values ​​of the characteristic variables are, for example, predicted by a model. Specifically, the values ​​of the characteristic variables are predicted by the model according to the explanatory variables. The model, for example, indicates the relationship between a plurality of characteristic variables and a plurality of explanatory variables. The model is, for example, trained based on training data. The model is, for example, a characteristic prediction model. The optimization is, for example, minimization or maximization. The Pareto solution includes, for example, the optimized values ​​of each characteristic variable and the parameters of the model when optimizing the values ​​of each characteristic variable.

[0015] In the conventional technology, there are cases where the Pareto solutions obtained by multi-objective optimization cannot be trusted. For example, there are cases where multi-objective optimization is performed using a characteristic prediction model trained using multiple training data with a relatively narrow distribution. Specifically, there are cases where multi-objective optimization is performed using a characteristic prediction model trained without using training data related to a specific explanatory variable region.

[0016] In this case, the characteristic prediction model cannot accurately obtain the predicted values ​​of each characteristic variable according to the region of a specific explanatory variable. Therefore, the multi-objective optimization cannot appropriately optimize the values ​​of multiple characteristic variables and cannot accurately obtain a Pareto solution set. For example, the multi-objective optimization uses a characteristic prediction model, but leaves Pareto solution candidates with relatively poor accuracy without selecting them, so the values ​​of multiple characteristic variables cannot be appropriately optimized and the Pareto solution set cannot be accurately obtained.

[0017] Therefore, in this embodiment, an information processing method that makes it possible to perform multi-objective optimization taking into account the reliability of a characteristic prediction model will be described.

[0018] (1-1) The information processing device 100 performs a first multi-objective optimization for each of a plurality of characteristic variables to generate a solution set of combinations of values ​​of the characteristic variables and index values ​​indicating the reliability of the values ​​of the characteristic variables. The values ​​of the characteristic variables are predicted by, for example, a model 101. The model 101 is trained based on, for example, a plurality of training data.

[0019] The model 101, for example, at least indicates a relationship between a characteristic variable and an explanatory variable, and makes it possible to predict the value of the characteristic variable. The model 101, for example, may further make it possible to calculate an index value indicating the reliability of the value of the characteristic variable. Specifically, the model 101 is a Gaussian process regression model. The index value has a property that, for example, the lower the reliability, the larger the value becomes. The index value is calculated, for example, by the model 101. For example, the index value may not be calculated by the model 101. For example, the index value may be calculated based on learning data.

[0020] The first multi-objective optimization is, for example, a process of generating a solution set of combinations of characteristic variable values ​​and index values ​​indicating the reliability of the characteristic variable values, using an objective function for searching the values ​​of the characteristic variables and an objective function for searching index values ​​indicating the reliability of the characteristic variable values. The objective function for searching the values ​​of the characteristic variables is, for example, an objective function for optimizing the values ​​of the characteristic variables. The optimization is, for example, minimization or maximization.

[0021] The objective function for searching for an index value indicating the reliability of the characteristic variable value is, for example, an objective function for optimizing the index value indicating the reliability of the characteristic variable value. The objective function for optimizing the index value indicating the reliability of the characteristic variable value is, for example, an objective function for minimizing the index value indicating the reliability of the characteristic variable value. The solution includes, for example, the optimized characteristic variable value and an index value indicating the reliability of the characteristic variable value, and further includes parameters of the model 101 when optimizing the characteristic variable value. The information processing device 100 generates, for example, a solution set shown in a graph 102. The horizontal axis of the graph 102 is, for example, the value of the characteristic variable, and the vertical axis of the graph 102 is, for example, the index value indicating the reliability of the characteristic variable value.

[0022] (1-2) For each characteristic variable, the information processing device 100 identifies an index value included in a combination that is a solution when the characteristic variable is a specified value among the generated solution sets. For example, the information processing device 100 accepts a designation of one of the solutions in the generated solution set based on an operational input by a user, and identifies an index value δ included in the combination that is the specified solution for each characteristic variable. This allows the information processing device 100 to identify one of the index values ​​δ that is a criterion for considering the reliability of the model 101 for each characteristic variable.

[0023] (1-3) The information processing device 100 generates a solution set of combinations of values ​​of each characteristic variable by performing a second multi-objective optimization. The values ​​of the characteristic variables are predicted by the model 101, for example. The second multi-objective optimization is a process of generating a solution set of combinations of values ​​of each characteristic variable using an objective function for searching values ​​of each characteristic variable, the objective function including a penalty term based on the specified index value δ, for example. The objective function for searching values ​​of the characteristic variables is, for example, an objective function for optimizing values ​​of the characteristic variables. The optimization is, for example, minimization or maximization.

[0024] The objective function for optimizing the value of a characteristic variable includes, for example, a penalty term based on an index value δ specified for the characteristic variable. Specifically, the penalty term included in the objective function for optimizing the value of the characteristic variable has a property that the value becomes large when an index value indicating the reliability of the value of the characteristic variable is larger than the index value δ specified for the characteristic variable. The solution includes, for example, the optimized values ​​of each characteristic variable, and further includes parameters of the model 101 when optimizing the values ​​of each characteristic variable. The information processing device 100 generates, for example, a solution set shown in graph 103. The horizontal axis of graph 103 is, for example, the value of a certain characteristic variable, and the vertical axis of graph 102 is, for example, the value of another characteristic variable.

[0025] This allows the information processing device 100 to optimize the values ​​of the respective characteristic variables. The information processing device 100 can, for example, perform a second multi-objective optimization that takes into account the reliability of the model 101, and can optimize the values ​​of the respective characteristic variables with high accuracy, thereby enabling the information processing device 100 to accurately obtain a solution set.

[0026] Therefore, the information processing device 100 can obtain a solution set with relatively high reliability, and can enable a user to use a solution set with relatively high usefulness, thereby improving convenience. For example, the user can select a desired solution from the solution set according to his / her own purpose. For example, the user can use parameters included in the selected desired solution according to his / her own purpose.

[0027] Furthermore, even when the information processing device 100 performs the second multi-objective optimization based on the model 101 trained using a plurality of training data with a relatively narrow distribution, the information processing device 100 can accurately obtain a solution set. Therefore, the information processing device 100 can reduce the workload involved in training the model 101.

[0028] Although the case where the index value has a property that the lower the reliability is, the larger the value is described here, this is not limiting. For example, the index value may have a property that the higher the reliability is, the larger the value is.

[0029] Here, the case where the index value has a property that the lower the reliability, the larger the value, and the objective function for optimizing the index value indicating the reliability of the value of the characteristic variable is an objective function for minimizing the index value indicating the reliability of the value of the characteristic variable has been described, but is not limited to this. For example, the index value may have a property that the lower the reliability, the larger the value, and the objective function for optimizing the index value indicating the reliability of the value of the characteristic variable may be an objective function for maximizing the index value indicating the reliability of the value of the characteristic variable. In this case, it is preferable that the penalty term included in the objective function for optimizing the value of the characteristic variable in the second multi-objective optimization has a property that the value becomes larger when the index value indicating the reliability of the value of the characteristic variable is smaller than the index value specified for the characteristic variable.

[0030] Here, the case where the information processing device 100 operates independently has been described, but the present invention is not limited to this. For example, the information processing device 100 may cooperate with another computer. For example, the information processing device 100 may perform a first multi-objective optimization for each characteristic variable, identify an index value included in a combination that is a solution, and transmit the identified index value to another computer capable of performing a second multi-objective optimization. In addition, for example, the information processing device 100 may form a client-server system as described later in FIG. 2.

[0031] (An example of the information processing system 200) Next, an example of an information processing system 200 to which the information processing device 100 shown in FIG. 1 is applied will be described with reference to FIG.

[0032] 2 is an explanatory diagram showing an example of an information processing system 200. In FIG. 2, the information processing system 200 includes an information processing device 100 and a client device 201.

[0033] In the information processing system 200, the information processing device 100 and the client device 201 are connected via a wired or wireless network 210. The network 210 is, for example, a local area network (LAN), a wide area network (WAN), or the Internet.

[0034] The information processing device 100 is a computer for obtaining a Pareto solution set of a combination of values ​​of each of a plurality of characteristic variables. The information processing device 100 receives, for example, a processing request from the client device 201. The processing request is, for example, a notification requesting to obtain a Pareto solution set of a combination of values ​​of each of a plurality of characteristic variables.

[0035] For example, when the information processing device 100 receives a processing request, it performs a first multi-objective optimization for each characteristic variable to generate a Pareto solution set of combinations of the values ​​of the characteristic variables and index values ​​indicating the reliability of the values ​​of the characteristic variables.

[0036] For example, the information processing device 100 specifies, for each characteristic variable, an index value included in a combination that becomes a Pareto solution when the characteristic variable is a specified value among the generated Pareto solution sets. Specifically, the information processing device 100 transmits the generated Pareto solution set for the characteristic variable to the client device 201 in association with each characteristic variable. Specifically, as a result of transmitting the Pareto solution set, the information processing device 100 receives an instruction from the client device 201 indicating to select one of the Pareto solutions in the generated Pareto solution set for each characteristic variable. Specifically, the information processing device 100 specifies, for each characteristic variable, an index value included in a combination that becomes a Pareto solution indicated by the received instruction among the generated Pareto solution sets as a reference value.

[0037] The information processing device 100 performs the second multi-objective optimization to generate a Pareto solution set of combinations of values ​​of each characteristic variable. The information processing device 100 transmits the generated Pareto solution set to the client device 201. The information processing device 100 is, for example, a server or a PC (Personal Computer).

[0038] The client device 201 transmits a processing request to the information processing device 100 based on, for example, an operation input by a user. The client device 201 receives, for example, a Pareto solution set generated for each characteristic variable associated with the characteristic variable from the information processing device 100. The client device 201 outputs, for example, a Pareto solution set generated for each characteristic variable associated with the characteristic variable so that the user can refer to it. The output format is, for example, display on a display, printout on a printer, or storage in a memory area.

[0039] The client device 201 accepts a selection of any one of the Pareto solutions in the generated Pareto solution set for each characteristic variable based on, for example, a user's operation input. The client device 201 transmits, for example, an instruction to the information processing device 100 to select any one of the Pareto solutions in the generated Pareto solution set for each characteristic variable.

[0040] The client device 201 receives the Pareto solution sets for the combinations of the values ​​of the characteristic variables from the information processing device 100. The client device 201 outputs the Pareto solution sets for the combinations of the values ​​of the characteristic variables so that the user can refer to them. The output format may be, for example, display on a display, printout on a printer, or storage in a memory area. The client device 201 may be, for example, a PC, a tablet terminal, or a smartphone.

[0041] Here, the case where the information processing device 100 is a computer different from the client device 201 has been described, but this is not limited thereto. For example, the information processing device 100 may have a function as the client device 201 and may also operate as the client device 201.

[0042] Here, for example, the functions of the information processing device 100 may be distributed and implemented in multiple computers. Specifically, a computer that performs the first multi-objective optimization, a computer that identifies index values ​​included in a combination that results in a Pareto solution, and a computer that performs the second multi-objective optimization may exist and work together.

[0043] (Example of hardware configuration of information processing device 100) Next, an example of the hardware configuration of the information processing device 100 will be described with reference to FIG.

[0044] Fig. 3 is a block diagram showing an example of a hardware configuration of the information processing device 100. In Fig. 3, the information processing device 100 has a CPU (Central Processing Unit) 301, a memory 302, a network I / F (Interface) 303, a recording medium I / F 304, and a recording medium 305. In addition, each component is connected to each other via a bus 300.

[0045] Here, the CPU 301 is responsible for the overall control of the information processing device 100. The memory 302 has, for example, a read only memory (ROM), a random access memory (RAM), and a flash ROM. Specifically, for example, the flash ROM and the ROM store various programs, and the RAM is used as a work area for the CPU 301. The programs stored in the memory 302 are loaded into the CPU 301, causing the CPU 301 to execute the coded processes.

[0046] The network I / F 303 is connected to the network 210 through a communication line, and is connected to other computers via the network 210. The network I / F 303 manages an internal interface with the network 210, and controls input and output of data from other computers. The network I / F 303 is, for example, a modem or a LAN adapter.

[0047] The recording medium I / F 304 controls reading / writing data from / to the recording medium 305 under the control of the CPU 301. The recording medium I / F 304 is, for example, a disk drive, a solid state drive (SSD), a universal serial bus (USB) port, etc. The recording medium 305 is a non-volatile memory that stores data written under the control of the recording medium I / F 304. The recording medium 305 is, for example, a disk, a semiconductor memory, a USB memory, etc. The recording medium 305 may be detachable from the information processing device 100.

[0048] In addition to the above-mentioned components, the information processing device 100 may have, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, etc. Furthermore, the information processing device 100 may have a plurality of recording medium I / Fs 304 and recording media 305. Furthermore, the information processing device 100 may not have the recording medium I / Fs 304 and the recording media 305.

[0049] (Example of Hardware Configuration of Client Device 201) An example of the hardware configuration of the client device 201 is similar to the example of the hardware configuration of the information processing device 100 shown in FIG. 3, and therefore a description thereof will be omitted.

[0050] (Example of functional configuration of information processing device 100) Next, an example of a functional configuration of the information processing device 100 will be described with reference to FIG.

[0051] 4 is a block diagram showing an example of a functional configuration of the information processing device 100. The information processing device 100 includes a storage unit 400, an acquisition unit 401, a learning unit 402, a first optimization unit 403, a specification unit 404, a second optimization unit 405, and an output unit 406.

[0052] The storage unit 400 is realized by, for example, a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3. In the following, a case where the storage unit 400 is included in the information processing device 100 will be described, but this is not limiting. For example, the storage unit 400 may be included in a device different from the information processing device 100, and the stored contents of the storage unit 400 may be accessible from the information processing device 100.

[0053] The acquiring unit 401 to the output unit 406 function as an example of a control unit. Specifically, the acquiring unit 401 to the output unit 406 realize their functions by, for example, causing the CPU 301 to execute a program stored in a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3, or by the network I / F 303. The processing results of each functional unit are stored in, for example, a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3.

[0054] The storage unit 400 stores various information that is referred to or updated in the processing of each functional unit. The storage unit 400 stores, for example, multiple pieces of learning data. The learning data are, for example, samples of combinations of values ​​of multiple explanatory variables and values ​​of characteristic variables that become multiple objective variables. The learning data is, for example, acquired by the acquisition unit 401.

[0055] The storage unit 400 stores, for example, a model. The model is learned, for example, based on learning data. The model makes it possible to predict the value of each of the multiple characteristic variables. The model may make it possible to calculate, for example, an index value indicating the reliability of the value of each of the multiple characteristic variables. The index value, for example, has a property that the higher the reliability, the smaller the value. The index value may have a property that the higher the reliability, the larger the value. The model is, for example, a Gaussian process regression model. The model is learned, for example, by the learning unit 402. The model may be acquired, for example, by the acquisition unit 401.

[0056] The storage unit 400 stores, for example, a result of performing a first multi-objective optimization. The first multi-objective optimization uses, for example, an objective function for searching values ​​of characteristic variables and an objective function for searching index values ​​indicating the reliability of the values ​​of the characteristic variables. Specifically, the first multi-objective optimization uses an objective function for optimizing values ​​of characteristic variables and an objective function for optimizing index values ​​indicating the reliability of the values ​​of the characteristic variables. The values ​​of the specific variables are predicted, for example, by a model. The index values ​​are calculated, for example, by a model.

[0057] The index value may be calculated, for example, based on the learning data. Specifically, the index value may be calculated based on the distance from each of the multiple learning data to the value of the characteristic variable. More specifically, the index value may be a statistical value regarding the distance from the value of the characteristic variable included in each of the multiple learning data to the value of the characteristic variable predicted by the model. The statistical value may be, for example, a minimum value, a maximum value, an average value, a median value, or a mode value. More specifically, the index value may be calculated by the k-nearest neighbor method.

[0058] More specifically, the index value may be expressed by a data density based on the distance from the value of the characteristic variable included in each of the multiple learning data to the value of the characteristic variable predicted by the model. The data density is calculated by, for example, kernel density estimation. The data density is calculated by, for example, OCSVM (One-Class Support Vector Machine). The data density is calculated by, for example, 1 / d ave d ave is the average distance.

[0059] Specifically, the storage unit 400 stores a solution set of combinations of characteristic variable values ​​and index values ​​indicating the reliability of the characteristic variable values ​​obtained as a result of performing the first multi-objective optimization. The solution set includes, for example, a plurality of solutions indicating one of combinations of characteristic variable values ​​and index values ​​indicating the reliability of the characteristic variable values. The solution may include, for example, model parameters that enable calculation of the characteristic variable values ​​included in the combination. The solution is called, for example, a Pareto solution. The first multi-objective optimization is performed, for example, by the first optimization unit 403.

[0060] The storage unit 400 stores, for example, a result of performing the second multi-objective optimization. The second multi-objective optimization uses, for example, an objective function for searching values ​​of each of a plurality of characteristic variables. Specifically, the second multi-objective optimization uses an objective function for optimizing values ​​of each of a plurality of characteristic variables. The values ​​of the characteristic variables are predicted, for example, by a model. The objective function includes, for example, a penalty term based on any of the index values.

[0061] Specifically, the storage unit 400 stores a solution set of combinations of values ​​of each characteristic variable obtained as a result of performing the second multi-objective optimization. The solution set includes, for example, a plurality of solutions each indicating one of combinations of values ​​of each characteristic variable. The solution may include, for example, parameters of a model that enable the combination to be calculated. The solution is, for example, called a Pareto solution. The second multi-objective optimization is performed by, for example, the second optimization unit 405.

[0062] The acquisition unit 401 acquires various information used for processing by each functional unit. The acquisition unit 401 stores the acquired various information in the storage unit 400 or outputs it to each functional unit. The acquisition unit 401 may also output the various information stored in the storage unit 400 to each functional unit. The acquisition unit 401 acquires various information based on, for example, an operation input by a user. The acquisition unit 401 may receive various information from, for example, a device different from the information processing device 100.

[0063] The acquiring unit 401 acquires learning data. For example, the acquiring unit 401 acquires the learning data by accepting input of the learning data based on an operation input by a user. For example, the acquiring unit 401 may acquire the learning data by receiving the learning data from another computer. The other computer is, for example, the client device 201.

[0064] The acquisition unit 401 acquires a model. For example, the acquisition unit 401 acquires the model by accepting an input of the model based on an operational input by a user. For example, the acquisition unit 401 may acquire the model by receiving it from another computer. The other computer is, for example, the client device 201.

[0065] The acquiring unit 401 acquires a processing request for generating a solution set of combinations of values ​​of each of a plurality of characteristic variables. The acquiring unit 401 acquires the processing request by accepting an input of the processing request based on, for example, an operation input by a user. The acquiring unit 401 may acquire the processing request by receiving it from another computer. The other computer is, for example, the client device 201.

[0066] The acquiring unit 401 accepts the designation of the value of a characteristic variable. For example, the acquiring unit 401 accepts the designation of the value of the characteristic variable in order to make it possible to identify any solution of a solution set of combinations of the value of the characteristic variable and an index value indicating the reliability of the value of the characteristic variable obtained as a result of performing the first multi-objective optimization. Specifically, the acquiring unit 401 accepts the designation of the value of the characteristic variable by receiving a notification designating the value of the characteristic variable from another computer. Specifically, the acquiring unit 401 may accept the designation of the value of the characteristic variable by accepting an input of the value of the characteristic variable based on an operation input by a user.

[0067] The acquiring unit 401 may accept the designation of the values ​​of the characteristic variables, for example, by accepting the designation of one of the solutions. Specifically, the acquiring unit 401 may accept the designation of one of the solutions by receiving a notification designating one of the solutions from another computer, and may accept the designation of the values ​​of the characteristic variables included in one of the solutions. Specifically, the acquiring unit 401 may accept the designation of one of the solutions based on an operational input by a user, and may accept the designation of the values ​​of the characteristic variables included in one of the solutions.

[0068] The acquisition unit 401 may receive a start trigger for starting processing of any of the functional units. The start trigger may be, for example, a predetermined operation input by a user. The start trigger may be, for example, reception of predetermined information from another computer. The start trigger may be, for example, output of predetermined information by any of the functional units.

[0069] The acquiring unit 401 may, for example, accept the acquisition of learning data as a start trigger for starting the processing of the learning unit 402. The acquiring unit 401 may, for example, accept the acquisition of a processing request as a start trigger for starting the processing of the first optimization unit 403. The acquiring unit 401 may, for example, accept the acceptance of a designation of a value of a characteristic variable as a start trigger for starting the processing of the second optimization unit 405.

[0070] The learning unit 402 learns a model for each characteristic variable that makes it possible to predict the value of the characteristic variable. The model is, for example, a mathematical formula. The model may be, for example, a neural network. Specifically, the model is a Gaussian process regression model. The Gaussian process regression model makes it possible to predict the value of the characteristic variable and to calculate an index value indicating the reliability of the value of the characteristic variable.

[0071] The learning unit 402 learns a model based on, for example, a plurality of pieces of learning data. Specifically, the learning unit 402 learns a Gaussian process regression model for each characteristic variable based on a plurality of pieces of learning data. This allows the learning unit 402 to predict the value of the characteristic variable. Furthermore, the learning unit 402 may be able to calculate an index value indicating the reliability of the value of the characteristic variable.

[0072] The first optimization unit 403 performs a first multi-objective optimization for each of a plurality of characteristic variables to generate a solution set of a combination of a value of the characteristic variable and an index value indicating the reliability of the value of the characteristic variable. The value of the characteristic variable is, for example, a value predicted by a trained model. Specifically, the value of the characteristic variable is predicted by a Gaussian process regression model. The index value is, for example, calculated by the Gaussian process regression model. The index value may be calculated by the first optimization unit 403 based on, for example, a plurality of learning data.

[0073] The first optimization unit 403 may perform the first multi-objective optimization while calculating an index value indicating the reliability of each characteristic variable value predicted by the model based on multiple learning data, for example. This allows the first optimization unit 403 to specify, for each characteristic variable, the relationship between the value of that characteristic variable and the index value indicating the reliability of the value of that characteristic variable.

[0074] The identifying unit 404 identifies, for each characteristic variable, an index value included in a combination that is a solution when the characteristic variable has a designated value from among the solution sets generated by the first optimization unit 403. For example, for each characteristic variable, the identifying unit 404 identifies the value of the characteristic variable whose designation has been accepted by the acquiring unit 401, and identifies, from among the generated solution sets, an index value included in a combination that is a solution when the characteristic variable has the designated value.

[0075] For example, the identifying unit 404 identifies, for each characteristic variable, an index value included in a combination that is a solution designated by the acquiring unit 401, from among the generated solution sets. This allows the identifying unit 404 to identify, for each characteristic variable, an index value that serves as a reference for considering the reliability of the value of the characteristic variable predicted by the model. This makes it easier for the identifying unit 404 to consider the reliability of the value of the characteristic variable predicted by the model for each characteristic variable.

[0076] Here, the acquiring unit 401 may not accept the value of the characteristic variable or the designation of any of the solutions. In this case, the identifying unit 404 automatically designates any of the solutions by, for example, selecting any of the solutions from the generated solution set for each characteristic variable based on the z-score or the curvature. Specifically, the identifying unit 404 automatically designates any of the solutions by selecting the solution with the maximum curvature from the generated solution set for each characteristic variable.

[0077] The identifying unit 404 may accept the designation of the characteristic variable value by, for example, identifying the value of the characteristic variable that is determined to be relatively favorable according to a certain criterion in the generated solution set for each characteristic variable. In this way, the identifying unit 404 can identify, for each characteristic variable, an index value that serves as a criterion for considering the reliability of the value of the characteristic variable predicted by the model. The identifying unit 404 can reduce the workload of the user by eliminating the need for the user to designate the value of the characteristic variable.

[0078] The identifying unit 404 judges whether or not the value of any of the multiple characteristic variables in the solution set of the combination of the values ​​of each characteristic variable generated by the second optimization unit 405 satisfies a target value. The target value is set based on, for example, a specified value. The target value is, for example, a specified value.

[0079] For example, if the target value is a value indicating a lower limit, the identifying unit 404 determines that the value of the characteristic variable satisfies the target value if the value of the characteristic variable is equal to or greater than the target value. For example, if the target value is a value indicating an upper limit, the identifying unit 404 determines that the value of the characteristic variable satisfies the target value if the value of the characteristic variable is equal to or less than the target value. Here, if the value of any of the characteristic variables does not satisfy the target value, the identifying unit 404 identifies a new index value for that characteristic variable that is different from the index value identified immediately before.

[0080] Here, for example, the index value indicating reliability may be an index value whose value increases as the reliability decreases, and the objective function for optimizing the index value indicating reliability may be an objective function for minimizing the index value indicating reliability. In this case, the identification unit 404, for example, determines whether or not the value of any of the characteristic variables in the solution set of the generated combination of the values ​​of each characteristic variable satisfies a target value. Then, for example, if the target value is not satisfied, the identification unit 404 identifies a new index value for any of the characteristic variables that is larger than the index value identified immediately before by a first value. This allows the identification unit 404 to re-execute the second multi-objective optimization and generate a more appropriate solution set.

[0081] When the value of any of the multiple characteristic variables in the generated solution set of the combination of the values ​​of the characteristic variables satisfies the target value, the identifying unit 404 may further determine whether or not it is included in a range based on the target value. For example, when the optimization of the index value indicating reliability indicates minimization, the range based on the target value is considered to be a range related to values ​​smaller than the target value.

[0082] For example, when the value of any of the characteristic variables is not included in a range based on the target value, the identifying unit 404 identifies a new index value for the characteristic variable that is smaller than the index value identified immediately before by a second value different from the first value. The second value is preferably smaller than the first value. This enables the identifying unit 404 to relax the criteria for considering the reliability of the characteristic variable value predicted by the model, making it easier to generate an appropriate solution set.

[0083] Here, for example, the index value indicating reliability may be an index value whose value increases as the reliability decreases, and the objective function for optimizing the index value indicating reliability may be an objective function for maximizing the index value indicating reliability. In this case, the identifying unit 404, for example, determines whether or not the value of any of the characteristic variables in the solution set of the generated combination of the values ​​of each characteristic variable satisfies a target value. Then, for example, if the target value is not satisfied, the identifying unit 404 identifies a new index value for any of the characteristic variables that is smaller than the index value identified immediately before by a first value. This allows the identifying unit 404 to re-execute the second multi-objective optimization and generate a more appropriate solution set.

[0084] When the value of any of the multiple characteristic variables in the generated solution set of the combination of the values ​​of the characteristic variables satisfies the target value, the identifying unit 404 may further determine whether or not it is included in a range based on the target value. For example, when the optimization of the index value indicating reliability indicates maximization, the range based on the target value is considered to be a range related to values ​​larger than the target value.

[0085] For example, when the value of any of the characteristic variables is not included in a range based on the target value, the identifying unit 404 identifies a new index value for the characteristic variable that is greater than the index value identified immediately before by a second value different from the first value. The second value is preferably smaller than the first value. This allows the identifying unit 404 to relax the criteria for considering the reliability of the characteristic variable value predicted by the model, making it easier to generate an appropriate solution set.

[0086] The second optimization unit 405 performs the second multi-objective optimization to generate a solution set of combinations of values ​​of each characteristic variable. The second multi-objective optimization uses, for example, an objective function for optimizing the value of each characteristic variable predicted by the model. The objective function includes, for example, a penalty term based on an index value identified by the identification unit 404. The penalty term has a property that its value changes depending on, for example, the magnitude relationship between an index value indicating the reliability of the value of the characteristic variable and the index value identified by the identification unit 404 for the characteristic variable. Specifically, the penalty term has a property that its value increases if the index value indicating the reliability of the value of the characteristic variable indicates a lower reliability than the index value identified by the identification unit 404 for the characteristic variable.

[0087] The second optimization unit 405, for example, determines whether an index value indicating the reliability of a value of any of the multiple characteristic variables in a solution candidate for a combination of the values ​​of the characteristic variables is a value indicating lower reliability than the specified index value. For example, when an index value indicating the reliability of a value of any of the characteristic variables is a value indicating lower reliability than the specified index value, the second optimization unit 405 sets an objective function for optimizing the value of the characteristic variable so as to include a penalty term. For example, when an index value indicating the reliability of a value of any of the characteristic variables is a value indicating higher reliability than the specified index value, the second optimization unit 405 sets an objective function for optimizing the value of the characteristic variable so as not to include a penalty term. The second optimization unit 405 performs the second multi-objective optimization using, for example, the set objective function.

[0088] The penalty term may have a property that the lower the reliability indicated by the index value indicating the reliability of the value of the characteristic variable is compared with the reliability indicated by the specified index value, the larger the value becomes. The second optimization unit 405, for example, sets an objective function for optimizing the value of each characteristic variable including the penalty term. The second optimization unit 405 performs a second multi-objective optimization using, for example, the set objective function. This allows the second optimization unit 405 to optimize the value of each characteristic variable. In addition, the second optimization unit 405 can identify parameters of a model capable of optimizing the value of each characteristic variable.

[0089] The output unit 406 outputs the processing result of at least one of the functional units. The output format is, for example, display on a display, printout on a printer, transmission to an external device via the network I / F 303, or storage in a storage area such as the memory 302 or the recording medium 305. In this way, the output unit 406 can notify the user of the processing result of at least one of the functional units, thereby improving the convenience of the information processing device 100.

[0090] The output unit 406 outputs, for example, a result of performing the first multi-objective optimization. Specifically, the output unit 406 outputs a solution set of combinations of characteristic variable values ​​and index values ​​indicating the reliability of the characteristic variable values, obtained as a result of performing the first multi-objective optimization. In this way, the output unit 406 can make it easier for a user to specify the characteristic variable values. Therefore, the output unit 406 can make it easier for the acquisition unit 401 to accept the specification of the characteristic variable values.

[0091] The output unit 406 outputs, for example, a result of performing the second multi-objective optimization. Specifically, the output unit 406 outputs a solution set of combinations of values ​​of each characteristic variable obtained as a result of performing the second multi-objective optimization. In this way, the output unit 406 can enable a user to refer to a solution set of combinations of values ​​of each characteristic variable. Therefore, the output unit 406 can enable a user to refer to values ​​of each characteristic variable and can enable a user to refer to parameters of a model that can realize any of the solutions, thereby improving convenience.

[0092] Here, the case where the information processing device 100 includes the acquisition unit 401, the learning unit 402, the first optimization unit 403, the identification unit 404, the second optimization unit 405, and the output unit 406 has been described, but the present invention is not limited to this. For example, the information processing device 100 may not include any of the functional units. Specifically, the information processing device 100 may not include the learning unit 402. In this case, specifically, the information processing device 100 may acquire the model by receiving it from another computer including the learning unit 402. Specifically, the information processing device 100 may not include the second optimization unit 405. In this case, specifically, the information processing device 100 cooperates with another computer including the second optimization unit 405.

[0093] (Operation example 1 of information processing device 100) Next, a first operation example of the information processing device 100 will be described with reference to FIGS.

[0094] 5 to 23 are explanatory diagrams showing an operation example 1 of the information processing device 100. Fig. 5 specifically shows the flow of the operation of the information processing device 100 in the operation example 1. In Fig. 5, the information processing device 100 has a plurality of learning data. The learning data indicates, for example, values ​​of a plurality of explanatory variables and correct values ​​of a plurality of characteristic variables corresponding to the values ​​of the plurality of explanatory variables.

[0095] (5-1) The information processing device 100 learns a Gaussian process regression model for each characteristic variable based on a plurality of learning data. The Gaussian process regression model is, for example, f(x) that enables calculation of an average μ corresponding to the value of the characteristic variable.

[0096] The Gaussian process regression model, for example, further makes it possible to calculate a deviation δ that indicates the instability of the characteristic variable value and corresponds to an index value indicating the reliability of the characteristic variable value. The deviation δ is, for example, a standard deviation. The deviation δ has a property that the higher the reliability, the smaller the value. The relationship between the mean μ, the deviation δ, and the training data is shown, for example, in graph 501.

[0097] (5-2) The information processing device 100 performs a first multi-objective optimization for each characteristic variable to generate a Pareto solution set of a combination of the value of the characteristic variable and the deviation of the value of the characteristic variable. The value of the characteristic variable is predicted by, for example, a Gaussian process regression model. The deviation of the value of the characteristic variable is calculated by, for example, a Gaussian process regression model.

[0098] Here, it is assumed that a smaller value of the characteristic variable is preferable for a user, and therefore the first multi-objective optimization is performed using, for example, an objective function for minimizing the value of the characteristic variable and an objective function for minimizing the deviation of the value of the characteristic variable.

[0099] The information processing device 100 may use an index value indicating the reliability of the characteristic variable value based on the distance from the characteristic variable value included in the learning data to the characteristic variable value predicted by the model, instead of the deviation of the characteristic variable value. The information processing device 100 generates, for each characteristic variable, a Pareto solution set shown in a graph 502, for example. Each point on the graph 502 indicates, for example, a Pareto solution.

[0100] The information processing device 100 outputs the generated Pareto solution set shown in the graph 502 for each characteristic variable so that the user can refer to it, and then accepts the specification of the value of any of the characteristic variables. For example, the user refers to the Pareto solution set shown in the graph 502 and specifies the value of any of the characteristic variables.

[0101] The information processing device 100 sets the deviation in the Pareto solution where the characteristic variable becomes a specified value for each characteristic variable as the deviation threshold value for the characteristic variable. For example, for the i-th characteristic variable, the information processing device 100 sets the deviation in the Pareto solution where the characteristic variable becomes a specified value as the deviation threshold value δ for the i-th characteristic variable. i Set to.

[0102] (5-3) The information processing device 100 performs a second multi-objective optimization for all of the characteristic variables to generate a Pareto solution set of combinations of the values ​​of each of the characteristic variables. The values ​​of each of the characteristic variables are predicted by, for example, a Gaussian process regression model.

[0103] For example, the information processing device 100 sets an objective function for optimizing the value of each characteristic variable, the objective function including a penalty term based on the specified deviation threshold value for each characteristic variable. Specifically, the information processing device 100 sets an objective function for optimizing the value of each characteristic variable, the penalty term being based on the specified deviation threshold value δ for the i-th characteristic variable. i Set up an objective function to optimize the i-th characteristic variable, including a penalty term based on

[0104] The penalty term is, for example, the deviation of the value of the i-th characteristic variable predicted by the Gaussian process regression model beyond a specified deviation threshold δ i If it is smaller than 0, it is set to 0. The penalty term is, for example, the deviation of the value of the i-th characteristic variable predicted by the Gaussian process regression model is greater than or equal to a specified deviation threshold δ i If the deviation threshold δ is greater than or equal to the specified deviation threshold δ, the deviation threshold δ is a positive value so that candidates for the Pareto solution that include the deviation threshold δ are more likely to be eliminated. iThe positive value may be, for example, a fixed value. The information processing device 100 generates a Pareto solution set shown in the graph 503 by performing the second multi-objective optimization using, for example, the set objective function. Each point on the graph 503 indicates, for example, a Pareto solution.

[0105] When the value of any of the characteristic variables in the Pareto solution set of the combination of the values ​​of the respective characteristic variables is equal to or greater than the target value, the information processing device 100 may reset the deviation threshold for the any of the characteristic variables and perform the second multi-objective optimization again. For example, when the value of the i-th characteristic variable is equal to or greater than the target value, the information processing device 100 may reset the deviation threshold δ for the i-th characteristic variable. i δ i +t and run the second multi-objective optimization again.

[0106] This allows the information processing device 100 to optimize the values ​​of each characteristic variable. The information processing device 100 can perform, for example, a second multi-objective optimization that takes into account the reliability of the Gaussian process regression model. Therefore, the information processing device 100 can optimize the values ​​of each characteristic variable with high precision, and can accurately obtain a Pareto solution set of a combination of the values ​​of each characteristic variable. Next, we move on to the description of Figs. 6 to 23.

[0107] 6 to 23 show an operation example 1 of the information processing device 100. In FIG. 6, a mixture optimization problem is considered as an example of a multi-objective optimization problem. The mixture optimization problem is a problem in which a composition ratio x i This is a multi-objective optimization problem in which the characteristics y1(x) and y2(x) are minimized by varying Σ i x i = 1. Composition ratio x i corresponds to the explanatory variables. The value y1 of the characteristic y1(x) corresponds to the predicted value of the characteristic variable that is the objective variable. The value y2 of the characteristic y2(x) corresponds to the predicted value of the characteristic variable that is the objective variable. The mixture optimization problem is defined by the objective functions shown in the following equations (1) and (2).

[0108] F1(x) = y1(x) → min (1)

[0109] F2(x) = y2(x) → min (2)

[0110] Here, for example, the characteristic y1(x) is defined by the following formula (3), and for example, the characteristic y2(x) is defined by the following formula (4).

[0111] y1(x)={Σ i=1 n α i (x i -p i ) 2} 2 (3)

[0112] y2(x)={Σ i=1 n β i (x i -q i ) 2} 2 (4)

[0113] Here, α i ≧0. i ≧0. In the following explanation, α1 to α 20 Specifically, p1 to p2 are the values ​​shown in Table 600. 20 Specifically, the values ​​shown in Table 600 are β1 to β 20 Specifically, the values ​​shown in Table 600 are q1 to q 20 Specifically, the values ​​are as shown in Table 600. Next, we move on to the explanation of FIG.

[0114] In FIG. 7, the information processing device 100 generates 30 pieces of learning data. The information processing device 100 generates 30 combination patterns of explanatory variable values ​​in which 2 to 5 components are randomly mixed, for example. Then, the information processing device 100 generates learning data in which, for each generated combination pattern, the combination pattern is associated with the characteristic values ​​y1 and y2 calculated based on the above formula (3) and formula (4), for example. In the example of FIG. 7, it is assumed that the information processing device 100 generates 30 pieces of learning data shown in table 700. One row of table 700 corresponds to one piece of learning data. Next, the description will move to FIG. 8 and FIG. 9.

[0115] 8 and 9, the information processing device 100 generates Gaussian process regression models corresponding to the characteristic values ​​y1 and y2, respectively, based on 30 pieces of learning data. For example, the information processing device 100 sets a parameter to Matern5 / 2, and generates the y1 model shown in the graph 800 of FIG. 8 as the Gaussian process regression model corresponding to the characteristic value y1. For example, the horizontal axis of the graph 800 is the value of the explanatory variable. For example, the vertical axis of the graph 800 is the characteristic value y1.

[0116] The information processing device 100 sets the parameters to Matern5 / 2, for example, and generates a y2 model shown in a graph 900 in Fig. 9 as a Gaussian process regression model corresponding to the characteristic value y2. For example, the horizontal axis of the graph 900 is the value of the explanatory variable. For example, the vertical axis of the graph 900 is the characteristic value y2. Next, the description of Fig. 10 will be made.

[0117] 10, the information processing device 100 performs multi-objective optimization using an objective function that optimizes a predicted value μ1(x) of a characteristic value y1 shown in the following formula (5) and an objective function that optimizes a deviation δ1(x) shown in the following formula (6) based on the y1 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 1000. Graph 1000 is a scatter plot. Each point on graph 1000 indicates a Pareto solution. The horizontal axis of graph 1000 is the predicted value μ1(x), and the vertical axis of graph 1000 is the deviation δ1(x).

[0118] F1(x) = μ1(x) → min (5)

[0119] F2(x) = δ1(x) → min (6)

[0120] The information processing device 100 outputs the Pareto solution set shown in the graph 1000 so that the user can refer to it. The information processing device 100 accepts a designation of a target value of 2.65 for the characteristic value y1 based on an operational input from the user, identifies a deviation δ1(x) corresponding to the designated target value of 2.65 in the Pareto solution set shown in the graph 1000, and sets it as the deviation threshold δ1. Next, moving on to the description of FIG. 11, an example of a Pareto solution included in the Pareto solution set shown in the graph 1000 will be described.

[0121] As shown in the multidimensional chart 1100 of Fig. 11, the Pareto solution includes a combination of the predicted value μ1(x) as pred value and the deviation δ1(x) as std. The Pareto solution further includes the combination of the explanatory variables x1 to x when the predicted value μ1(x)=pred value and the deviation δ1(x)=std. 20 Next, we move on to the description of FIG.

[0122] 12, the information processing device 100 performs multi-objective optimization using an objective function that optimizes a predicted value μ2(x) of a characteristic value y2 shown in the following formula (7) based on the y2 model, and an objective function that optimizes a deviation δ2(x) shown in the following formula (8). As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 1200. Graph 1200 is a scatter plot. Each point on graph 1200 indicates a Pareto solution. The horizontal axis of graph 1200 is the predicted value μ2(x), and the vertical axis of graph 1200 is the deviation δ2(x).

[0123] F1(x) = μ2(x) → min (7)

[0124] F2(x) = δ2(x) → min (8)

[0125] The information processing device 100 outputs the Pareto solution set shown in the graph 1200 so that the user can refer to it. The information processing device 100 accepts the specification of a target value of 5.0 for the characteristic value y2 based on an operational input from the user, identifies the deviation δ2(x) corresponding to the specified target value of 5.0 in the Pareto solution set shown in the graph 1200, and sets it as the deviation threshold value δ2. Next, we move on to the description of FIG.

[0126] In FIG. 13, the information processing device 100 sets an objective function that optimizes a predicted value μ1(x) of a characteristic value y1 shown in the following equation (9) based on the y1 model and the y2 model, and an objective function that optimizes a predicted value μ2(x) of a characteristic value y2 shown in the following equation (10).

[0127] F1(x) = μ1(x) → min (9)

[0128] F2(x) = μ2(x) → min (10)

[0129] The information processing device 100 evaluates the individuals in the multi-objective optimization by using a set deviation threshold δ j Therefore, the deviation of the individual characteristic value σ j If is large, it is judged as a violation of the deviation constraint, and F j A penalty is added to . An individual is a candidate for a Pareto solution.

[0130] For example, the information processing device 100 adds a penalty term to the above formula (9) and formula (10) to set the following formula (11) and formula (12). P i is σ i >δ i If so, then σ i +C i and σ i >δ i Otherwise, it is 0. C i is, for example, a fixed value. i For example, the characteristic value y i is the maximum absolute value of α. For example, α is 1.

[0131] F1(x)=μ1(x)+αΣ i=1 Ny P i →min···(11)

[0132] F2(x)=μ2(x)+αΣ i=1 Ny P i →min···(12)

[0133] The information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 1300. The graph 1300 is a scatter plot. Each point on the graph 1300 indicates a Pareto solution. The horizontal axis of the graph 1300 is the predicted value μ1(x), and the vertical axis of the graph 1300 is the predicted value μ2(x).

[0134] This allows the information processing device 100 to easily generate a Pareto solution set with high accuracy, taking into account the reliability of the y1 model and the y2 model. Next, moving on to the description of Fig. 14, an example of a Pareto solution included in the Pareto solution set shown in the graph 1300 will be described.

[0135] As shown in the multidimensional chart 1400 of FIG. 14, the Pareto solution includes a combination of F1, which is the predicted value μ1(x), and F2, which is the predicted value μ2(x). The Pareto solution further includes a combination of F1_std, which is the deviation δ1(x) of F1, and F2_std, which is the deviation δ2(x) of F2. The Pareto solution further includes a combination of explanatory variables x1 to x when the predicted value μ1(x)=F1 and the predicted value μ2(x)=F2. 20 Next, we move on to the description of FIG.

[0136] 15, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 1501. The information processing device 100 identifies the minimum value of 3.73 for the characteristic value y1 and the minimum value of 5.23 for the characteristic value y2 in the Pareto solution set shown in the graph 1300 as shown in table 1501.

[0137] The information processing device 100 judges whether the minimum value 3.73 of the characteristic value y1 is equal to or smaller than the target value 2.65 of the characteristic value y1. Here, since the minimum value 3.73 of the characteristic value y1 is larger than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the minimization of the characteristic value y1 is insufficient, and resets the deviation threshold δ1 to δ1+t, as shown in table 1502. t is the step size. t is, for example, 0.05.

[0138] The information processing device 100 judges whether the minimum value 5.23 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 5.23 of the characteristic value y2 is greater than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the minimization of the characteristic value y2 is insufficient, and resets the deviation threshold value δ2 to δ2+t, as shown in Table 1502. Next, the description will move to FIG. 16.

[0139] 16, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 1600. Graph 1600 is a scatter plot. Each point on graph 1600 indicates a Pareto solution. The horizontal axis of graph 1600 is the predicted value μ1(x), and the vertical axis of graph 1600 is the predicted value μ2(x).

[0140] This allows the information processing device 100 to regenerate the Pareto solution set with higher accuracy after updating the deviation threshold δ1 and the deviation threshold δ2, etc. Next, we move on to the description of FIG.

[0141] 17, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 1701. As shown in table 1701, the information processing device 100 identifies the minimum value of 3.19 for the characteristic value y1 and the minimum value of 5.14 for the characteristic value y2 in the Pareto solution set shown in the graph 1600.

[0142] The information processing device 100 judges whether the minimum value 3.19 of the characteristic value y1 is equal to or smaller than the target value 2.65 of the characteristic value y1. Here, since the minimum value 3.19 of the characteristic value y1 is greater than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the characteristic value y1 has not been minimized sufficiently, and resets the deviation threshold δ1 to δ1+t, as shown in Table 1702.

[0143] The information processing device 100 judges whether the minimum value 5.14 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 5.14 of the characteristic value y2 is greater than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that minimization of the characteristic value y2 is insufficient, and resets the deviation threshold value δ2 to δ2+t, as shown in Table 1702. Next, we move on to the explanation of FIG. 18.

[0144] 18, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 1800. Graph 1800 is a scatter plot. Each point on graph 1800 indicates a Pareto solution. The horizontal axis of graph 1800 is the predicted value μ1(x), and the vertical axis of graph 1800 is the predicted value μ2(x).

[0145] This allows the information processing device 100 to regenerate the Pareto solution set with higher accuracy after updating the deviation threshold δ1 and the deviation threshold δ2, etc. Next, we move on to the description of FIG.

[0146] 19, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 1901. As shown in table 1901, the information processing device 100 identifies the minimum value of the characteristic value y1, 2.56, and the minimum value of the characteristic value y2, 5.03, in the Pareto solution set shown in the graph 1800.

[0147] The information processing device 100 judges whether the minimum value 2.56 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1. Here, since the minimum value 2.56 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the characteristic value y1 has been minimized to the extent desired by the user, and does not update the deviation threshold δ1.

[0148] The information processing device 100 judges whether the minimum value 5.03 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 5.03 of the characteristic value y2 is greater than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the minimization of the characteristic value y2 is insufficient, and resets the deviation threshold value δ2 to δ2+t, as shown in Table 1902. Next, we move on to the explanation of FIG. 20.

[0149] 20, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 2000. Graph 2000 is a scatter plot. Each point on graph 2000 indicates a Pareto solution. The horizontal axis of graph 2000 is the predicted value μ1(x), and the vertical axis of graph 2000 is the predicted value μ2(x).

[0150] This allows the information processing device 100 to regenerate the Pareto solution set with higher accuracy after updating the deviation threshold δ1 and the deviation threshold δ2, etc. Next, we move on to the description of FIG.

[0151] 21, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 2101. As shown in table 2101, the information processing device 100 identifies the minimum value of the characteristic value y1, 2.57, and the minimum value of the characteristic value y2, 4.94, in the Pareto solution set shown in the graph 2000.

[0152] The information processing device 100 judges whether the minimum value 2.57 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1. Here, since the minimum value 2.57 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the characteristic value y1 has been minimized to an extent that meets the user's request, and does not update the deviation threshold δ1.

[0153] The information processing device 100 judges whether the minimum value 4.94 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 4.94 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the characteristic value y2 has been minimized to an extent that meets the user's request, and does not update the deviation threshold δ2.

[0154] Since the information processing device 100 does not need to update the deviation threshold δ1 and the deviation threshold δ2, it does not repeat the multi-objective optimization and ends the process. As a result, the information processing device 100 can generate a Pareto solution set with high accuracy so that the characteristic value y1 and the characteristic value y2 satisfy the target value. Therefore, the information processing device 100 can generate a Pareto solution set that meets the user's request. Next, we move on to the description of FIG. 22.

[0155] 22, an example of a Pareto solution set obtained by the conventional technology is shown in graph 2200. Graph 2200 is a scatter plot. Each point on graph 2200 represents a Pareto solution. The horizontal axis of graph 2200 is the predicted value μ1(x), and the vertical axis of graph 2200 is the predicted value μ2(x). Next, we move on to the explanation of FIG. 23.

[0156] In FIG. 23, as shown in table 2300, in the Pareto solution set shown in graph 2200 obtained by the conventional technology, the relative error rate E y1 max is 11.20, and the relative error rate E of the characteristic value y2 y2 max On the other hand, in the Pareto solution set shown in the graph 2000 obtained by the information processing device 100, the relative error rate E y1 max is 10.41, and the relative error rate E of the characteristic value y2 y2 max is 5.52. In this way, the information processing device 100 can generate a Pareto solution set with higher accuracy than the conventional technology.

[0157] Here, the case where the information processing device 100 sets the deviation threshold to a relatively small value and repeatedly performs the second multi-objective optimization while updating the deviation threshold to a large value until the characteristic value y1 and the characteristic value y2 are equal to or less than the target value has been described, but the present invention is not limited to this. For example, the information processing device 100 may set the deviation threshold to a relatively large value and repeatedly perform the second multi-objective optimization while updating the deviation threshold to a small value until the characteristic value y1 and the characteristic value y2 exceed the target value. In this case, the information processing device 100 may adopt the result of the second multi-objective optimization immediately before the characteristic value y1 and the characteristic value y2 exceed the target value as the final result.

[0158] (Setting process procedure in operation example 1) Next, an example of a setting process procedure in the operation example 1 executed by the information processing device 100 will be described with reference to Fig. 24. The setting process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0159] Fig. 24 is a flowchart showing an example of a setting process procedure in the operation example 1. In Fig. 24, the information processing device 100 sets i=1 (step S2401).

[0160] Next, the information processing device 100 generates a Gaussian process regression model for the i-th characteristic value (step S2402). Then, the information processing device 100 performs multi-objective optimization of the predicted value and the deviation using the generated Gaussian process regression model (step S2403).

[0161] Next, the information processing device 100 accepts the selection of any of the Pareto solutions in the Pareto solution set (step S2404). Then, the information processing device 100 calculates the deviation of the selected Pareto solution by a deviation threshold value δ i (step S2405).

[0162] Next, the information processing device 100 <N y It is determined whether or not (step S2406). y is the number of types of feature values. Here, i <N y If i=i+1 (step S2406: Yes), the information processing device 100 sets i=i+1 (step S2407) and returns to the process of step S2402. <N y If not (step S2406: No), the information processing device 100 ends the setting process.

[0163] (Procedure for solution finding in operation example 1) Next, an example of a solution finding process procedure in the operation example 1 executed by the information processing device 100 will be described with reference to Fig. 25. The solution finding process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0164] Fig. 25 is a flowchart showing an example of a solution-finding process procedure in the operation example 1. In Fig. 25, the information processing device 100 generates one or more initial individuals each indicating a Pareto solution candidate, and sets them in a population (step S2501). Then, the information processing device 100 evaluates the deviation of each feature value in each initial individual using a Gaussian process regression model (step S2502).

[0165] Next, the information processing device 100 selects a parent individual from the population of individuals (step S2503).Then, the information processing device 100 generates a child individual from the selected parent individual and adds it to the population of individuals (step S2504).

[0166] Next, the information processing device 100 generates a mutated individual and adds it to the population (step S2505). Then, the information processing device 100 evaluates the deviation of each feature value of each individual in the population using a Gaussian process regression model (step S2506).

[0167] Next, the information processing device 100 calculates the deviation threshold value δ i It is determined whether there is an individual having a feature value with a smaller deviation than the deviation threshold δ (step S2507). i If there is no individual including a feature value having a smaller deviation (step S2507: No), the information processing device 100 proceeds to the process of step S2509. i If there is an individual including a feature value having a smaller deviation (step S2507: Yes), the information processing device 100 proceeds to the process of step S2508.

[0168] In step S2508, the information processing device 100 selects the deviation threshold δ i A penalty is assigned to individuals including feature values ​​with smaller deviations (step S2508). Next, the information processing device 100 selects and removes individuals included in the population from the population (step S2509).

[0169] Then, the information processing device 100 determines whether the upper limit of the number of generations has been reached (step S2510). If the upper limit of the number of generations has not been reached (step S2510: No), the information processing device 100 returns to the process of step S2503. On the other hand, if the upper limit of the number of generations has been reached (step S2510: Yes), the information processing device 100 ends the solution finding process.

[0170] (Update process procedure in operation example 1) Next, an example of an update process procedure in the operation example 1 executed by the information processing device 100 will be described with reference to Fig. 26. The update process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0171] Fig. 26 is a flowchart showing an example of an update processing procedure in the operation example 1. In Fig. 26, the information processing device 100 acquires a multi-objective optimization result by the solution-finding processing (step S2601).

[0172] Next, the information processing device 100 calculates μ i min <y i s It is determined whether or not (step S2602). i min is the minimum value of the i-th characteristic value in the multi-objective optimization result. y i s is the i-th characteristic value in the selected Pareto solution.

[0173] Here, μ i min <y i s If not (step S2602: No), the information processing device 100 i = δ i +t (step S2603), and the process returns to step S2601. i min <y i s If so (step S2602: Yes), the information processing device 100 ends the update process.

[0174] (Operation Example 2 of Information Processing Device 100) Next, a second operation example of the information processing device 100 will be described with reference to Figs. 27 to 32. In the first operation example, the deviation threshold value Δ iIn contrast, the operational example 2 includes a process of updating the deviation threshold value δ i In addition to updating the value to be larger, the deviation threshold δ i This is an example of the operation when a process of updating the value to be smaller is included.

[0175] 27 to 32 are explanatory diagrams showing an operation example 2 of the information processing device 100. In Figs. 27 to 32, a case of solving a mixture optimization problem will be described as in the operation example 1. As in the operation example 1, the information processing device 100 generates a y1 model as a Gaussian process regression model corresponding to a characteristic value y1 based on learning data. As in the operation example 1, the information processing device 100 generates a y2 model as a Gaussian process regression model corresponding to a characteristic value y2.

[0176] It is assumed that the information processing device 100 receives a designation of a target value of 2.65 for the characteristic value y1, similar to the operation example 1, identifies a deviation δ1(x) corresponding to the designated target value 2.65 in the Pareto solution set shown in the graph 1000, and sets it as the deviation threshold value δ1. It is assumed that the information processing device 100 receives a designation of a target value of 5.0 for the characteristic value y2, similar to the operation example 1, identifies a deviation δ2(x) corresponding to the designated target value 5.0 in the Pareto solution set shown in the graph 1200, and sets it as the deviation threshold value δ2. The information processing device 100 sets the above formula (11) and formula (12) similar to the operation example 1. Next, the description of FIG. 27 will be moved to.

[0177] 27, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 2700. Graph 2700 is a scatter plot. Each point on graph 2700 indicates a Pareto solution. The horizontal axis of graph 2700 is the predicted value μ1(x), and the vertical axis of graph 2700 is the predicted value μ2(x).

[0178] This allows the information processing device 100 to easily generate a Pareto solution set with high accuracy by taking into account the reliability of the y1 model and the y2 model. Next, we move on to the description of FIG.

[0179] 28, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 2801. The information processing device 100 identifies the minimum value of 3.73 for the characteristic value y1 and the minimum value of 5.23 for the characteristic value y2 in the Pareto solution set shown in the graph 2700 as shown in table 2801.

[0180] The information processing device 100 judges whether the minimum value 3.73 of the characteristic value y1 is equal to or smaller than the target value 2.65 of the characteristic value y1. Here, since the minimum value 3.73 of the characteristic value y1 is larger than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the minimization of the characteristic value y1 is insufficient, and resets the deviation threshold value δ1 to δ1+t, as shown in table 2802. t is the step size. t is, for example, 0.2.

[0181] The information processing device 100 judges whether the minimum value 5.23 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 5.23 of the characteristic value y2 is greater than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the minimization of the characteristic value y2 is insufficient, and resets the deviation threshold value δ2 to δ2+t, as shown in table 2802. Next, we move on to the explanation of FIG. 29.

[0182] 29, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 2900. Graph 2900 is a scatter plot. Each point on graph 2900 indicates a Pareto solution. The horizontal axis of graph 2900 is the predicted value μ1(x), and the vertical axis of graph 2900 is the predicted value μ2(x).

[0183] This allows the information processing device 100 to regenerate the Pareto solution set with higher accuracy after updating the deviation threshold δ1 and the deviation threshold δ2, etc. Next, we move on to the description of FIG.

[0184] 30, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 3001. The information processing device 100 identifies the minimum value of 2.50 for the characteristic value y1 and the minimum value of 4.72 for the characteristic value y2 in the Pareto solution set shown in the graph 2900 as shown in table 3001.

[0185] The information processing device 100 judges whether the minimum value 2.50 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1. Here, since the minimum value 2.50 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the characteristic value y1 has been minimized to the extent desired by the user. The information processing device 100 further judges whether the minimum value 2.50 of the characteristic value y1 is within an allowable range equal to or less than the target value 2.65 of the characteristic value y1. The length of the allowable range is, for example, 0.15.

[0186] The information processing device 100 judges whether the minimum value 2.50 of the characteristic value y1 is greater than the target value 2.65-0.15 of the characteristic value y1, for example. Since the minimum value 2.50 of the characteristic value y1 is not greater than the target value 2.65-0.15=2.50 of the characteristic value y1, the information processing device 100 determines that the search space is too wide and resets the deviation threshold δ1 to δ1-t' as shown in table 3002. For example, t'=1 / 4t.

[0187] The information processing device 100 judges whether the minimum value 4.72 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 4.72 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the characteristic value y2 has been minimized to a degree that meets the user's request. The information processing device 100 further judges whether the minimum value 4.72 of the characteristic value y2 is within an allowable range equal to or less than the target value 5.00 of the characteristic value y2.

[0188] The information processing device 100 judges whether the minimum value 4.72 of the characteristic value y2 is greater than the target value 5.00-0.15 of the characteristic value y2, for example. Since the minimum value 4.72 of the characteristic value y2 is not greater than the target value 5.00-0.15=4.85 of the characteristic value y2, the information processing device 100 judges that the search space is too wide and resets the deviation threshold δ2 to δ2-t' as shown in table 3002. Next, the description of FIG. 31 will be moved to.

[0189] 31, the information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (11) and formula (12) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 3100. The graph 3100 is a scatter plot. Each point on the graph 3100 indicates a Pareto solution. The horizontal axis of the graph 3100 is the predicted value μ1(x), and the vertical axis of the graph 3100 is the predicted value μ2(x).

[0190] As a result, the information processing device 100 can regenerate the Pareto solution set with higher accuracy after updating the deviation threshold δ1 and the deviation threshold δ2, etc. The information processing device 100 can regenerate the Pareto solution set with higher accuracy after appropriately narrowing the search range, for example. Next, we move on to the description of FIG. 32.

[0191] 32, the information processing device 100 reads out a target value of 2.65 for the characteristic value y1 and a target value of 5.00 for the characteristic value y2 as shown in table 3201. As shown in table 3201, the information processing device 100 identifies the minimum value of 2.52 for the characteristic value y1 and the minimum value of 4.86 for the characteristic value y2 in the Pareto solution set shown in the graph 2000.

[0192] The information processing device 100 judges whether the minimum value 2.52 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1. Here, since the minimum value 2.52 of the characteristic value y1 is equal to or less than the target value 2.65 of the characteristic value y1, the information processing device 100 judges that the characteristic value y1 has been minimized to a degree that meets the user's request. The information processing device 100 further judges whether the minimum value 2.52 of the characteristic value y1 is within an allowable range equal to or less than the target value 2.65 of the characteristic value y1.

[0193] The information processing device 100 determines whether the minimum value 2.52 of the characteristic value y1 is greater than the target value 2.65-0.15 of the characteristic value y1, for example. Since the minimum value 2.52 of the characteristic value y1 is greater than the target value 2.65-0.15=2.50 of the characteristic value y1, for example, the information processing device 100 does not update the deviation threshold δ1.

[0194] The information processing device 100 judges whether the minimum value 4.86 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2. Here, since the minimum value 4.86 of the characteristic value y2 is equal to or less than the target value 5.00 of the characteristic value y2, the information processing device 100 judges that the characteristic value y2 has been minimized to a degree that meets the user's request. The information processing device 100 further judges whether the minimum value 4.86 of the characteristic value y2 is within an allowable range equal to or less than the target value 5.00 of the characteristic value y2.

[0195] The information processing device 100 determines whether the minimum value 4.86 of the characteristic value y2 is greater than the target value 5.00-0.15 of the characteristic value y2, for example. Since the minimum value 4.86 of the characteristic value y2 is greater than the target value 5.00-0.15=4.85 of the characteristic value y2, for example, the information processing device 100 does not update the deviation threshold δ2.

[0196] Since the information processing device 100 does not need to update the deviation threshold δ1 and the deviation threshold δ2, it does not repeat the multi-objective optimization and ends the process. As a result, the information processing device 100 can generate a Pareto solution set with high accuracy so that the characteristic value y1 and the characteristic value y2 satisfy the target value. Therefore, the information processing device 100 can generate a Pareto solution set that meets the user's request.

[0197] (Setting process procedure in operation example 2) An example of a setting process procedure in the second operation example is similar to the example of the setting process procedure in the first operation example shown in FIG. 24, and therefore description thereof will be omitted.

[0198] (Procedure for solution finding in operation example 2) An example of a solution-finding process procedure in the second operational example is similar to the example of the solution-finding process procedure in the first operational example shown in FIG. 25, and therefore description thereof will be omitted.

[0199] (Update process procedure in operation example 2) Next, an example of an update process procedure in the operation example 2 executed by the information processing device 100 will be described with reference to Fig. 33. The update process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0200] Fig. 33 is a flowchart showing an example of an update processing procedure in the operation example 2. In Fig. 33, the information processing device 100 acquires a multi-objective optimization result by the solution-finding processing (step S3301).

[0201] Next, the information processing device 100 i min <y i s It is determined whether or not μ i min <y i s If not (step S3302: No), the information processing device 100 i = δ i +t (step S3303), and the process returns to step S3301. i min <y i s If so (step S3302: Yes), information processing device 100 proceeds to the process of step S3304.

[0202] In step S3304, the information processing device 100 i min >y i s -ε i It is determined whether or not ε i is, for example, 0.15. Here, μ i min >y i s -ε i If it is (step S3304: Yes), the information processing device 100 ends the update process. i min >y i s -ε i If not (step S3304: No), information processing device 100 proceeds to the process of step S3305.

[0203] In step S3305, the information processing device 100 i =βt i (step S3305). β is, for example, 1 / 4. t i The initial value of δ is, for example, 0.2. i = δ i -t i (step S3306). Then, information processing device 100 returns to the process of step S3301.

[0204] (Operation example 3 of information processing device 100) Next, an operation example 3 of the information processing device 100 will be described with reference to Fig. 34 to Fig. 38. Operation example 1 and operation example 2 are operation examples corresponding to a case where a Pareto solution is easily searched for a characteristic value having a relatively small deviation and a relatively high reliability. In contrast, operation example 3 is an operation example corresponding to a case where a Pareto solution is searched for a characteristic value having a relatively large deviation and a relatively low reliability.

[0205] 34 to 38 are explanatory diagrams showing an operation example 3 of the information processing device 100. Specifically, Fig. 34 shows a flow of the operation of the information processing device 100 in the operation example 3. In Fig. 34, the information processing device 100 has a plurality of learning data. The learning data indicates, for example, values ​​of a plurality of explanatory variables and correct values ​​of a plurality of characteristic variables corresponding to the values ​​of the plurality of explanatory variables.

[0206] (34-1) The information processing device 100 learns a Gaussian process regression model for each characteristic variable based on a plurality of learning data. The Gaussian process regression model is, for example, f(x) that enables calculation of an average μ corresponding to the value of the characteristic variable.

[0207] The Gaussian process regression model, for example, further enables calculation of a deviation δ, which indicates the instability of the characteristic variable value and corresponds to an index value indicating the reliability of the characteristic variable value. The deviation δ is, for example, a standard deviation. The deviation δ has a property that the higher the reliability, the smaller the value. The deviation δ corresponds, for example, to the degree of exploration. The relationship between the average μ, the deviation δ, and the learning data is shown in, for example, graph 3401.

[0208] (34-2) The information processing device 100 performs a first multi-objective optimization for each characteristic variable to generate a Pareto solution set of combinations of the value of the characteristic variable and the deviation of the value of the characteristic variable. The value of the characteristic variable is predicted by, for example, a Gaussian process regression model. The deviation of the value of the characteristic variable is calculated by, for example, a Gaussian process regression model.

[0209] Here, it is assumed that a smaller value of the characteristic variable is preferable for a user. For this reason, the first multi-objective optimization is performed, for example, using an objective function that minimizes the value of the characteristic variable and an objective function that maximizes the deviation of the value of the characteristic variable. By using an objective function that maximizes the deviation of the value of the characteristic variable, the first multi-objective optimization can easily search for Pareto solutions for characteristic values ​​that are considered to have a relatively large deviation, relatively low reliability, and relatively little learning data.

[0210] The information processing device 100 may use an index value indicating the reliability of the characteristic variable value based on the distance from the characteristic variable value included in the learning data to the characteristic variable value predicted by the model, instead of the deviation of the characteristic variable value. The information processing device 100 generates, for each characteristic variable, a Pareto solution set shown in the graph 3402, for example. Each point on the graph 3402 indicates, for example, a Pareto solution.

[0211] The information processing device 100 outputs the generated Pareto solution set shown in the graph 3402 for each characteristic variable so that the user can refer to it, and then accepts the specification of the value of any of the characteristic variables. For example, the user refers to the Pareto solution set shown in the graph 3402 and specifies the value of any of the characteristic variables.

[0212] The information processing device 100 sets the deviation in the Pareto solution where the characteristic variable becomes a specified value for each characteristic variable as the deviation threshold value for the characteristic variable. For example, for the i-th characteristic variable, the information processing device 100 sets the deviation in the Pareto solution where the characteristic variable becomes a specified value as the deviation threshold value δ for the i-th characteristic variable. i Set to.

[0213] (34-3) The information processing device 100 performs a second multi-objective optimization for all of the characteristic variables to generate a Pareto solution set of combinations of the values ​​of each of the characteristic variables. The values ​​of each of the characteristic variables are predicted by, for example, a Gaussian process regression model.

[0214] For example, the information processing device 100 sets an objective function for optimizing the value of each characteristic variable, the objective function including a penalty term based on the specified deviation threshold value for each characteristic variable. Specifically, the information processing device 100 sets an objective function for optimizing the value of each characteristic variable, the penalty term being based on the specified deviation threshold value δ for the i-th characteristic variable. i Set up an objective function to optimize the i-th characteristic variable, including a penalty term based on

[0215] The penalty term is, for example, the deviation of the value of the i-th characteristic variable predicted by the Gaussian process regression model beyond a specified deviation threshold δ i If the deviation of the value of the i-th characteristic variable predicted by the Gaussian process regression model is greater than or equal to a specified deviation threshold δ i If it is smaller than δ, it is a positive value so that candidates for the Pareto solution including the value are more likely to be selected. The positive value is, for example, a specified deviation threshold δ i The positive value may be, for example, a fixed value. The information processing device 100 generates a Pareto solution set shown in the graph 3403 by performing the second multi-objective optimization using, for example, the set objective function. Each point on the graph 3403 indicates, for example, a Pareto solution.

[0216] This allows the information processing device 100 to optimize the values ​​of each characteristic variable. The information processing device 100 can, for example, implement a second multi-objective optimization that takes into account the reliability of the Gaussian process regression model and the degree of search, and can obtain various Pareto solution sets of combinations of the values ​​of each characteristic variable. This allows the information processing device 100 to improve its convenience. Next, we move on to the description of Figs. 35 to 38.

[0217] Specifically, Fig. 35 to Fig. 38 show an operation example 3 of the information processing device 100. In Fig. 35 to Fig. 38, a case of solving a mixture optimization problem will be described as in the operation example 1. In Fig. 35, it is assumed that the information processing device 100 generates a y1 model as a Gaussian process regression model corresponding to a characteristic value y1 based on learning data as in the operation example 1. It is assumed that the information processing device 100 generates a y2 model as a Gaussian process regression model corresponding to a characteristic value y2 as in the operation example 1.

[0218] 35, the information processing device 100 performs multi-objective optimization using an objective function that optimizes a predicted value μ1(x) of a characteristic value y1 shown in the following formula (13) and an objective function that optimizes a deviation δ1(x) shown in the following formula (14) based on the y1 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 3500. Graph 3500 is a scatter plot. Each point on graph 3500 indicates a Pareto solution. The horizontal axis of graph 3500 is the predicted value μ1(x), and the vertical axis of graph 3500 is the deviation δ1(x).

[0219] F1(x) = μ1(x) → min (13)

[0220] F2(x) = δ1(x) → max (14)

[0221] The information processing device 100 outputs the Pareto solution set shown in the graph 3500 so that the user can refer to it. The information processing device 100 accepts the specification of a target value of 3.8 for the characteristic value y1 based on an operational input from the user, identifies the deviation δ1(x) corresponding to the specified target value of 3.8 in the Pareto solution set shown in the graph 3500, and sets it as the deviation threshold value δ1. Next, the description will move to FIG. 36.

[0222] 36, the information processing device 100 performs multi-objective optimization using an objective function that optimizes a predicted value μ2(x) of a characteristic value y2 shown in the following formula (15) and an objective function that optimizes a deviation δ2(x) shown in the following formula (16) based on the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 3600. Graph 3600 is a scatter plot. Each point on graph 3600 indicates a Pareto solution. The horizontal axis of graph 3600 is the predicted value μ2(x), and the vertical axis of graph 3600 is the deviation δ2(x).

[0223] F1(x) = μ2(x) → min (15)

[0224] F2(x) = δ2(x) → max (16)

[0225] The information processing device 100 outputs the Pareto solution set shown in the graph 3600 so that the user can refer to it. The information processing device 100 accepts the specification of a target value of 5.4 for the characteristic value y2 based on an operational input from the user, identifies the deviation δ2(x) corresponding to the specified target value of 5.4 in the Pareto solution set shown in the graph 3600, and sets it as the deviation threshold value δ2. Next, we move on to the description of FIG. 37.

[0226] In FIG. 37, the information processing device 100 sets an objective function that optimizes the predicted value μ1(x) of the characteristic value y1 shown in the following equation (17) based on the y1 model and the y2 model, and an objective function that optimizes the predicted value μ2(x) of the characteristic value y2 shown in the following equation (18).

[0227] F1(x) = μ1(x) → min (17)

[0228] F2(x) = μ2(x) → min (18)

[0229] The information processing device 100 evaluates the individuals in the multi-objective optimization by using a set deviation threshold δ j Therefore, the deviation of the individual characteristic value σ j If is small, it is judged that the deviation constraint is violated, and F j A penalty is added to . An individual is a candidate for a Pareto solution.

[0230] For example, the information processing device 100 adds a penalty term to the above formula (17) and formula (18) to set the following formula (19) and formula (20). P i is σ i <δ i If so, then (σ i -δ i ) 2 +C i and σ i <δ i Otherwise, it is 0. C i is, for example, a fixed value. i For example, the characteristic value y i is the maximum absolute value of α. For example, α is 10.

[0231] F1(x)=μ1(x)+αΣ i=1 Ny P i →min···(19)

[0232] F2(x)=μ2(x)+αΣ i=1 Ny P i →min···(20)

[0233] The information processing device 100 performs multi-objective optimization using the objective functions shown in the above formula (19) and formula (20) based on the y1 model and the y2 model. As a result of performing the multi-objective optimization, the information processing device 100 generates a Pareto solution set shown in graph 3700. The graph 3700 is a scatter plot. Each point on the graph 3700 indicates a Pareto solution. The horizontal axis of the graph 3700 is the predicted value μ1(x), and the vertical axis of the graph 3700 is the predicted value μ2(x).

[0234] In this way, the information processing device 100 can obtain various Pareto solution sets of combinations of the values ​​of the characteristic variables taking into account the reliability of the y1 model and the y2 model and the degree of exploration. Next, we move on to the description of FIG.

[0235] 38, the information processing device 100 specifies the minimum value σ1 of the deviation of the predicted value μ1(x) and the minimum value σ2 of the deviation of the predicted value μ2(x) as indicators of the degree of exploration, as shown in table 3800. The information processing device 100 outputs a graph 3700 showing the Pareto solution set and a table 3800 showing the deviation serving as an indicator of the degree of exploration so that the user can refer to them. In this way, the information processing device 100 can visualize the Pareto solution set, making it easier for the user to select a desired Pareto solution.

[0236] (Setting process procedure in operation example 3) An example of a setting process procedure in the operation example 3 is similar to the example of the setting process procedure in the operation example 1 shown in FIG. 24, and therefore description thereof will be omitted.

[0237] (Procedure for solution finding process in operation example 3) Next, an example of a solution finding process procedure in the operation example 3 executed by the information processing device 100 will be described with reference to Fig. 39. The solution finding process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0238] Fig. 39 is a flowchart showing an example of a solution-finding process procedure in the operation example 3. In Fig. 39, the information processing device 100 generates one or more initial individuals each indicating a Pareto solution candidate, and sets them in a population (step S3901). Then, the information processing device 100 evaluates the deviation of each feature value in each initial individual using a Gaussian process regression model (step S3902).

[0239] Next, the information processing device 100 selects a parent individual from the population of individuals (step S3903).Then, the information processing device 100 generates a child individual from the selected parent individual and adds it to the population of individuals (step S3904).

[0240] Next, the information processing device 100 generates a mutated individual and adds it to the population (step S3905). Then, the information processing device 100 evaluates the deviation of each feature value of each individual in the population using a Gaussian process regression model (step S3906).

[0241] Next, the information processing device 100 calculates the deviation threshold value δ i It is determined whether there is an individual including a feature value having a larger deviation than the deviation threshold δ (step S3907). i If there is an individual including a feature value having a larger deviation (step S3907: Yes), the information processing device 100 proceeds to the process of step S3908. i If there is no individual including a feature value having a larger deviation (step S3907: No), the information processing device 100 proceeds to the process of step S3909.

[0242] In step S3908, the information processing device 100 selects the deviation threshold δ i A penalty is assigned to individuals including feature values ​​with a larger deviation (step S3908). Then, the information processing device 100 proceeds to the process of step S3909.

[0243] In step S3909, the information processing device 100 selects individuals included in the population and removes them from the population (step S3909). Next, the information processing device 100 determines whether the upper limit of the number of generations has been reached (step S3910). If the upper limit of the number of generations has not been reached (step S3910: No), the information processing device 100 returns to the process of step S3903. On the other hand, if the upper limit of the number of generations has been reached (step S3910: Yes), the information processing device 100 ends the solution-finding process.

[0244] (An example of single-objective optimization) Next, an example of single-objective optimization in the case where there is one type of characteristic variable serving as the objective variable will be described with reference to FIG.

[0245] Fig. 40 is an explanatory diagram showing an example of single-objective optimization. In Fig. 40, (40-1) the information processing device 100 learns a Gaussian process regression model shown in a graph 4001 for one characteristic variable based on a plurality of learning data, similarly to the operation example 1.

[0246] The information processing device 100 may optimize the characteristic value of one characteristic variable while minimizing the deviation, as in the operation example 1, or may optimize the characteristic value of one characteristic variable while maximizing the deviation, as in the operation example 3. The case where the characteristic value of one characteristic variable is optimized while minimizing the deviation will be described later in (40-2-1). The case where the characteristic value of one characteristic variable is optimized while maximizing the deviation will be described later in (40-2-2).

[0247] (40-2-1) The information processing device 100 performs multi-objective optimization for one characteristic variable using an objective function that optimizes the value of the characteristic variable and an objective function that minimizes the deviation of the value of the characteristic variable. The value of the characteristic variable is predicted, for example, by a Gaussian process regression model. The deviation of the value of the characteristic variable is calculated, for example, by a Gaussian process regression model. This enables the information processing device 100 to generate a Pareto solution set of combinations of the value of one characteristic variable and the deviation of the value of the characteristic variable.

[0248] The information processing device 100 outputs a graph 4002 showing the generated Pareto solution set so that the user can refer to it. In this way, the information processing device 100 can visualize the Pareto solution set. Then, the information processing device 100 can make it easier for the user to select a desired Pareto solution from the Pareto solution set shown in the graph 4002.

[0249] (40-2-2) The information processing device 100 performs multi-objective optimization for one characteristic variable using an objective function that optimizes the value of the characteristic variable and an objective function that maximizes the deviation of the value of the characteristic variable. The value of the characteristic variable is predicted, for example, by a Gaussian process regression model. The deviation of the value of the characteristic variable is calculated, for example, by a Gaussian process regression model. This enables the information processing device 100 to generate a Pareto solution set of combinations of the value of one characteristic variable and the deviation of the value of the characteristic variable.

[0250] The information processing device 100 outputs the graph 4003 showing the generated Pareto solution set so that the user can refer to it. In this way, the information processing device 100 can visualize the Pareto solution set. Then, the information processing device 100 can make it easier for the user to select a desired Pareto solution from the Pareto solution set shown in the graph 4003.

[0251] As described above, the information processing device 100 can perform the first multi-objective optimization for each characteristic variable by using an objective function that optimizes the value of the characteristic variable and an objective function that optimizes an index value indicating the reliability of the value. The information processing device 100 can perform the first multi-objective optimization for each characteristic variable to generate a solution set of a combination of the value of the characteristic variable and an index value indicating the reliability of the value of the characteristic variable. The information processing device 100 can specify, for each characteristic variable, an index value included in a combination that is a solution when the characteristic variable is a specified value, from among the generated solution sets. The information processing device 100 can perform the second multi-objective optimization by using an objective function that optimizes the value of each characteristic variable predicted by the model, including a penalty term based on the specified index value. The information processing device 100 can perform the second multi-objective optimization to generate a solution set of a combination of the values ​​of each characteristic variable. As a result, the information processing device 100 can perform the second multi-objective optimization taking into account the reliability of the model, accurately optimize the value of each characteristic variable, and accurately obtain a solution set.

[0252] According to the information processing device 100, it is possible to learn a Gaussian process regression model that can predict the value of each characteristic variable and can calculate an index value indicating the reliability of the value, based on a plurality of learning data. According to the information processing device 100, it is possible to set an objective function that optimizes the value of each characteristic variable predicted by the learned Gaussian process regression model. According to the information processing device 100, it is possible to set an objective function that optimizes the index value indicating the reliability of the value calculated by the learned Gaussian process regression model, for each characteristic variable. Thereby, the information processing device 100 can reduce the workload imposed on the user when preparing a model, and can make it possible to calculate an index value indicating the reliability of the value of the characteristic variable.

[0253] According to the information processing device 100, an index value indicating the reliability of each characteristic variable value predicted by a model can be calculated based on the distance from each of the multiple learning data to the corresponding value. This allows the information processing device 100 to calculate an index value indicating the reliability of the characteristic variable value without using a model.

[0254] According to the information processing device 100, in a solution set of the generated combination of the values ​​of each of the characteristic variables, it is possible to determine whether or not the value of any of the multiple characteristic variables satisfies a target value. According to the information processing device 100, if the value of any of the characteristic variables does not satisfy the target value, it is possible to specify a new index value different from the index value specified immediately before for any of the characteristic variables. According to the information processing device 100, it is possible to perform a second multi-objective optimization using an objective function that optimizes the values ​​of each of the characteristic variables predicted by the model, including a penalty term based on the specified new index value. As a result, the information processing device 100 can repeat the second multi-objective optimization to obtain a solution set with even greater accuracy.

[0255] According to the information processing device 100, as an index value indicating reliability, an index value whose value increases as the reliability decreases can be used. According to the information processing device 100, as an objective function for optimizing an index value indicating reliability, an objective function for minimizing an index value indicating reliability can be used. According to the information processing device 100, when the value of any characteristic variable does not satisfy a target value, a new index value that is larger than the index value specified immediately before for any characteristic variable by a first value can be specified. This allows the information processing device 100 to specify a more appropriate index value in order to obtain a solution set with even greater accuracy.

[0256] According to the information processing device 100, when the value of any of the characteristic variables meets the target value but is not included in a range based on the target value, a new index value that is smaller than the previously specified index value by a second value different from the first value can be specified for any of the characteristic variables. This allows the information processing device 100 to specify a more appropriate index value in order to obtain a solution set with higher accuracy.

[0257] According to the information processing device 100, an index value indicating reliability that increases as the reliability decreases can be used. According to the information processing device 100, an objective function that maximizes the index value indicating reliability can be used as an objective function that optimizes the index value indicating reliability. According to the information processing device 100, when the value of any characteristic variable does not satisfy the target value, a new index value that is smaller than the index value specified immediately before by a first value can be specified for any characteristic variable. This allows the information processing device 100 to specify a more appropriate index value in order to obtain a solution set with even greater accuracy.

[0258] According to the information processing device 100, when the value of any characteristic variable satisfies the target value but is not included in a range based on the target value, a new index value that is greater than the previously specified index value by a second value different from the first value can be specified for any characteristic variable. This allows the information processing device 100 to specify a more appropriate index value in order to obtain a solution set with higher accuracy.

[0259] According to the information processing device 100, the target value can be set based on a specified value, thereby making it easier for the user to find a desired solution.

[0260] According to the information processing device 100, when an index value indicating the reliability of a value of any characteristic variable is a value indicating lower reliability than a specified index value, a penalty term can be included in an objective function for optimizing the value of the characteristic variable. This enables the information processing device 100 to take the reliability of the model into consideration when performing the second multi-objective optimization.

[0261] The information processing method described in this embodiment can be realized by executing a prepared program on a computer such as a PC or a workstation. The information processing program described in this embodiment is recorded on a computer-readable recording medium, and is executed by being read from the recording medium by the computer. The recording medium may be a hard disk, a flexible disk, a CD (Compact Disc)-ROM, an MO (Magneto Optical disc), a DVD (Digital Versatile Disc), or the like. The information processing program described in this embodiment may also be distributed via a network such as the Internet.

[0262] The following supplementary notes are further disclosed regarding the above-described embodiment.

[0263] (Appendix 1) For each of a plurality of characteristic variables, a first multi-objective optimization is performed using a first objective function for searching for a value of the characteristic variable predicted by the model, and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing program that causes a computer to execute a process.

[0264] (Appendix 2) A Gaussian process regression model is trained based on a plurality of training data, which is capable of predicting the value of each of the plurality of characteristic variables and calculating an index value indicating the reliability of the value. causing the computer to execute a process; The process of performing the first multi-objective optimization includes: The information processing program according to claim 1, characterized in that for each of the plurality of characteristic variables, the first multi-objective optimization is performed using the first objective function for searching for a value of the characteristic variable predicted by the trained Gaussian process regression model, and the second objective function for searching for an index value indicating the reliability of the value calculated by the trained Gaussian process regression model, thereby generating a solution set of combinations of the value and the index value.

[0265] (Appendix 3) The information processing program according to appendix 1, characterized in that an index value indicating the reliability of each value of the plurality of characteristic variables predicted by the model is calculated based on a distance from each of a plurality of learning data to the value.

[0266] (Appendix 4) In the generated solution set of combinations of the values ​​of the plurality of characteristic variables, if the value of any of the plurality of characteristic variables does not satisfy the target value, a new index value different from the index value previously specified is specified for any of the characteristic variables; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified new index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; 4. The information processing program according to any one of claims 1 to 3, which causes the computer to execute a process.

[0267] (Note 5) The index value indicating the reliability is an index value whose value increases as the reliability decreases, The second objective function for searching for an index value indicating the reliability is an objective function for minimizing the index value indicating the reliability, The process of identifying the new index value includes: The information processing program according to claim 4, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of the respective values ​​of the plurality of characteristic variables does not satisfy the target value, a new index value that is a first value greater than the index value previously identified for any of the characteristic variables is identified.

[0268] (Appendix 6) The process of identifying the new index value includes: The information processing program described in Appendix 5, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of values ​​of the plurality of characteristic variables generated satisfies the target value and is not included in a range based on the target value, a new index value is identified for any of the characteristic variables that is smaller than the index value identified immediately before by a second value different from the first value.

[0269] (Appendix 7) The index value indicating the reliability is an index value whose value is larger as the reliability is lower, The second objective function for searching for an index value indicating the reliability is an objective function for maximizing the index value indicating the reliability, The process of identifying the new index value includes: The information processing program described in Appendix 4, characterized in that if a value of any of the plurality of characteristic variables in a solution set of combinations of the respective values ​​of the plurality of characteristic variables does not satisfy the target value, a new index value is identified for any of the characteristic variables that is smaller by a first value than the index value identified immediately before.

[0270] (Appendix 8) The process of identifying the new index value includes: The information processing program according to claim 7, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of the respective values ​​of the plurality of characteristic variables satisfies the target value but is not within a range based on the target value, a new index value is identified for any of the characteristic variables that is greater than the index value identified immediately before by a second value different from the first value.

[0271] (Supplementary Note 9) The information processing program according to any one of Supplementary Notes 4 to 8, wherein the target value is set based on the specified value.

[0272] (Appendix 10) When an index value indicating the reliability of a value of any one of the plurality of characteristic variables in a solution candidate of a combination of the values ​​of each of the plurality of characteristic variables is a value indicating a lower reliability than the specified index value, an objective function for searching the value of the characteristic variable is set so as to include a penalty term in the objective function for searching the value of the characteristic variable. 10. The information processing program according to any one of claims 1 to 9, which causes the computer to execute a process.

[0273] (Appendix 11) For one characteristic variable, a multi-objective optimization is performed using a first objective function for searching for a value of the characteristic variable predicted by a model and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; An information processing program that causes a computer to execute a process.

[0274] (Appendix 12) For each of a plurality of characteristic variables, a first multi-objective optimization is performed using a first objective function for searching for a value of the characteristic variable predicted by the model, and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing method characterized in that the processing is executed by a computer.

[0275] (Appendix 13) For each of a plurality of characteristic variables, a first multi-objective optimization is performed using a first objective function for searching for a value of the characteristic variable predicted by the model and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing device comprising a control unit. [Explanation of symbols]

[0276] 100 Information processing device 101 Model 102, 103, 501~503, 800, 900, 1000, 1200, 1300, 1600, 1800, 2000, 2200, 2700, 2900, 3100, 3401~3403, 3500, 3600, 3700, 4001~4003 Graph 200 Information Processing Systems 201 Client device 210 Network 300 Bus 301 CPU 302 Memory 303 Network Interface 304 Recording media I / F 305 Recording media 400 Storage section 401 Acquisition Department 402 Learning Department 403 1st Optimization Section 404 Specific part 405 2nd Optimization Section 406 Output section 600,700,1501,1502,1701,1702,1901,1902,2101,2300,2801,2802,3001,3002,3201,3800 Table 1100,1400 Multidimensional Charts

Claims

1. performing a first multi-objective optimization using a first objective function for searching for a value of each of a plurality of characteristic variables predicted by a model and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing program that causes a computer to execute a process.

2. learning a Gaussian process regression model for each of the plurality of characteristic variables based on a plurality of learning data, the Gaussian process regression model being capable of predicting the value of the characteristic variable and calculating an index value indicating the reliability of the value; causing the computer to execute a process; The process of performing the first multi-objective optimization includes:

2. The information processing program according to claim 1, further comprising: performing the first multi-objective optimization for each of the plurality of characteristic variables using the first objective function for searching for a value of the characteristic variable predicted by the trained Gaussian process regression model, and the second objective function for searching for an index value indicating reliability of the value calculated by the trained Gaussian process regression model, thereby generating a solution set of combinations of the value and the index value.

3. In a solution set of the generated combinations of the values ​​of the plurality of characteristic variables, if a value of any of the plurality of characteristic variables does not satisfy a target value, a new index value different from the index value previously specified is specified for any of the characteristic variables; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified new index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; 3. The information processing program according to claim 1, which causes the computer to execute a process.

4. The index value indicating the reliability is an index value whose value increases as the reliability is lower, The second objective function for searching for an index value indicating the reliability is an objective function for minimizing the index value indicating the reliability, The process of identifying the new index value includes: The information processing program according to claim 3, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of values ​​of the plurality of characteristic variables generated does not satisfy the target value, a new index value is identified for any of the characteristic variables that is larger than the index value identified immediately before by a first value.

5. The process of identifying the new index value includes: The information processing program according to claim 4, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of values ​​of the plurality of characteristic variables generated satisfies the target value and is not included in a range based on the target value, a new index value is identified for any of the characteristic variables that is smaller than the index value identified immediately before by a second value different from the first value.

6. The index value indicating the reliability is an index value whose value increases as the reliability is lower, The second objective function for searching for an index value indicating the reliability is an objective function for maximizing the index value indicating the reliability, The process of identifying the new index value includes: The information processing program according to claim 3, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of values ​​of the plurality of characteristic variables generated does not satisfy the target value, a new index value is identified for any of the characteristic variables that is smaller by a first value than the index value identified immediately before.

7. The process of identifying the new index value includes: The information processing program according to claim 6, characterized in that, when a value of any of the plurality of characteristic variables in a solution set of combinations of values ​​of the plurality of characteristic variables satisfies the target value and is not included in a range based on the target value, a new index value is identified for any of the characteristic variables that is greater than the index value identified immediately before by a second value different from the first value.

8. when an index value indicating the reliability of a value of any one of the plurality of characteristic variables in a solution candidate for a combination of the values ​​of the plurality of characteristic variables is a value indicating a lower reliability than the specified index value, an objective function for searching for the value of the characteristic variable is set so as to include a penalty term in the objective function for searching for the value of the characteristic variable; 8. The information processing program according to claim 1, which causes the computer to execute a process.

9. performing a first multi-objective optimization using a first objective function for searching for a value of each of a plurality of characteristic variables predicted by a model and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing method characterized in that the processing is executed by a computer.

10. performing a first multi-objective optimization using a first objective function for searching for a value of each of a plurality of characteristic variables predicted by a model and a second objective function for searching for an index value indicating the reliability of the value, thereby generating a solution set of combinations of the value and the index value; Identifying, for each of the plurality of characteristic variables, an index value included in a combination that is a solution when the characteristic variable is a specified value in the generated solution set; performing a second multi-objective optimization using an objective function for searching values ​​of each of the plurality of characteristic variables predicted by the model, the objective function including a penalty term based on the identified index value, thereby generating a solution set of combinations of values ​​of each of the plurality of characteristic variables; An information processing device comprising a control unit.

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