Calculation program, calculation method, and information processing device

Abstract

This computation program executes: a process for using each of a plurality of objective functions as a first evaluation function to perform single-objective optimization on an initial solution, thereby calculating a single-objective optimal solution that has a better value than the initial solution; and a process for using, as a second evaluation function, a linear weighted sum obtained by weighting each of the plurality of objective functions in accordance with the single-objective optimal solution to perform multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution.　

Description

[Technical Field]

[0001] This matter relates to arithmetic programs, arithmetic methods, and information processing devices. [Background technology]

[0002] Techniques have been disclosed for optimizing the order in which products are introduced into a production line, using multiple objective functions such as production cost and production completion time (see, for example, Patent Documents 1 to 4). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-83200 [Patent Document 2] Japanese Patent Publication No. 2002-366587 [Patent Document 3] U.S. Patent Publication No. 2015 / 0019173 [Patent Document 4] U.S. Patent Publication No. 2016 / 0306899 [Overview of the project] [Problems that the invention aims to solve]

[0004] However, when performing multi-objective optimization with multiple objective functions, the solution space becomes large. Consequently, it takes a long time to start the search from the initial input order as the initial solution and to calculate the set of Pareto optimal solutions that are candidates for the optimal solution.

[0005] In one aspect, the present invention aims to provide an information processing device, an arithmetic method, and an arithmetic program that can reduce computation time. [Means for solving the problem]

[0006] In one aspect, the arithmetic program performs, for an initial solution, a process of calculating a single-objective optimal solution having a better value than the initial solution by executing single-objective optimization using each of a plurality of objective functions as a first evaluation function, and a process of performing multi-objective optimization on the second evaluation function starting from the single-objective optimal solution using, as a second evaluation function, a linear weighted sum obtained by weighting each of the plurality of objective functions according to the single-objective optimal solution. An arithmetic program characterized by causing the program to execute the processes.

Effect of the Invention

[0007] The calculation time can be shortened.

Brief Description of the Drawings

[0008] [Figure 1] It is a diagram illustrating a Pareto solution. [Figure 2] It is a diagram illustrating a case where a genetic algorithm is used for a multi-objective optimization engine. [Figure 3] It is a diagram illustrating the linear weighted sum method. [Figure 4] (a) is a functional block diagram showing the overall configuration of the information processing apparatus according to Example 1, and (b) is a hardware configuration diagram of the information processing apparatus. [Figure 5] It is a diagram illustrating the flowchart of Example 1. [Figure 6] (a) and (b) are explanatory diagrams of Example 1. [Figure 7] It is a diagram illustrating the flowchart of Example 2. [Figure 8] (a) and (b) are explanatory diagrams of Example 2. [Figure 9] It is a diagram showing the calculation results. [Figure 10] It is a diagram showing the calculation results. [Figure 11] It is a diagram for explaining hypervolume. [Figure 12] It is a diagram illustrating a production line model. [Figure 13] (a) to (c) are diagrams illustrating product information. [Figure 14] It is a diagram showing the calculation results. [Figure 15] It is a diagram showing the calculation results.

Embodiments for Carrying Out the Invention

[0009] Optimization problems exist in the sites of various industries, including the manufacturing industry and the distribution industry. For example, in the optimization problem of production planning in a manufacturing site, there is a problem where the relationship between the manufacturing time required for a certain production plan and the cost that occurs in proportion to the operating time of the equipment is a trade-off. For example, there is a trade-off problem such that if the manufacturing time is shortened, the operating cost of legacy equipment with a high operating cost increases as the operating time increases.

[0010] The multi-objective optimization problem of simultaneously optimizing a plurality of objective functions in a trade-off relationship is generally a problem of obtaining Pareto solutions. In the above example, the manufacturing time required for a certain production plan and the cost that occurs in proportion to the operating time of the equipment are the objective functions, respectively. The explanatory variable is the production plan, for example, the input order of each product in the production process. A Pareto solution is a solution in which there is at least one objective function that is superior among a plurality of objective functions compared to any other solution. FIG. 1 is a diagram illustrating a Pareto solution. In FIG. 1, the solution of (f1,f2)=(9,3) is not a Pareto solution because there is no superior objective function when compared with (f1,f2)=(8,2).

[0011] In the example of FIG. 1, since each objective function is optimized to be minimized, the Pareto solution located on the lower left side is obtained. The line connecting each Pareto solution (the arrangement of each Pareto solution) is called a Pareto front. From among the Pareto solutions obtained by multi-objective optimization calculation, the user selects an optimal solution that suits the purpose. Therefore, in order to give the user a more optimal and larger number of options, in multi-objective optimization calculation, it is required to calculate a more optimal and wide-ranging Pareto front in as short a calculation time as possible.

[0012] For example, when performing multi-objective optimization calculation by setting a plurality of objective functions to be optimized as the evaluation function of a multi-objective optimization engine, it is conceivable. FIG. 2 is a diagram illustrating a case where a genetic algorithm is used as an example for the multi-objective optimization engine. The genetic algorithm is a method that incorporates genetic elements and obtains a solution such that each objective function is minimized from an initial solution group. In the example of FIG. 2, the direction of moving to the left and the lower side from the initial solution corresponds to the search direction. In such a method, in a practical problem with a large problem scale, it is often impossible to calculate an exact solution within real time, so it is required to calculate a more optimal solution within a finite calculation time.

[0013] Therefore, it is conceivable to perform a weighting on a plurality of objective functions to be optimized, set one evaluation function, and perform an optimization calculation using a single-objective optimization engine. FIG. 3 is a diagram illustrating the linear weighted sum method in this case. For example, from an initial solution group, objective function f1(x1)·w + objective function f2(x1)·(1 - w) is obtained, and from this solution, objective function f1(x2)·w + objective function f2(x2)·(1 - w) is obtained, and further objective function f1(x3)·w + objective function f2(x3)·(1 - w) is obtained. "w" corresponds to the weight and is a value of 0 < w < 1. However, in such a method, it is difficult to obtain appropriate weights for a plurality of indicators with different scales as the evaluation function. Also, it is difficult to shorten the calculation time.

[0014] Therefore, in the following embodiments, an information processing apparatus, an operation method, and an operation program capable of shortening the calculation time will be described.

Embodiment

[0015] FIG. 4(a) is a functional block diagram showing the overall configuration of an information processing apparatus 100 according to Embodiment 1. The information processing apparatus 100 is a server for optimization processing or the like. As illustrated in FIG. 4(a), the information processing apparatus 100 functions as an objective function setting unit 10, an optimization execution unit 20, an intermediate process recording unit 30, a result output unit 40, and the like.

[0016] Figure 4(b) is a hardware configuration diagram of the information processing device 100. As illustrated in Figure 4(b), the information processing device 100 includes a CPU 101, RAM 102, storage device 103, input device 104, display device 105, etc.

[0017] The CPU (Central Processing Unit) 101 is a central processing unit. The CPU 101 includes one or more cores. The RAM (Random Access Memory) 102 is a volatile memory that temporarily stores programs executed by the CPU 101, data processed by the CPU 101, etc. The storage device 103 is a non-volatile storage device. As the storage device 103, for example, a ROM (Read Only Memory), a solid-state drive (SSD) such as flash memory, or a hard disk driven by a hard disk drive can be used. The storage device 103 stores the calculation program. The input device 104 is a device for the user to input necessary information, such as a keyboard or mouse. The display device 105 is a display device that displays the results output by the result output unit 40 on a screen. The various parts of the information processing device 100 are realized when the CPU 101 executes the calculation program. Note that dedicated hardware such as circuits may be used as the various parts of the information processing device 100.

[0018] The objective function setting unit 10 sets multiple objective functions. The objective function setting unit 10 may set two objective functions, or it may set three or more objective functions. In this embodiment, the objective function setting unit 10 sets N objective functions f1 to f N The optimization execution unit 20 sets the objective function f1~f N The optimization process is performed to optimize the system. The progress recording unit 30 records the results obtained during the optimization execution by the optimization execution unit 20. The result output unit 40 outputs the results of the optimization performed by the optimization execution unit 20.

[0019] The process of calculating the Pareto optimal solution will be explained below, following the flowchart in Figure 5 and the explanatory diagrams in Figures 6(a) and 6(b). Figures 6(a) and 6(b) are explanatory diagrams for the two objective functions f1 and f2.

[0020] First, the objective function setting unit 10 sets the N objective functions (f) that you want to optimize. n Set n (1 to N) (Step S1). Each objective function is, for example, the production completion time in the production process, the production costs, etc. A shorter production completion time is better, and a lower cost is better.

[0021] Next, the optimization execution unit 20 sets n to 1 (step S2). This allows it to first focus on the objective function f1.

[0022] Next, the optimization execution unit 20 sets the initial values ​​of each explanatory variable to random values ​​(step S3). There may be one initial value or multiple initial values. The initial values ​​may also be entered by the user using the input device 104.

[0023] Next, the optimization execution unit 20 calculates the objective function f1~f according to the explanatory variables. N The value of is calculated (step S4). If step S4 is performed for the first time, the objective function f1~f is calculated from the initial values ​​of the explanatory variables. N The value of is calculated. If there are multiple initial values, an initial solution group is generated as illustrated in Figure 6(a).

[0024] Next, the progress recording unit 30 records the explanatory variables used in step S4 and the objective functions f1~f calculated in step S4. N The value is recorded (step S5). Therefore, the intermediate progress recording unit 30 records the initial solution group.

[0025] Next, the optimization execution unit 20 performs the objective function f n We determine whether the optimal solution has converged (step S6). Here, the objective function f nThe system determines whether this value is the best possible value. Alternatively, it may determine whether a better solution has been obtained than the initial value.

[0026] If "No" is determined in step S6, the optimization execution unit 20 updates the explanatory variables so that the evaluation function is optimized by the single-objective optimization engine (step S7). Then, the process is executed again from step S4.

[0027] If "Yes" is determined in step S6, the optimization execution unit 20 determines whether n is greater than or equal to N (step S8). By executing step S8, it is possible to determine whether single-objective optimization has been completed for all objective functions.

[0028] If "No" is determined in step S8, the optimization execution unit 20 adds 1 to n to make it n+1 (step S9). Then, the process is executed again from step S3.

[0029] If "Yes" is determined in step S8, the optimization execution unit 20 extracts the Pareto solution from all calculation results (step S10). This allows the extraction of the Pareto solution obtained by optimizing each objective function individually, as illustrated in Figure 6(a). The extracted Pareto solution is recorded by the intermediate progress recording unit 30.

[0030] Next, the optimization execution unit 20 calculates a linear weighted sum weighted according to the arrangement of the Pareto solutions extracted in step S10 (step S11). For example, weighting is applied perpendicular to the approximation plane that approximates the arrangement of the Pareto solutions. If there are two objective functions, the approximation line of the Pareto solutions is used instead of the approximation plane mentioned above. In Figure 6(a), an approximation line approximating the Pareto solutions is obtained. The approximation method is not particularly limited, but for example, the least squares method is used. In Figure 6(b), the approximation line and the direction intersecting the approximation line (for example, the perpendicular direction) are drawn. This direction corresponds to the search direction for the solution.

[0031] Next, the optimization execution unit 20 sets the objective functions f1 to f N and performs multi-objective optimization using the linear weighted sum as the evaluation function (step S12). The initial value of the explanatory variable in this case is the explanatory variable corresponding to the Pareto solution extracted in step S10.

[0032] Next, the optimization execution unit 20 calculates a Pareto solution using the execution result of step S12 (step S13). The Pareto solution is depicted in Fig. 6(b). The calculation result of step S13 is output by the result output unit 40.

[0033] As described above, a plurality of N objective functions f n (x) (n = 1,..., N) are respectively set as the evaluation functions of single-objective optimization, and optimized by a single-objective optimization engine to solve the optimal solution and its explanatory variable of each single-objective optimization. Starting from each optimal solution of the single-objective optimization, a linear weighted sum with each objective function weighted in the direction perpendicular to the Pareto front is set as the evaluation function, and multi-objective optimization calculation is performed to solve the Pareto solution. While minimizing each objective function, the search direction of the optimal solution is set by the linear weighted sum to solve the true Pareto front.

[0034] In this method, single-objective optimization is performed for each objective function before multi-objective optimization. Since multi-objective optimization is performed starting from the optimal solution obtained by single-objective optimization, the calculation time until reaching the true Pareto front is shortened. Note that the computational load of single-objective optimization is significantly smaller than that of multi-objective optimization. Therefore, compared with the case of performing multi-objective optimization without performing single-objective optimization, the computational load is reduced as a result, and the calculation time can be shortened.

Example

[0035] In Example 1, the results of the optimal calculation process in single-objective optimization were used, but it is not limited to this. In Example 2, the case where the results of the optimal calculation process in single-objective optimization are not used will be described.

[0036] The process for calculating the Pareto optimal solution in Example 2 will be explained below, following the flowchart in Figure 7 and the explanatory diagrams in Figures 8(a) and 8(b). Figures 8(a) and 8(b) are explanatory diagrams for the two objective functions f1 and f2.

[0037] First, the objective function setting unit 10 sets the N objective functions (f) that you want to optimize. n Set n (1 to N) (step S21). Each objective function is, for example, the production completion time in the production process, the production costs, etc. A shorter production completion time is better, and a lower cost is better.

[0038] Next, the optimization execution unit 20 sets n to 1 (step S22). This allows it to first focus on the objective function f1.

[0039] Next, the optimization execution unit 20 sets the initial values ​​of the explanatory variables to random values ​​(step S23). There may be one initial value or multiple initial values. The initial values ​​may also be entered by the user using the input device 104.

[0040] Next, the optimization execution unit 20 calculates the objective function f1~f according to the explanatory variables. N The value of is calculated (step S24). If step S24 is executed for the first time, the objective function f1~f is calculated from the initial values ​​of the explanatory variables. N The value of is calculated. If there are multiple initial values, an initial solution group is generated as illustrated in Figure 6(a).

[0041] Next, the optimization execution unit 20 performs the objective function f n We determine whether the optimal solution has converged (step S25). Here, the objective function f n The system determines whether this value is the best possible value. Alternatively, it may determine whether a better solution has been obtained than the initial value.

[0042] If "No" is determined in step S25, the optimization execution unit 20 updates the explanatory variables to optimize the evaluation function using a single-objective optimization engine (step S26). Then, the process is executed again from step S24.

[0043] If "Yes" is determined in step S26, the optimization execution unit 20 determines whether n is greater than or equal to N (step S27). By executing step S27, it is possible to determine whether single-objective optimization has been completed for all objective functions.

[0044] If "No" is determined in step S27, the optimization execution unit 20 adds 1 to n to make it n+1 (step S28). Then, the process is executed again from step S23.

[0045] If "Yes" is determined in step S27, the optimization execution unit 20 extracts the optimal solution for each objective function (step S29). As illustrated in Figure 8(a), the solution with the lowest value of f1 and the solution with the lowest value of f2 are extracted as the optimal solution. Each extracted optimal solution is recorded by the intermediate progress recording unit 30.

[0046] Next, the optimization execution unit 20 calculates a linear sum weighted according to the arrangement of the optimal solutions extracted in step S29 (step S30). For example, weighting is applied perpendicular to the plane connecting the optimal solutions. If there are two objective functions, a straight line connecting the optimal solutions is used. In Figure 8(a), a straight line connecting the optimal solutions is obtained. In Figure 8(b), the line connecting the optimal solutions and the direction intersecting that line (for example, the perpendicular direction) are drawn. This direction corresponds to the search direction for the solution.

[0047] Next, the optimization execution unit 20 performs the objective function f1~f N Then, multi-objective optimization is performed using a linear weighted sum as the evaluation function (step S31). In this case, the initial values ​​of the explanatory variables are those corresponding to the optimal solution extracted in step S29.

[0048] Next, the optimization execution unit 20 calculates the Pareto solution using the execution result of step S31 (step S32). The Pareto solution is shown in Figure 8(b). The result of step S32 is output by the result output unit 40.

[0049] As described above, multiple N objective functions fn(x) (n=1,…,N) to be optimized are set as evaluation functions for single-objective optimization and optimized using a single-objective optimization engine, and the optimal solution and its explanatory variables for each single-objective optimization are found. Starting from each optimal solution of the single-objective optimization, each objective function f n Then, a multi-objective optimization calculation is performed to find the Pareto solution by setting a linear weighted sum, which assigns weights to each objective function perpendicular to the Pareto front, as the evaluation function. While minimizing each objective function, the search direction for the optimal solution is set using the linear weighted sum, and the true Pareto front is found.

[0050] In this method, single-objective optimization is performed for each objective function before multi-objective optimization. Because multi-objective optimization is performed starting from the optimal solution obtained through single-objective optimization, the computation time to reach the true Pareto front is shortened. Furthermore, since the computational load of single-objective optimization is significantly smaller than that of multi-objective optimization, the computational load is reduced and computation time is shortened compared to performing multi-objective optimization without single-objective optimization.

[0051] (Simulation results for Example 1) The simulation results for Example 1 are described below. f1 and f2 are used as objective functions. Multiobjective optimization was performed to minimize these objective functions. As an example, the standard problem shown below was used. This standard problem is disclosed in "Eckart Zitzler, Kalyanmoy Ded, and Lothar Thiele, Comparison of Multiobjective Evolutionary Algorithms: Empirical Results, Evolutionary Computation, vol. 8, Issue 2, pp. 173–195 (2000)."

number

[0052] The following equations are used as examples of objective functions f1 and f2.

number

number

[0053] Here, g(x²,…,x m ) can be expressed as shown in the following formula.

number

[0054] Furthermore, we assume that m = 30 and that the following equation holds true.

number

[0055] For each of the above objective functions, single-objective optimization was performed. Explanatory variables x = (x1, x2, ..., x 30 The initial values ​​were random, and the single-objective optimization engine was updated to minimize the objective function. For each single-objective optimization, the results of the calculation process (explanatory variable x and the values ​​of f1(x) and f2(x)) were also output. From all calculation results, including the results of the single-objective optimizations, the Pareto solution and its explanatory variables were obtained. Figure 9 shows the calculation results. As shown in the results of Figure 9, the single-objective optimizations were concentrated in the region where the value of f1(x) was small and the region where the value of f2(x) was small.

[0056] Next, starting with the Pareto solutions for f1(x) and f2(x), multi-objective optimization was performed using a linear weighted sum weighted perpendicular to the approximation line of the Pareto front, and three objective functions: f1(f) and f2(x). The results are shown in Figure 10. Figure 10 also shows the Pareto solution obtained using the method in Figure 2. Comparing the method in Figure 2 with the method in Example 1 using the same number of calculations (approximately 4900), it can be seen that the method in Example 1 was able to calculate a more optimal Pareto front. Therefore, it can be seen that the calculation time required to obtain the same Pareto front was shortened. When comparing the hypervolume, the method in Example 1 had a hypervolume 1.3% lower than the method in Figure 2.

[0057] Figure 11 is a diagram illustrating hypervolume. Hypervolume is a performance indicator of Pareto solutions. Specifically, hypervolume represents the area or volume of the region formed by a certain reference point and the set of solutions obtained by the algorithm in the objective function space. For example, the reference point can be (0,0), and the standardized values ​​of each objective function can be used. When there are two objective functions, the area shown in Figure 11 is the hypervolume. The larger this hypervolume, the wider the solution spreads, and therefore, it can be judged that a good result has been obtained.

[0058] (Simulation results for Example 2) Next, we will describe the simulation results for Example 2. In Example 2, the objective function was set using a specific layout of the manufacturing site.

[0059] Figure 12 illustrates a production line model. As illustrated in Figure 12, the production line model includes branches and mergers, with multiple products being fed in one by one. Multiple operations are performed sequentially for each of these products. At least some of the operations differ for each of these products.

[0060] The production line model in Figure 12 consists of process 1 and process 2. The product passes through process 1 and process 2 according to the product input sequence, repeatedly branching and merging, finally reaching the inspection and packaging stages before shipment. In process 1, three identical manufacturing machines 1 are arranged. Before work begins at each manufacturing machine 1, a changeover (the process of changing the settings of the processing machine's jigs and equipment according to the type of product being produced) is performed.

[0061] Process 2 does not require a changeover. Process 2 consists of three manufacturing machines 2 and two legacy machines with different specifications from manufacturing machines 2. Legacy machines are machines that are costly and time-consuming to operate.

[0062] For example, the changeover process requires two workers. Therefore, a maximum of two devices can be used to perform the changeover simultaneously. The cost of each device increases in proportion to its operating time.

[0063] As an example, a plan to optimize manufacturing time and cost is devised using a layout like this. For instance, if you try to shorten manufacturing time by reducing changeovers, the use of legacy equipment will increase, leading to higher costs. Therefore, there is a trade-off between manufacturing time and cost.

[0064] Figures 13(a) to 13(c) illustrate product information. Figure 13(a) illustrates master information from the production master. Figure 13(b) illustrates operating costs from the production master. Figure 13(c) illustrates changeover cycle time from the production master.

[0065] As illustrated in Figure 13(a), for each product type A to E, the number of units produced, the processing cycle time of manufacturing equipment 1, the processing cycle time of manufacturing equipment 2, the processing cycle time of legacy equipment, and the changeover specifications are associated. As illustrated in Figure 13(b), a device operating cost coefficient is associated with each manufacturing device. By multiplying this coefficient by the processing cycle time, the operating cost is calculated. As illustrated in Figure 13(c), the changeover cycle time is associated with the next product / previous product combination. The previous product for a given device is the type of product whose manufacturing process has been carried out by that device up to that point. The next product is the type of product whose manufacturing process will be carried out by that device next. Each product combination is linked to the "next product / previous product" number.

[0066] The objective function consisted of two components: manufacturing time and cost. We assumed extremely short computation time by utilizing a high-speed, single-objective solving engine. Random values ​​were set as initial values. Figure 14 shows the results. The horizontal axis represents manufacturing time, and the vertical axis represents cost. Single-objective optimal solutions were obtained for both manufacturing time and cost.

[0067] Next, starting from the single-objective optimal solutions for manufacturing time and cost, multi-objective optimization was performed using a linear weighted sum weighted perpendicular to the line connecting the optimal solutions, along with three objective functions: manufacturing time and cost. The results are shown in Figure 15. The method in Figure 2 obtained the same result (HV = 0.576) as the Pareto front obtained by the method in Example 2 (approximately 600 calculations), but with 1600 calculations, thus reducing the computational load by approximately 60%. Comparing the results of the method in Figure 2 and the method in Example 2 with the same number of calculations (approximately 600), a wider range of optimal Pareto fronts (HV approximately twice as high) was calculated.

[0068] In the examples above, genetic algorithms were used as the optimization algorithm, but this is not the only option. Other optimization algorithms, such as evolutionary algorithms, may also be used.

[0069] In each of the above examples, the optimization execution unit 20 calculates a single-objective optimal solution that is better than the initial solution by performing single-objective optimization on the initial solution using each of the multiple objective functions as the first evaluation function, and uses a linear weighted sum obtained by weighting each of the multiple objective functions according to the single-objective optimal solution as the second evaluation function, and performs multi-objective optimization on the second evaluation function starting from the single-objective optimal solution.

[0070] Although embodiments of the present invention have been described in detail above, the present invention is not limited to these specific embodiments, and various modifications and changes are possible within the scope of the gist of the present invention as described in the claims. [Explanation of Symbols]

[0071] 10. Objective Function Setting Section 20 Optimization Execution Unit 30 Interim Record Section 40 Result Output Section 100 Information Processing Devices 101 CPU 102 RAM 103 Storage device 104 Input device 105 Display device

Claims

1. On the computer, The process involves performing single-objective optimization on the initial solution, using each of the two objective functions as the first evaluation function, to calculate a single-objective optimal solution that is better than the initial solution. A computation program characterized by performing the following steps: calculating an approximate straight line of the Pareto solution obtained by performing the aforementioned single-objective optimization, and using a linear weighted sum obtained by weighting each of the two objective functions in the direction intersecting the approximate straight line as a second evaluation function, and performing multi-objective optimization on the second evaluation function starting from the single-objective optimal solution.

2. The calculation program according to claim 1, characterized in that the direction intersecting the approximate line is a direction perpendicular to the approximate line.

3. A computer, The process involves performing single-objective optimization on the initial solution, using each of the two objective functions as the first evaluation function, to calculate a single-objective optimal solution that is better than the initial solution. A computation program characterized by performing a process of multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by weighting each of the two objective functions in a direction intersecting the line connecting the single-objective optimal solution obtained by the execution of the single-objective optimization, as the second evaluation function.

4. The calculation program according to claim 3, characterized in that the direction intersecting the line connecting the single-objective optimal solutions is perpendicular to the line connecting the single-objective optimal solutions.

5. A computer, The process involves performing single-objective optimization on the initial solution, using each of the three objective functions as the first evaluation function, to calculate a single-objective optimal solution that is better than the initial solution. A computation program characterized by performing the following steps: calculating an approximate plane of the Pareto solution obtained by performing the aforementioned single-objective optimization, and using a linear weighted sum obtained by weighting each of the three objective functions in the direction intersecting the approximate plane as a second evaluation function, and performing multi-objective optimization on the second evaluation function starting from the single-objective optimal solution.

6. The calculation program according to claim 5, characterized in that the direction intersecting the approximate plane is a direction perpendicular to the approximate plane.

7. A computer, The process involves performing single-objective optimization on the initial solution, using each of the three objective functions as the first evaluation function, to calculate a single-objective optimal solution that is better than the initial solution. A computation program characterized by performing a process of multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by performing the single-objective optimization as a second evaluation function, which is weighted for each of the three objective functions in a direction intersecting the plane connecting the single-objective optimal solutions obtained by the execution of the single-objective optimization.

8. The calculation program according to claim 7, characterized in that the direction intersecting the plane connecting the single-objective optimal solutions is a direction perpendicular to the plane connecting the single-objective optimal solutions.

9. The process involves performing single-objective optimization on the initial solution, using each of the two objective functions as the first evaluation function, to calculate a single-objective optimal solution that is better than the initial solution. The process involves calculating an approximate straight line of the Pareto solution obtained by performing the aforementioned single-objective optimization, and using a linear weighted sum obtained by weighting each of the two objective functions in the direction intersecting the approximate straight line as a second evaluation function, and performing multi-objective optimization on the second evaluation function starting from the single-objective optimal solution, A method of calculation characterized by being performed by a computer.

10. A process for calculating a single-objective optimal solution that is better than the initial solution by performing single-objective optimization on the initial solution using each of the two objective functions as the first evaluation function, A process in which a multi-objective optimization is performed on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by weighting each of the two objective functions in a direction intersecting the line connecting the single-objective optimal solution obtained by the execution of the single-objective optimization, and A method of calculation characterized by being performed by a computer.

11. A process for calculating a single-objective optimal solution that is better than the initial solution by performing single-objective optimization on the initial solution using each of the three objective functions as the first evaluation function, The process involves calculating an approximate plane of the Pareto solution obtained by performing the aforementioned single-objective optimization, and using a linear weighted sum obtained by weighting each of the three objective functions in the direction intersecting the approximate plane as a second evaluation function, and performing multi-objective optimization on the second evaluation function starting from the single-objective optimal solution, A method of calculation characterized by being performed by a computer.

12. A process for calculating a single-objective optimal solution that is better than the initial solution by performing single-objective optimization on the initial solution using each of the three objective functions as the first evaluation function, A process in which a multi-objective optimization is performed on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by performing the single-objective optimization as a second evaluation function, with each of the three objective functions weighted in a direction intersecting the plane connecting the single-objective optimal solutions obtained by the aforementioned single-objective optimization, and A method of calculation characterized by being performed by a computer.

13. An information processing device comprising: an execution unit that, with respect to the initial solution, performs single-objective optimization using each of the two objective functions as a first evaluation function to calculate a single-objective optimal solution that is better than the initial solution; calculates an approximate straight line of the Pareto solution obtained by the single-objective optimization; and uses a linear weighted sum obtained by weighting each of the two objective functions in the direction intersecting the approximate straight line as a second evaluation function to perform multi-objective optimization on the second evaluation function starting from the single-objective optimal solution.

14. An information processing device comprising: an execution unit that performs single-objective optimization on an initial solution using each of two objective functions as a first evaluation function to calculate a single-objective optimal solution that is better than the initial solution; and performs multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by weighting each of the two objective functions in a direction intersecting the line connecting the single-objective optimal solutions obtained by the execution of the single-objective optimization as a second evaluation function.

15. An information processing device comprising: an execution unit that performs single-objective optimization on an initial solution using each of the three objective functions as a first evaluation function to calculate a single-objective optimal solution that is better than the initial solution; calculates an approximate plane of the Pareto solution obtained by performing the single-objective optimization; and performs multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by weighting each of the three objective functions in a direction intersecting the approximate plane as a second evaluation function.

16. An information processing device comprising: an execution unit that performs single-objective optimization on an initial solution using each of three objective functions as a first evaluation function to calculate a single-objective optimal solution that is better than the initial solution; and performs multi-objective optimization on the second evaluation function, starting from the single-objective optimal solution, using a linear weighted sum obtained by weighting each of the three objective functions in a direction intersecting the plane connecting the single-objective optimal solutions obtained by the execution of the single-objective optimization as a second evaluation function.

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