Calculation method, calculation program, and information processing device

Abstract

This computation method involves causing a computer to execute: a first process of repeating generational evolution by a first optimization algorithm that performs generational evolution by a genetic algorithm in which variations are given to input variables for each individual such that a target function meets a predetermined condition; and a second process of repeating generational evolution by a second optimization algorithm that performs generational evolution by a genetic algorithm in which, for each individual obtained at or after a predetermined generation in the first process, giving variations to input variables and obtaining an individual are repeated multiple times such that a statistical value of a target function of each of the obtained individuals meets a predetermined condition.　

Description

[Technical field]

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

[0002] In various industries, there are optimization problems that need to be solved to achieve good results. For these optimization problems, optimization algorithms are being researched to find exact solutions that achieve the highest computational results. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Z. Xue, and F. Pedroso de Lima: Robust Design Optimization on an Inline Three-Cylinder Engine Balance Shaft with Many Stochastic Variables. SAE Technical Paper, 12 (2019) 2019-01-0329. [Non-Patent Document 2] S. Tsutsui: Genetic Algorithms with a Robust Solution Searching Scheme. IEEE transactions on Evolutionary Computation, 1 (1997) 201-208. Summary of the Invention [Problem to be solved by the invention]

[0004] However, in actual work sites, work may not be performed according to the exact solution. In such cases, the effect that would be obtained with the exact solution may be significantly reduced. Therefore, highly robust optimization algorithms are being researched (for example, see Non-Patent Documents 1 and 2).

[0005] However, in the method described in Non-Patent Document 1, the calculation time increases monotonically with an increase in the number of sampling points. Therefore, it is difficult to obtain an optimal solution in a practical calculation time. On the other hand, in the method described in Non-Patent Document 2, the evaluation value of one sampling point has a large influence on the selection of a solution, so the position of the Pareto solution calculated as the optimal solution tends to be overestimated.

[0006] In one aspect, the present invention has an object to provide a calculation program, a calculation method, and an information processing device that can obtain an effective optimal solution while reducing calculation time. [Means for solving the problem]

[0007] In one aspect, the computing method is performed by a computer, and includes a first process of repeating generational evolution using a first optimization algorithm that varies input variables for each individual and generates a generational evolution using a genetic algorithm so that the objective function satisfies a predetermined condition, and a second process of repeating generational evolution using a second optimization algorithm that repeats the process of generating individuals by varying input variables multiple times for individuals from the predetermined generation onwards obtained in the first process, and generates generational evolution using a genetic algorithm so that the statistical value of the objective function of each obtained individual satisfies a predetermined condition. Effect of the Invention

[0008] It is possible to obtain an optimal solution with high effectiveness while reducing the calculation time. [Brief description of the drawings]

[0009] [Figure 1] FIG. 13 is a diagram illustrating an example of an optimization result regarding the arrangement of products in a packaging box. [Diagram 2] FIG. 1A is a functional block diagram illustrating an overall configuration of an information processing apparatus according to a first embodiment, and FIG. 1B is a block diagram illustrating a hardware configuration of each unit of the information processing apparatus. [Diagram 3]FIG. 1A is a diagram illustrating a model of a packaging box, FIG. 1B is a diagram illustrating product information stored in a storage unit, and FIG. 1C is a diagram illustrating an exact solution. [Figure 4] FIG. 13 is a diagram illustrating a flowchart for finding an optimal solution using the MORDO method. [Diagram 5] 11 is a diagram illustrating an example of a calculation result obtained by an optimization method that does not take variance into account and a calculation result obtained by the MORDO method. [Figure 6] FIG. 13 is a diagram illustrating an example of the variance of Pareto solutions expressed by bubble size. [Figure 7] FIG. 10 is a diagram illustrating a flowchart for finding an optimal solution using the Robust GA method. [Figure 8] FIG. 13 is a diagram illustrating an example of a calculation result using the MORDO method and a calculation result using the Robust GA. [Figure 9] FIG. 13 is a diagram illustrating an example of the variance of Pareto solutions expressed by bubble size. [Figure 10] 11 is a flowchart illustrating an example of a process executed by an information processing device. [Figure 11] 11 is a diagram illustrating an example of a calculation result in the Robust GA method and a calculation result in the Hybrid method according to the embodiment. FIG. [Figure 12] FIG. 13 is a diagram illustrating an example of the variance of Pareto solutions expressed by bubble size. [Figure 13] FIG. 13 is a diagram showing two types of test cases (case 1 and case 2) in which the initial arrangement of packing is changed. [Figure 14] FIG. 13 is a diagram illustrating a modified example. [Figure 15] 11 is a diagram for explaining an example in which a result output from a result output unit is output to an operating device. FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Before describing the embodiments, an overview of the optimization algorithm will be given.

[0011] Optimization problems exist in various industries, including distribution and manufacturing. Optimization algorithms that find exact solutions to these problems and achieve the highest computational efficiency are being researched.

[0012] Here, the exact solution is the solution with the highest evaluation index. For example, in a production line, the evaluation indexes include the production completion time, delivery date, and production cost. In a packing operation, the evaluation indexes include the amount of wasted materials and the work time. An optimization algorithm is an algorithm that optimizes one or more evaluation indexes as an objective function so that the objective function becomes good. In a production line, the input variables are conditions such as the initial input order of products to the production line, as well as the work time required for each product. In a packing operation, the input variables are conditions such as the initial packing order of products, as well as the size of each product, the weight of each product, and the size of the box. The obtained solution is the input order of products to the production line, etc. In a packing operation, the obtained solution is the packing order of products, etc.

[0013] Optimization algorithms can obtain the exact solution that maximizes the evaluation index. However, when trying to apply the exact solution obtained by these optimization algorithms to the actual site, various variations can occur at the actual site, making it difficult to perform the work exactly according to the exact solution, and the work content may end up slightly deviating from the exact solution.

[0014] Here, the exact solution obtained by the conventional method is often a solution that has a high local effect. Therefore, if the work content deviates from the exact solution (= tolerance occurs), the effect will be drastically reduced and the expected effect may not be obtained.

[0015] For example, in the case of packing work, differences in the proficiency of workers can cause the time required for the work to be longer, and errors in the size of the products handled can cause the packing work to be unable to be completed according to the exact solution. These are things that can happen in the real world. If these kinds of events occur, the work content will deviate from the exact solution.

[0016] FIG. 1 is a diagram illustrating an example of an optimization result for the arrangement of products in a packing box. By packing products tightly into a packing box, the amount of wasted material can be reduced. Therefore, it is possible to find an optimal solution for packing products into a packing box using an optimization algorithm. FIG. 1 is a diagram illustrating an optimal solution. In FIG. 1, the horizontal axis indicates the solution space of the input conditions, and the vertical axis indicates the amount of wasted material. In the example of FIG. 1, evaluation is performed using one evaluation index, the amount of wasted material.

[0017] For example, the optimal solution on the right side of Figure 1 is the strict solution because it reduces the amount of wasted materials the most. While this strict solution significantly reduces the amount of wasted materials, the solution exists locally, so even if the work content deviates even slightly from the strict solution, the amount of wasted materials increases significantly. On the other hand, the optimal solution on the left side does not reduce the amount of wasted materials as much as the strict solution, but compared to the strict solution, the solution does not exist locally (the difference in the amount of wasted materials with neighboring solutions is small). Therefore, even if the work content deviates slightly from the optimal solution, the amount of wasted materials does not increase significantly. In actual work sites, there is a demand for a highly robust optimization algorithm that can obtain results close to the optimal solution even if the work content deviates from the optimal solution. EXAMPLES

[0018] Fig. 2(a) is a functional block diagram showing an overall configuration of an information processing device 100 according to a first embodiment. The information processing device 100 is, for example, a server for optimization processing. As illustrated in Fig. 2(a), the information processing device 100 includes a storage unit 10, an acquisition unit 20, a first calculation unit 30, a second calculation unit 40, a determination unit 50, and an output unit 60. In the first embodiment, optimization in a packing operation will be described as an example.

[0019] Fig. 2(b) is a block diagram illustrating an example of a hardware configuration of each unit of the information processing device 100. As illustrated in Fig. 2(b), the information processing device 100 includes a CPU 101, a RAM 102, a storage device 103, an input device 104, a display device 105, and the like.

[0020] 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 a program executed by the CPU 101, data processed by the CPU 101, and the like. The storage device 103 is a non-volatile storage device. For example, a ROM (Read Only Memory), a solid state drive (SSD) such as a flash memory, or a hard disk driven by a hard disk drive can be used as the storage device 103. The storage device 103 stores an arithmetic program. The input device 104 is an input device such as a mouse or a keyboard. Alternatively, the input device 104 is an interface such as an external memory such as a USB memory. The display device 105 is a device that displays the processing results of the information processing device 100, and is a display or the like. Each part of the information processing device 100 is realized by the CPU 101 executing the arithmetic program. Note that each part of the information processing device 100 may be hardware such as a dedicated circuit.

[0021] The storage unit 10 stores a model of a packing box. FIG. 3(a) is a diagram illustrating an example of a model of a packing box. As illustrated in FIG. 3(a), the storage unit 10 stores the shape of the bottom surface of the packing box (width direction length×height direction length). When a worker faces a packing box, the worker faces one of the sides of the bottom surface of the packing box. The width direction of the packing box is the direction in which the side that the worker faces extends. The height direction of the packing box is the direction in which the adjacent side perpendicular to the side that the worker faces extends, and is the direction away from the worker (depth direction).

[0022] The storage unit 10 also stores product information related to the products to be sequentially arranged in the packaging box. Fig. 3(b) is a diagram illustrating an example of product information stored in the storage unit 10. In the example of Fig. 3(b), product information on 17 products is stored. Each product is approximately hexahedral. As illustrated in Fig. 3(b), each product is assigned a product number, and further, the product shape (height length x width length x thickness) is associated with the weight.

[0023] FIG. 3(c) is a diagram illustrating an example of an exact solution that can reduce the gaps and waste material amount the most for each product in FIG. 3(b). As illustrated in FIG. 3(c), products 1 to 17 are arranged in a packing box without any gaps, and the height of all the packed products is small. In this case, the amount of waste material can be significantly reduced, but if there is an intersection in the product sizes, the work cannot be done according to the exact solution. Therefore, it is desirable to use a highly robust optimization method.

[0024] Here, we will explain the MORDO (multi-objective robust design optimization) method as a highly robust optimization method. The MORDO method is a method in which calculations are repeated with multiple variations given by the Monte Carlo method. Specifically, this method prepares solutions with variations given to input variables, and when evaluating the optimization calculation, it obtains the optimal solution by using statistical values ​​such as the average value and standard deviation obtained by the repeatedly given variations in the variables as the objective function.

[0025] 4 is a diagram illustrating an example of a flowchart for finding an optimal solution using the MORDO method. As illustrated in FIG. 4, first, an initial parent is prepared (step S1). The parent is the initial solution.

[0026] Next, the first generation parent is given variations using Gaussian noise or the like (step S2). For example, multiple types of variations are generated. For example, for the product shape of each piece of product information stored in the storage unit 10, 1% increase in size, 2% increase in size, 1% decrease in size, 2% decrease in size, etc. are generated as each variation.

[0027] Next, when variations are given to the parents of the first generation, the objective function of each individual corresponding to each variation is evaluated (step S3). That is, the objective function of the solution obtained for each variation value is evaluated.

[0028] Next, multiple excellent individuals are selected such that the objective function satisfies a predetermined condition (step S4). Next, multiple children are generated by crossbreeding the excellent individuals (step S5). Next, mutations are caused in the multiple children (step S6).

[0029] Next, Gaussian noise is used to give variation to each individual after mutation (step S7). This variation is the same as that in step S2. Next, the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation is evaluated (step S8). By executing steps S7 and S8 multiple times, it is possible to give variation to each individual multiple times. After steps S7 and S8 are executed multiple times, the average value and variance of the objective function of each individual are calculated for the variation given multiple times (step S9). Next, the average value and variance of each individual are evaluated (step S10). Then, the process is executed again from step S4. After the process from step S4 to step S10 is repeated a predetermined number of times, the execution of the flowchart ends.

[0030] In this way, the solution with the highest evaluation value is finally calculated as the optimal solution. The MORDO method repeatedly evaluates a sufficient number of sampling points in the vicinity of the input variables, resulting in a highly robust solution.

[0031] FIG. 5 is a diagram illustrating the calculation results of an optimization algorithm that does not consider variance and the calculation results of the MORDO method. Each plot in FIG. 5 shows the evaluation index value for each arrangement order. In the example of FIG. 5, the height of all the products packed in the box and the work time are used as the evaluation index value. FIG. 6 is a diagram illustrating the results of expressing the variance of the Pareto solution by bubble size. As illustrated in FIG. 5 and FIG. 6, in the MORDO method, the Pareto front position is slightly receded compared to the optimization algorithm that does not consider variance, but the variance of the solution is small, and a highly robust solution can be obtained.

[0032] However, in the MORDO method, the calculation time increases monotonically with the increase in the number of sampling points. Therefore, in optimization problems that use solvers such as "finite element analysis" that have a high calculation cost for each evaluation value, it is difficult to obtain an optimal solution using the MORDO method in a practical calculation time.

[0033] Next, we will explain the Robust GA (robust genetic algorithm) method as another highly robust optimization method. The Robust GA method uses a GA (genetic algorithm) as an optimization engine, and performs generational evolution by generating variation for each evaluation of generational evolution by the genetic algorithm.

[0034] Fig. 7 is a diagram illustrating an example of a flowchart for finding an optimal solution by the Robust GA method. As illustrated in Fig. 7, first, an original parent is prepared (step S11). Next, Gaussian noise is used to give variation to the original parent (step S12). This variation is the same as that in step S2 of Fig. 4. Next, the objective function of each individual corresponding to each variation when the variation is given to the original parent is evaluated (step S13).

[0035] Next, a plurality of excellent individuals are selected such that the objective function satisfies a predetermined condition (step S14). Next, the excellent individuals are crossed to generate a plurality of offspring (step S15). Next, mutation is caused in the plurality of offspring (step S16).

[0036] Next, Gaussian noise is used to give variation to each individual after mutation (step S17). This variation is the same as that in step S12. Next, the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation is evaluated (step S18). After that, Step S14 After the processes from step S14 to step S18 are repeated a predetermined number of times, the execution of the flowchart ends.

[0037] In this way, solutions with variations are prepared as input variables, and the objective function obtained by applying the variations only once is used as the evaluation value. Solutions with low robustness are eliminated during the generation evolution process, and the final highly robust solution is calculated as the optimal solution.

[0038] FIG. 8 is a diagram illustrating the calculation results of the MORDO method and the Robust GA. Each plot in FIG. 8 shows the evaluation index value for each arrangement order. In the example of FIG. 8, the height of all the products packed in the box and the work time are used as the evaluation index value. FIG. 9 is a diagram illustrating the results of expressing the variance of the Pareto solutions by bubble size. FIG. 9 also shows the calculation results of the optimization algorithm of FIG. 6. As illustrated in FIG. 8 and FIG. 9, the Robust GA method obtains a highly robust Pareto solution with a small variance of the solution in the same position as the optimization algorithm that does not consider the variance. However, compared to the MORDO method, the variance of the solution is large and the robustness is low.

[0039] In this Robust GA method, since only one sampling point is taken near the input variable, there is no calculation loss and it is possible to evaluate many solutions. However, since the evaluation value of only one sampling point has a large influence on the selection of the solution, the position of the Pareto solution calculated as the optimal solution tends to be overestimated.

[0040] Therefore, in this embodiment, a hybrid method is adopted in which a switch generation is set and the MORDO method and the Robust GA method are used. Specifically, in younger generations where the number of generations is less than the number of switch generations, the Robust GA method is used to eliminate solutions with low robustness while reducing calculation costs. In generations where the number of generations is greater than the number of switch generations, the MORDO method, which can obtain solutions with higher robustness, is used.

[0041] In this way, by switching from the Robust GA method to the MORDO method midway, it is possible to eliminate less robust solutions that may have been overestimated by the Robust GA method. Therefore, it is possible to calculate a highly robust optimal solution in a practical amount of time. However, if the MORDO method is used first and then the Robust GA method is switched midway, the final solution will be the most elite solution, which will reduce robustness.

[0042] 10 is a flowchart showing an example of processing executed by the information processing device 100 according to the present embodiment. First, the first calculation unit 30 prepares an original parent by using the model and product information of the packaging box stored in the storage unit 10 (step S21).

[0043] Next, the first calculation unit 30 applies variation to the first generation parent by using Gaussian noise or the like (step S22). For example, multiple types of variation are generated. For example, for the product shape of each piece of product information stored in the storage unit 10, a size increase of 1%, a size increase of 2%, a size decrease of 1%, a size decrease of 2%, and the like are generated as each variation.

[0044] Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the original parent is given a variation (step S23). That is, the objective function of the solution obtained for each variation is evaluated. For example, the judgment unit 50 judges whether each individual is good by judging whether the objective function of each individual is equal to or greater than a threshold. When there are multiple objective functions, the judgment unit 50 judges whether each individual is good by judging whether each objective function is equal to or greater than a threshold. Alternatively, the judgment unit 50 judges whether each individual is good by judging whether the arithmetic mean when a weight is set for each objective function is equal to or greater than a threshold.

[0045] Next, the first calculation unit 30 selects multiple excellent individuals that provide a good objective function (step S24). Next, the first calculation unit 30 crosses the excellent individuals to generate multiple children (step S25). Next, the first calculation unit 30 causes mutations in the multiple children (step S26). Next, the first calculation unit 30 determines whether the number of generations has exceeded the switch generation (step S27).

[0046] If step S27 is judged as "No", the first calculation unit 30 gives variation to each individual after mutation using Gaussian noise or the like (step S28). The variation in this case is the same as that in step S22. Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation (step S29). For example, the same evaluation as in step S23 is performed. Then, the process is repeated from step S24.

[0047] If step S27 is judged as "Yes", the second calculation unit 40 gives variation to each individual after mutation using Gaussian noise or the like (step S31). The variation in this case is the same as that in step S22. Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation (step S32). By executing steps S31 and S32 multiple times, it is possible to give variation multiple times to each individual. After executing steps S31 and S32 multiple times, the second calculation unit 40 calculates the average value and variance of the objective function of each individual for the variation given multiple times (step S33).

[0048] Next, the judgment unit 50 evaluates the average value and variance of each individual (step S34). For example, the judgment unit 50 judges whether the average value is equal to or greater than a threshold value, and judges whether the variance is equal to or less than a threshold value. Then, the process is executed again from step S24. After step S24 is repeated a predetermined number of times, the execution of the flowchart ends. The output unit 60 outputs the obtained optimization result to the display device 105. As a result, the display device 105 displays the optimization result.

[0049] FIG. 11 is a diagram illustrating the calculation results of the Robust GA method and the Hybrid method according to the present embodiment. Each plot in FIG. 11 shows the evaluation index value for each arrangement order. FIG. 12 is a diagram illustrating the results of expressing the variance of the Pareto solutions by bubble size. FIG. 12 also shows the calculation results of the optimization algorithm not considering the variance in FIG. 6, the calculation results of the MORDO method, and the calculation results of the Robust GA method in FIG. 9. As illustrated in FIG. 11 and FIG. 12, the Hybrid method obtained a Pareto front at a position almost similar to that of the MORDO method. Furthermore, compared with the Robust GA method, the Pareto solutions obtained had smaller solution variance and higher robustness.

[0050] FIG. 13 is a diagram showing two types of test cases (case 1 and case 2) in which the initial arrangement of the packing boxes is changed. For each case, the calculation results of the optimization algorithm that does not consider the variance, the calculation results of the MORDO method, the calculation results of the Robust GA method, and the calculation results of the Hybrid method according to this embodiment are shown. The calculation time of each optimization algorithm is also shown. Of the three bar graphs, the left side shows the results of Case 1, the middle shows the results of Case 2, and the right side shows the calculation time. In each case, the maximum value by all methods is displayed as 100% based on the average value of the variance of the solution group that forms the Pareto front. It can be seen that the calculation cost of the Hybrid method according to this embodiment is slightly higher than that of the Robust GA method, but is significantly reduced compared to the MORDO method. From the above, it can be seen that in this embodiment, by repeating generation evolution with the Robust GA method and then repeating generation evolution with the MORDO method, a highly robust and effective optimal solution can be obtained while suppressing the calculation time.

[0051] In this embodiment, the average value and variance of the objective function are evaluated, but other statistical values ​​such as the median and standard deviation may be used.

[0052] (Modification) Next, a modified example will be described. As illustrated in Fig. 14, first, the first calculation unit 30 prepares an original parent by using a model of a packaging box and product information stored in the storage unit 10 (step S41). Next, the first calculation unit 30 imparts variation to the original parent by using Gaussian noise or the like (step S42). Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the variation is imparted to the original parent (step S43).

[0053] Next, the first calculation unit 30 selects a plurality of excellent individuals that have a good objective function (step S44). Next, the first calculation unit 30 generates a plurality of children by crossing the excellent individuals (step S45). Next, the first calculation unit 30 causes mutations in the plurality of children (step S46). Next, the first calculation unit 30 gives variation to each individual after mutation using Gaussian noise or the like (step S47). Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation (step S48). Next, the judgment unit 50 evaluates the objective function of each individual when the variation is given (step S49). After that, the process is repeated from step S44. In this case, the number of repetitions is set to be greater than the number of switch generations.

[0054] When the repetition of step S44 reaches a predetermined number exceeding the switch generation, after execution of step S49, the second calculation unit 40 extracts a solution of a generation greater than or equal to the switch generation (step S50). Next, the second calculation unit 40 gives variation to each individual after mutation using Gaussian noise or the like (step S51). Next, the judgment unit 50 evaluates the objective function of each individual corresponding to each variation when the variation is given to each individual after mutation (step S52). Then, the process is repeated from step S51.

[0055] When the number of repetitions to step S51 reaches a predetermined number, after execution of step S52, the second calculation unit 40 calculates the average value and variance of the objective function for the predetermined number of variations (step S53). Next, the judgment unit 50 evaluates the objective function when the variations are given (step S54). For example, the judgment unit 50 judges whether the average value is equal to or greater than a threshold value, and judges whether the variance is equal to or less than a threshold value. Thereafter, the execution of the flowchart ends. The output unit 60 outputs the obtained optimization result to the display device 105. As a result, the display device 105 displays the optimization result.

[0056] In this modified example as well, by repeating generational evolution using the Robust GA method and then repeating generational evolution using the MORDO method for individuals from a certain generation onwards, it is possible to obtain a highly robust and effective optimal solution while reducing calculation time.

[0057] In each of the above examples, the results output by the output unit 60 are output to the display device 105, but may be output to the operating device 200. FIG. 15 is a block diagram illustrating this case. The operating device 200 is a robot that sequentially places objects to be packed in a box in a packing operation, and a robot that sequentially inputs objects to be produced into a production line in a production line. As illustrated in FIG. 15, the results output by the output unit 60 are output to the operating device 200. The operating device 200 operates so as to realize the optimal solution received from the output unit 60. The operating device 200 includes a CPU, a RAM, a storage device, etc., and, for example, the storage device stores a control program, etc. that controls the operation of the operating device 200, the RAM stores the optimal solution received from the output unit 60, and the CPU controls the operation of the operating device 200 based on the control program and the optimal solution.

[0058] In each of the above examples, the first calculation unit 30 is an example of a first calculation unit that repeats generational evolution using a first optimization algorithm that varies input variables for each individual and generates a generational evolution using a genetic algorithm so that the objective function satisfies a predetermined condition. The second calculation unit 40 is an example of a second calculation unit that repeats generational evolution using a second optimization algorithm that repeats the process of obtaining individuals by varying input variables multiple times for individuals from a predetermined generation onwards obtained by the first calculation unit, and generates generational evolution using a genetic algorithm so that the statistical value of the objective function of each obtained individual satisfies a predetermined condition. The output unit 60 is an example of an output unit that outputs the individuals obtained by repeating the process by the second calculation unit to a display device.

[0059] Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications and variations are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0060] 10 Storage area 20 Acquisition Department 30 1st calculation section 40 Second calculation section 50 Judgment section 60 Output section 100 Information processing device 105 Display device

Claims

1. a first process for repeating generational evolution a predetermined number of times using a first optimization algorithm that varies input variables once for each individual and performs generational evolution using a genetic algorithm so that the value of the objective function satisfies a predetermined condition; a second process of repeating generational evolution using a second optimization algorithm, which repeats a process of giving variations to input variables to obtain individuals multiple times for each individual obtained by the first process and evolved for the predetermined number of generations using the first optimization algorithm, and repeats generational evolution using a second optimization algorithm, which performs generational evolution using a genetic algorithm so that a statistical value of a value of an objective function of each obtained individual satisfies a predetermined condition; A computation method characterized by being executed by a computer.

2. The computation method according to claim 1, characterized in that in the second process, for the individuals of the predetermined generation, the process of obtaining individuals by varying input variables is repeated a plurality of times, and the individuals are evolved in generations so that a statistical value of an objective function of each of the obtained individuals satisfies a predetermined condition.

3. In the first process, generation evolution is repeated until a generation exceeds the predetermined generation; 2. The method according to claim 1, wherein in the second process, individuals from the predetermined generation onward obtained by the second optimization algorithm are extracted, and for the extracted individuals, a process of giving variations to input variables to obtain individuals is repeated a plurality of times, and the individuals are evolved in generations so that a statistical value of an objective function of each of the obtained individuals satisfies a predetermined condition.

4. 4. The calculation method according to claim 1, wherein an average value and a variance are used as the statistical value.

5. 5. The computing method according to claim 1, wherein the computer executes a process of displaying on a display device individuals obtained by repeating generational evolution in the second process.

6. On the computer, a first process for repeating generational evolution a predetermined number of times using a first optimization algorithm that varies input variables once for each individual and performs generational evolution using a genetic algorithm so that the value of the objective function satisfies a predetermined condition; a process of repeating generational evolution in a second process in which, for each individual obtained in the first process and evolved for the predetermined number of generations by the first optimization algorithm, a process of giving variation to input variables to obtain an individual is repeated a plurality of times, and generational evolution is performed by a genetic algorithm so that a statistical value of a value of an objective function of each obtained individual satisfies a predetermined condition; A computing program characterized by executing the above.

7. a first calculation unit that repeats generational evolution a predetermined number of times using a first optimization algorithm that varies an input variable once for each individual and performs generational evolution using a genetic algorithm so that a value of a target function satisfies a predetermined condition; and a second calculation unit that repeats generational evolution using a second optimization algorithm, in which, for each individual obtained by the first calculation unit and evolved for the predetermined number of generations using the first optimization algorithm, a variation is introduced into input variables to obtain an individual multiple times, and generational evolution is performed using a genetic algorithm so that a statistical value of a target function value of each obtained individual satisfies a predetermined condition.

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