Information processing device, information processing method, and control program

Abstract

In order to enable the speed of optimization to be improved while suppressing any increase in processing load, this information processing device (1), which optimizes a plurality of objective functions using a genetic algorithm, comprises an optimization unit (20) that, in a first selection process for selecting an individual to serve as a parent individual of the genetic algorithm and / or a second selection process for selecting an individual to serve as a crossover target of the genetic algorithm, selects an individual using the degree of protrusion, which indicates the extent to which each individual being selected protrudes, in a direction in which an ideal solution exists, relative to other individuals.

Description

Information Processing Apparatus, Information Processing Method, and Control Program

[0001] The present disclosure relates to an information processing apparatus, an information processing method, and a control program.

[0002] In multi-objective optimization, it is desirable to obtain solutions that are diverse, faster, and closer to the true Pareto solutions.

[0003] As a conventional technique used to obtain solutions close to Pareto solutions in multi-objective optimization, a genetic algorithm (GA) using data envelopment analysis (DEA) is known (for example, Non-Patent Document 1).

[0004] Non-Patent Document 1 discloses a technique for improving the optimization speed by using a generalized data envelopment analysis in environmental selection and crossover selection.

[0005] Yin Lifeng, Hirotaka Nakayama, Tetsuzo Tanino, Masao Arakawa, "A Method for Multi-Objective Optimization Using Generalized Data Envelopment Analysis and Genetic Algorithm", Transactions of the Society of Instrument and Control Engineers, Vol.13, No.4, pp.179-185, 2000

[0006] Although the genetic algorithm using data envelopment analysis can be expected to improve the optimization speed, on the other hand, there is a problem that the amount of calculation is large and the processing load becomes high.

[0007] The present disclosure has been made in view of the above, and an object thereof is to obtain an information processing apparatus capable of realizing an improvement in the optimization speed while suppressing an increase in the processing load.

[0008] In order to solve the above-described problems and achieve the object, the present disclosure is an information processing apparatus that optimizes a plurality of objective functions using a genetic algorithm, and includes a first selection process for selecting an individual to be a parent individual of the genetic algorithm and a second selection process for selecting an individual to be a crossover target of the genetic algorithm. An optimization unit that performs selection of a solid using a protrusion degree indicating how much each of the individuals to be selected protrudes in a direction in which an ideal solution exists when compared with other individuals is provided.

[0009] The information processing device described herein has the effect of improving the optimization speed while suppressing an increase in processing load.

[0010] A figure showing an example of the configuration of the information processing device according to Embodiment 1. A flowchart showing an example of the operation of the information processing device according to Embodiment 1 in deriving a Pareto solution. A first figure for explaining the protrusion degree used when the information processing device according to Embodiment 1 selects an object to be crossed. A second figure for explaining the protrusion degree used when the information processing device according to Embodiment 1 selects an object to be crossed. A figure showing an example of the application of the information processing device according to Embodiment 1. A flowchart showing an example of the operation of the second selection unit of the information processing device according to Embodiment 2 in selecting an individual object to be crossed. A figure for explaining the shape modification of the solution performed by the information processing device according to Embodiment 2. A figure for explaining the calculation of the protrusion degree by the second selection unit of the information processing device according to Embodiment 2. A figure showing an example of the operation of the information processing device according to Embodiment 3. A figure showing another example of the operation of the information processing device according to Embodiment 3. A figure showing an example of the hardware that realizes the information processing devices according to Embodiments 1 to 4.

[0011] The information processing apparatus, information processing method, and control program according to embodiments of this disclosure will be described in detail below with reference to the drawings.

[0012] Embodiment 1. Figure 1 shows an example of the configuration of the information processing device 1 according to Embodiment 1. The information processing device 1 is a device that performs multi-objective optimization using a genetic algorithm and derives Pareto solutions for multiple objective functions.

[0013] The information processing device 1 includes an information acquisition unit 11 that acquires information from other external devices, an initial solution setting unit 12 that sets an initial solution which is the initial value of the solution to be optimized, an optimization unit 20 which is composed of a first selection unit 13, a second selection unit 14 and a gene manipulation unit 15 and performs optimization of the solution using a genetic algorithm, a simulation unit 16 which performs a simulation using each of a plurality of solution candidates which are candidates for Pareto solutions and calculates an evaluation value for each solution candidate, and an output unit 17 which outputs the results of the optimization process by the optimization unit 20. Note that the simulation unit 16 may be implemented by a simulator device separate from the information processing device 1. That is, the simulation unit 16 may be provided outside the information processing device 1.

[0014] The operation of the information processing device 1 will now be explained. Figure 2 is a flowchart showing an example of the operation by which the information processing device 1 according to Embodiment 1 derives a Pareto solution.

[0015] The information processing device 1 first performs sampling to select multiple solution candidates from a range defined by one or more predetermined constraints and set them as initial solutions (step S11). This sampling is performed by the initial solution setting unit 12. The selection range of solution candidates is indicated by a constraint function. The constraint function is acquired at a predetermined timing by, for example, the information acquisition unit 11 and held in a storage unit (not shown in the figure). The initial solution setting unit 12 selects solution candidates to be used as initial solutions using known methods such as random sampling and Latin hypersquare sampling.

[0016] The information processing device 1 then selects parent individuals (step S12). Specifically, the first selection unit 13 obtains and confirms the evaluation values ​​of each of the multiple initial solutions from the simulation unit 16, and selects a predetermined number of initial solutions in order from those with the highest evaluations to be the parent individuals. The process by which the first selection unit 13 selects parent individuals is the first selection process.

[0017] Here, the simulation unit 16 calculates an evaluation value for each initial solution using an evaluation function that weights and adds up each of the multiple objective functions according to their importance.

[0018] The information processing device 1 then checks whether the termination conditions are satisfied, that is, whether the termination conditions for the optimization process, which consist of the above-described step S12 and the following-described steps S14 to S16, are satisfied (step S13). The information processing device 1 determines that the termination conditions are satisfied, for example, when the optimization process is executed repeatedly a predetermined number of times. The information processing device 1 may also determine that the termination conditions are satisfied when a certain amount of time has elapsed since the start of the optimization process, or it may determine that the termination conditions are satisfied by other means. Whether or not the termination conditions are satisfied is determined, for example, by the first selection unit 13.

[0019] If the termination condition is not met (step S13: No), the information processing device 1 selects individuals to be crossed over (step S14). Specifically, the second selection unit 14 selects solution candidates from among the parent individuals selected by the first selection unit 13 to be the individuals to be subjected to the crossover process of the genetic algorithm. The process by which the second selection unit 14 selects individuals to be crossed over is the second selection process. The second selection unit 14 uses a known non-dominant sort and a sort using the degree of prominence described later (hereinafter sometimes referred to as the degree of prominence sort) to select a predetermined number of individuals to be crossed over. For example, when selecting N individuals (where N is an integer greater than or equal to 2) to be crossed over, the second selection unit 14 first performs a non-dominant sort to determine the rank of each individual. Next, the second selection unit 14 selects individuals in order from the highest rank, and if the number of selected individuals (hereinafter referred to as the number of selections) exceeds the required number N, it calculates the degree of prominence for each individual at the rank when the number of selections exceeds the required number N, and selects individuals in order from those with the largest degree of prominence until the number of selections becomes N. Rank 1 is the highest rank.

[0020] Let's explain a specific example. If the total number of individuals of rank 1 and rank 2 is less than the required number N, and the total number of individuals of rank 1, rank 2, and rank 3 is greater than the required number N, that is, if all individuals of rank 3 are selected in addition to individuals of rank 1 and rank 2, the number of selections will be greater than the required number N, then the second selection unit 14 selects some of the individuals of rank 3 in descending order of prominence, so that the total number of individuals of rank 1 and rank 2 plus the selected individuals of rank 3 is equal to the required number N. Note that depending on the relationship between the number of individuals of each rank and the required number N, which is the number of crossover targets, the selection of crossover targets may be completed before the prominence sort is performed, that is, N crossover targets may be selected by non-dominance sort alone, and the process may end at that point.

[0021] Here, we will explain the degree of protrusion used by the second selection unit 14 when selecting the object to be crossed.

[0022] Figure 3 is a first diagram illustrating the prominence index used by the information processing device 1 according to Embodiment 1 when selecting an object to be crossed. Figure 3 shows examples of the positions of multiple solution candidates (individuals a to e) for two objective functions y1 and y2. Figure 3 also shows an example in which the second selection unit 14 evaluates individual a from individuals a to e and calculates the prominence index of individual a. The worst point shown in Figure 3 is the point where all objective functions are maximized, and serves as the reference point when calculating the prominence index. Note that the reference point when calculating the prominence index may be other than the worst point. For example, a point in the vicinity of the worst point, i.e., any point within a certain range including the worst point, may be used as the reference point, or the position of the individual with the lowest evaluation (smallest evaluation value) among all existing individuals may be used as the reference point. Furthermore, different reference points may be set for each rank. For example, when calculating the prominence of individuals of rank J (J=1,2,3,...), the position of the individual with the lowest evaluation within the rank J population may be used as the reference point. Alternatively, when calculating the prominence of individuals of rank J, the position of one individual randomly selected from the rank J+1 population may be used as the reference point.

[0023] When calculating the degree of prominence, the second selection unit 14 first orthogonally projects the vectors from the worst point to each of the non-evaluated individuals (individuals other than those being evaluated) onto the vector from the worst point to the individual being evaluated, thereby obtaining the orthogonal projection vector for each of the non-evaluated individuals. Next, the second selection unit 14 uses the largest norm among the obtained orthogonal projection vectors as a reference and calculates the degree of prominence, which indicates how much the norm of the vector from the worst point to the individual being evaluated protrudes from the reference norm. Specifically, the second selection unit 14 calculates the ratio of the reference norm to the norm of the vector from the worst point to the individual being evaluated as the degree of prominence. In the example shown in Figure 3, the norm of the orthogonal projection vector corresponding to individual c is (|c|cosθ). c ) is the norm (|b|cosθ) of the orthogonal projection vector corresponding to the other individuals b, d, and e. b It is greater than (etc.). For this reason, the second selection unit 14 sets individual c as the reference solution and calculates the ProminentScore(a) of individual a to be evaluated according to the following formula (1). In the example shown in Figure 3, the ProminentScore(a) of individual a to be evaluated is approximately 1.2.

[0024]

[0025] Let's look at another example. Figure 4 is a second diagram illustrating the degree of protrusion used by the information processing device 1 according to Embodiment 1 when selecting an object to cross. Figure 4 shows an example in which the second selection unit 14 evaluates individual b from individuals a to e and calculates the degree of protrusion for individual b. In Figure 4, the positions of individuals a to e and the worst point are the same as in Figure 3.

[0026] In the example shown in Figure 4, the norm of the orthogonal projection vector corresponding to individual a is (|a|cosθ). a ) is greater than the norm of the orthogonal projection vector corresponding to other individuals. Therefore, individual a becomes the reference solution for individual b being evaluated. The second selection unit 14 calculates the ProminentScore(b) of individual b being evaluated according to the following equation (2). In the example shown in Figure 4, the ProminentScore(b) of individual a being evaluated is approximately 0.7.

[0027]

[0028] The second selection unit 14 calculates the protrusion of individuals c, d, and e shown in Figures 3 and 4 using the same procedure as for the protrusion of individuals a and b.

[0029] Individuals with a high degree of prominence are closer to the ideal solution and receive higher evaluations than other individuals with low prominence. Each individual's degree of prominence indicates how much it protrudes in the direction of the ideal solution compared to other individuals. The ideal solution is the one where all objective functions are minimized. The location of the ideal solution is also called the utopia point.

[0030] The second selection unit 14 selects individuals to be crossed over in order from those with the highest rank determined by the non-dominant sort, and calculates the degree of prominence for each individual of a rank whose number of selected individuals exceeds a predetermined required number N.

[0031] Let's return to the explanation of the operation of the information processing device 1. After selecting the crossover target in step S14, the information processing device 1 performs the crossover process (step S15), and then performs the mutation process (step S16). Specifically, the gene manipulation unit 15 performs the crossover process and the mutation process on the crossover target individual to generate offspring individuals.

[0032] In the crossover process, the gene manipulation unit 15 generates two offspring individuals by, for example, selecting two individuals from the individuals to be crossed and performing the crossover. More specifically, the gene manipulation unit 15 generates offspring individuals by swapping some of the decision variables included in the objective function representing each of the two individuals. In the mutation process, the gene manipulation unit 15 generates offspring individuals by, for example, selecting a predetermined number of individuals to induce mutations and changing some of the decision variables included in the objective function representing each of the selected individuals to other values. The crossover and mutation processes performed by the gene manipulation unit 15 are the same as those performed by known general genetic algorithms.

[0033] After executing step S16, the information processing device 1 returns to step S12 and performs parent individual selection again. In this parent individual selection, the information processing device 1 selects a new parent individual from among a plurality of individuals, which include the individual selected in the previous parent individual selection (parent individual) and the individuals generated in the immediately preceding steps S15 and S16 (child individual). The information processing device 1 then repeatedly executes steps S14 to S16 and S12 described above, targeting the newly selected parent individual, until it determines in step S13 that the termination condition is satisfied.

[0034] Furthermore, if the termination condition is met (step S13: Yes), the information processing device 1 terminates the optimization process and outputs the optimization result (step S17). Specifically, the output unit 17 outputs the individual selected as the parent individual in the immediately preceding step S12 as the optimized solution candidate.

[0035] In this example, the gene manipulation unit 15 performs both crossover and mutation processing when generating offspring individuals. However, it is not mandatory to perform both crossover and mutation processing when generating offspring individuals. The frequency of crossover processing and the frequency of mutation processing may be set to different values. For example, the system may be configured to perform mutation processing after repeating crossover processing n times (where n is an integer greater than or equal to 2), that is, to perform mutation processing once for every n crossover processes.

[0036] Furthermore, in the selection of parent individuals in step S12, a selection method similar to the selection of crossover targets in step S14 may be used, that is, a selection method that combines non-dominance sort and prominence sort.

[0037] Furthermore, in step S14 above, we performed crossover target selection using non-dominant sort and prominence sort, but we may also use a tournament system and the aforementioned prominence, which are commonly used in crossover target selection in general genetic algorithms. That is, we may select individuals for crossover using a tournament system that uses the aforementioned prominence as the fitness used for selecting individuals.

[0038] Next, an application example of the information processing apparatus 1 will be described. FIG. 5 is a diagram showing an application example of the information processing apparatus 1 according to the first embodiment. FIG. 5 shows an example in which the information processing apparatus 1 is applied to a water treatment facility 101 that purifies and discharges the inflowing sewage.

[0039] When applied to the water treatment facility 101, the information processing apparatus 1 acquires the prediction result of the inflow volume of sewage into the water treatment facility 101 and the sensor values output by various sensors provided in the water treatment facility 101, performs multi-objective optimization on the acquired information, and outputs candidates for parameters used for the control of the water treatment facility 101.

[0040] The prediction result of the inflow volume of sewage into the water treatment facility 101 is obtained, for example, by using a model that predicts the inflow volume based on the rainfall in the vicinity of the water treatment facility 101. Information on the rainfall in the vicinity of the water treatment facility 101 may be obtained by using a service that provides meteorological information in real time. Examples of the sensor values output by various sensors provided in the water treatment facility 101 include the water levels in the inflow canal, pump well, etc., the water quality before water treatment, the water quality after water treatment, the pumping volume by the pumping pump, etc. Examples of the parameters used for the control of the water treatment facility 101 include the pumping volume from the pump well to the water treatment tank, the output of the pumping pump, the amount of water discharged from the water treatment tank to the outside, etc.

[0041] An operator who monitors and controls the water treatment facility 101 makes an operation plan for the water treatment facility 101 while considering, for example, risk avoidance, cost reduction, and the quality of the discharged water. That is, the operator plans the operation of the water treatment facility 101 so that the processing area in the water treatment facility 101 does not flood, the power consumption is minimized, and the quality of the discharged water meets the specified standards, based on the situation of the processing area and the amount of water flowing into the water treatment facility 101.

[0042] The information processing apparatus 1 applied to the water treatment facility 101 optimizes the control parameters necessary for the operation plan of the water treatment facility 101 on behalf of the operator of the water treatment facility 101, and outputs candidates for the optimized control parameters.

[0043] In this case, the information processing apparatus 1 performs multi-objective optimization for the objective function f1 related to risk avoidance, the objective function f2 related to cost reduction, and the objective function f3 related to the quality of the treated wastewater. These objective functions f1 to f3 are represented by, for example, the following equations (3) to (5).

[0044]

[0045] For the objective function f1 related to risk avoidance represented by Equation (3), y1(t) is the water level of the inflow channel at time t.

[0046]

[0047] For the objective function f2 related to cost reduction represented by Equation (4), y2(t) is the power consumption at time t. The objective function f2 represents the average value of the power consumption at time t.

[0048]

[0049] For the objective function f3 related to the quality of the treated wastewater represented by Equation (5), COD (Chemical Oxygen Demand) indicates the scientific oxygen demand for the treated wastewater, TN (Total Nitrogen) indicates the total amount of nitrogen contained in the treated wastewater, and TP (Total Phosphorus) indicates the total amount of phosphorus contained in the treated wastewater. COD(t) is the scientific oxygen demand at time t, TN(t) is the total amount of nitrogen contained in the treated wastewater at time t, and TP(t) is the total amount of phosphorus contained in the treated wastewater at time t. Also, Q Total is represented by the following equation (6).

[0050]

[0051] The first term on the right side of the objective function f3 is the maximum value of the ratio to the water quality instantaneous regulation value at all times, and the largest ratio among the ratios corresponding to COD, TN, and TP respectively is adopted as the maximum value. Also, Q in the second term on the right side of the objective function f3 Total is the maximum value of the ratio to the total amount regulation value of the water quality, and the largest ratio among the ratios corresponding to COD, TN, and TP respectively is adopted as the maximum value.

[0052] Furthermore, the information processing device 1 applied to the water treatment facility 101 optimizes the above objective functions f1 to f3 within the range that satisfies the conditions defined by the constraint functions g1 to g5 represented by the following equations (7) to (11).

[0053]

[0054] In the constraint function g1 expressed by equation (7), y1 is the water level in the inflow channel. The constraint function g1 indicates the constraint on the water level in the inflow channel.

[0055]

[0056]

[0057] In the constraint functions g2 and g3 expressed in equation (8 and 9), u(t) is the amount of water pumped from the pump well to the water treatment tank at time t. Constraint function g2 indicates the constraint on the amount of water pumped from the pump well to the water treatment tank during clear weather, and constraint function g3 indicates the constraint on the amount of water pumped from the pump well to the water treatment tank during rainy weather.

[0058]

[0059] In the constraint function g4 expressed by equation (10), u(t) is the power consumption at time t. The constraint function g4 indicates a constraint to keep the peak power below the contracted power value.

[0060]

[0061] Q of the constraint function g5 expressed by equation (11) Total Q constitutes the objective function f3 described above. Total It is the same as the following. The constraint function g5 is the maximum ratio Q to the total amount regulation value for water quality. Total This section outlines constraints to keep the total amount below the regulatory limit during rainy weather.

[0062] The information processing device 1 applied to the water treatment facility 101 samples candidate solutions for the objective functions f1 to f3 from the range that satisfies the constraints defined by the constraint functions g1 to g5 above, and sets a predetermined number of initial solutions. After setting the initial solutions, the information processing device 1 optimizes the candidate solutions by executing the process described using Figures 2 to 4 (the process in steps S12 to S16 of the flowchart shown in Figure 2).

[0063] Here, an example of applying the information processing device 1 to a water treatment facility 101 has been described, but it can also be applied to facilities other than water treatment facilities 101. For example, the information processing device 1 can be applied to systems and devices that have multiple parameters that require setting and adjustment, such as air conditioning systems, processing machines for processing workpieces, and design drawing creation devices. When applying the information processing device 1 to an air conditioning system, for example, objective functions related to power costs and comfort are set, and the information processing device 1 performs optimization processing on multiple objective functions to derive candidate parameters such as temperature, humidity, and airflow to be set in the air conditioning system.

[0064] As described above, the information processing device 1 according to this embodiment performs multi-objective optimization using a genetic algorithm. In the crossover target of the genetic algorithm, individuals are selected using a non-dominant sort and a prominence index that indicates how much an individual protrudes towards the utopia point relative to other individuals. The prominence index is calculated by orthogonally projecting the vector from the worst point to the individual to be evaluated with the vectors from the worst point to each of the other individuals (individuals not to be evaluated) to generate orthogonal projection vectors for each of the other individuals, and then using the norm of the vector from the worst point to the individual to be evaluated and the norm of the orthogonal projection vectors for each of the other individuals. According to the information processing device 1 according to this embodiment, since individuals closer to the utopia point are selected as crossover targets and crossover and mutation processing is performed, the time required to obtain a solution candidate close to the true Pareto solution can be shortened. Furthermore, the computational amount can be reduced compared to the case where envelope analysis is used for selecting crossover targets.

[0065] In this embodiment, the second selection unit 14 calculates the degree of prominence for individuals of a rank where the number of individuals to be crossed exceeds a predetermined number. However, depending on the distribution of individuals, there may be individuals with a high degree of prominence among individuals of a rank lower than the rank where the number of selected individuals exceeds the predetermined number. For this reason, the second selection unit 14 may calculate the degree of prominence for individuals of the rank where the number of selected individuals exceeds the predetermined number, and for individuals of the rank one level below it. This prevents the oversight of excellent individuals with a high degree of prominence, making it possible to reliably select excellent individuals. The second selection unit 14 may also calculate the degree of prominence for all individuals of the rank where the number of selected individuals exceeds the predetermined number, and for all individuals of a rank lower than this rank. In this case, it becomes possible to select excellent individuals more reliably.

[0066] Furthermore, in this embodiment, the second selection unit 14 uses prominence when selecting crossover targets. However, the first selection unit 13 may use prominence when selecting parent individuals, and the second selection unit 14 may use a known method, such as a known NSGA-II (Non-dominated Sorting Genetic Algorithms II) that uses non-dominant sorting and congestion sorting, when selecting crossover targets. By using prominence in the selection of parent individuals, individuals closer to the utopia point are selected as parent individuals, and the time required to obtain a solution candidate closer to the true Pareto solution can be shortened compared to the case where parent individuals are selected without using prominence. Alternatively, non-dominant sorting and congestion sorting in NSGA-II may be used in the selection of parent individuals, and non-dominant sorting and prominence may be used in the selection of crossover targets. Since NSGA-II is a method with excellent diversity, using this method allows for the selection of a wider variety of solutions as parent individuals, and consequently, a wider variety of derived solutions can be achieved.

[0067] Furthermore, in this embodiment, the worst point is used as the reference point, and the degree of prominence is calculated using the vector from the worst point to each individual. However, the utopia point may also be used as the reference point, and the degree of prominence may be calculated using the vector from the utopia point to each individual. In this case, the orthogonal projection vector with the smallest norm among the orthogonal projection vectors of each individual not being evaluated is selected, and the degree of prominence is obtained by dividing the norm of the selected orthogonal projection vector by the norm of the vector from the utopia point to the individual being evaluated.

[0068] Embodiment 2. Next, an information processing device according to Embodiment 2 will be described. The information processing device according to Embodiment 2 has the same configuration as the information processing device 1 according to Embodiment 1, but the process of selecting the object to be crossed differs from that of Embodiment 1. In this embodiment, the part that differs from Embodiment 1, specifically the process by which the second selection unit 14 shown in Figure 1 selects the object to be crossed in step S14 of the flowchart shown in Figure 2, will be described, and the other steps S11 to S13 and S15 to S17 are the same as in Embodiment 1, so their description will be omitted.

[0069] Figure 6 is a flowchart showing an example of the operation in which the second selection unit 14 of the information processing device 1 according to Embodiment 2 selects an individual to be crossed over.

[0070] The second selection unit 14 of the information processing device 1 according to Embodiment 2 first performs a known non-superiority sort (step S21). That is, the second selection unit 14 selects individuals of each rank in order from rank 1, within a range in which the number of individuals selected as crossover targets does not exceed a predetermined number. The non-superiority sort performed in step S21 is the same process as the non-superiority sort performed by the information processing device 1 according to Embodiment 1 in the crossover target selection in step S14 described above.

[0071] The second selection unit 14 then modifies the shape of the solution (step S22). The second selection unit 14 modifies the shape of the solution using a known Pareto front modeling method, such as the AGE-MOEA-II (Adaptive Geometry Estimation based Multi-Objective Evolutionary Algorithm-II) Pareto front modeling method. This modification of the solution shape using Pareto front modeling is described below.

[0072] In modifying the shape of a solution using Pareto front modeling, for a given solution c, we search for p that satisfies the following equation (12). In equation (12), M represents the number of objective functions.

[0073]

[0074] Next, we estimate the shape of the solution represented by the following equation (13) using the known Newton-Raphson method.

[0075]

[0076] The shape estimation result using multiple points is expressed by the following equation (14).

[0077]

[0078] Raising all solutions to the power of p transforms the shapes formed by solutions of the same rank into straight lines, and raising all solutions to the power of 2p transforms the shapes formed by solutions of the same rank into circular arcs.

[0079] Figure 7 shows an image of the solution shape modification using Pareto front modeling of AGE-MOEA-II. Figure 7 is a diagram illustrating the solution shape modification performed by the information processing device 1 according to Embodiment 2.

[0080] Figure 7(a) shows the solution before the shape change. When all solutions are raised to the power of p by a p that satisfies equation (12) above, solutions of the same rank become straight lines, as shown in Figure 7(b). Furthermore, when all solutions are raised to the power of 2p, solutions of the same rank become circular arcs, as shown in Figure 7(c). As a result, it becomes possible to evaluate the diversity of solutions by the cosine similarity between two adjacent solutions. When multiple solutions are evenly distributed, the cosine similarity between two adjacent solutions will be the same value. Therefore, by calculating the cosine similarity between each of the multiple solutions and an adjacent solution, and checking the calculated similarity, it is possible to determine whether the solutions are evenly distributed.

[0081] The second selection unit 14 then performs the protrusion sort described in Embodiment 1 on the solutions after they have been changed to an arc shape (step S23). That is, as shown in Figure 8, the second selection unit 14 obtains an orthogonal projection vector by projecting the vector from the worst point to each of the solutions not to be evaluated onto the vector from the worst point to the solution to be evaluated, and calculates the protrusion based on the orthogonal projection vector and the vector from the worst point to the solution to be evaluated. The second selection unit 14 selects the required number of solutions as intersection targets in descending order of protrusion. Figure 8 is a diagram illustrating the calculation of the protrusion by the second selection unit 14 of the information processing device 1 according to Embodiment 2.

[0082] As described above, the second selection unit 14 of the information processing device 1 according to Embodiment 2 selects a certain number of crossover target solutions by non-preferential sorting, and then, when selecting additional solutions for the remaining number, changes the shape of the solutions to an arc shape and calculates the prominence of the modified solutions. The second selection unit 14 continues to select additional solutions based on the prominence until a predetermined number of solutions are selected. By changing the shape of the solutions to an arc shape, it becomes possible to evaluate the diversity of the solutions using cosine similarity.

[0083] In step S22 described above, the second selection unit 14 does not need to change the shape formed by all the solutions, but rather only the shape formed by the selected solution. The selected solution is the solution that is subject to the prominence sort described above. For example, when selecting N individuals (where N is an integer greater than or equal to 2) as crossover targets, if the sum of the solutions from rank 1 to rank K is less than N, and the sum of the solutions from rank 1 to rank K+1 is greater than N, then the solution of rank K+1 becomes the selected solution. In this case, the second selection unit 14 changes the shape formed by the multiple solutions of rank K into an arc shape.

[0084] Furthermore, although this embodiment describes a configuration in which the shape of the solution is changed when selecting the object to be crossed, if the protrusion degree is used in selecting the parent individual, the shape of the solution may be changed to an arc shape, the protrusion degree may be calculated, and then the parent individual may be selected.

[0085] Embodiment 3. Next, an information processing device according to Embodiment 3 will be described. The information processing device according to Embodiment 3 has the same configuration as the information processing device 1 according to Embodiment 1, but the process of selecting the object to be crossed differs from that of Embodiment 1. In this embodiment, the part that differs from Embodiment 1, specifically the process by which the second selection unit 14 shown in Figure 1 selects the object to be crossed in step S14 of the flowchart shown in Figure 2, will be described, and the other steps S11 to S13 and S15 to S17 are the same as in Embodiment 1, so their description will be omitted.

[0086] In Embodiments 1 and 2, an information processing device 1 was described that selects the required number of individuals (solution candidates) in descending order of prominence when selecting crossover targets. However, if individuals are simply selected in descending order of prominence, adjacent solutions may be selected, potentially leading to a loss of solution diversity. Therefore, this embodiment describes a method for ensuring solution diversity.

[0087] The information processing device 1 according to Embodiment 3, when performing a prominence sort, that is, when selecting individuals to be crossed based on their prominence, considers the prominence of the individuals at the endpoints to be greater than that of the other individuals, thereby ensuring that individuals at the endpoints are selected preferentially over other individuals. For example, as shown in Figure 9, the prominence of the two individuals at the endpoints is considered to be greater than that of the other individuals. Figure 9 is a diagram showing an example of the operation of the information processing device 1 according to Embodiment 3. As a result, individuals at the endpoints are preferentially selected as crossing targets, and the range of solutions for the crossing targets can be broadened. As a result, the new solutions generated by the crossing become solutions closer to the endpoints, making it easier to ensure diversity of solutions.

[0088] In this embodiment, we have described the prominence sort used for selecting crossover targets, but the same applies when using the prominence sort for selecting parent individuals. That is, when the first selection unit 13 uses the prominence sort for selecting parent individuals, it considers the prominence of the two endpoint individuals to be greater than that of the other individuals, and thus selects the endpoint individuals preferentially over the other individuals. This allows for a wider range of individuals to be selected as parent individuals during generational change, thereby ensuring diversity among parent individuals.

[0089] Furthermore, when the gene manipulation unit 15 selects two individuals from among the multiple individuals selected by the second selection unit 14 to perform the crossover process, it selects two individuals with high prominence. Individuals with high prominence are superior individuals that are closer to the ideal solution than other individuals. As shown in Figure 10, in the crossover process, new solutions tend to be generated in the vicinity of the crossovered individuals. Figure 10 is a diagram showing another example of the operation of the information processing device 1 according to Embodiment 3. By combining two superior individuals and performing the crossover process, the generated new solutions are also superior solutions, improving convergence, that is, shortening the time required to obtain a solution close to the ideal solution.

[0090] Embodiment 4. Next, an information processing device according to Embodiment 4 will be described. The information processing device according to Embodiment 4 has the same configuration as the information processing device 1 according to Embodiment 1.

[0091] The information processing device 1 according to Embodiment 1 terminates the optimization process when the optimization process has been repeatedly executed a predetermined number of times, or when a certain amount of time has elapsed since the start of the optimization process. In contrast, the information processing device 1 according to this embodiment determines whether or not to terminate the optimization process based on the analysis results of the prominence of each individual, which are repeatedly calculated during the optimization process.

[0092] The information processing device 1 according to this embodiment calculates the prominence of individuals ranked as rank 1 in the non-dominant sort in each generation of the genetic algorithm, and terminates the optimization process when the prominence of rank 1 individuals converges, for example, when the change in prominence between generations falls below a predetermined threshold. Note that the number of rank 1 individuals may not be the same across generations of the genetic algorithm. For this reason, the information processing device 1 calculates the average value of the prominence of rank 1 individuals in each generation of the genetic algorithm, and terminates the optimization process when the change in the average value of prominence between generations falls below a threshold. As the solution converges, that is, as the solution is optimized and approaches the true Pareto solution, the change in the solution's prominence becomes smaller. For this reason, the information processing device 1 determines the degree of convergence of the solution by checking the state of change in prominence, and terminates the optimization process when the solution has been sufficiently optimized.

[0093] Alternatively, the information processing device 1 according to this embodiment calculates the prominence of individuals ranked 1 in the non-dominant sort in each generation of the genetic algorithm, and terminates the optimization process when the variance of the prominence of rank 1 individuals converges, for example, when the change in the variance of the prominence between generations falls below a predetermined threshold. As the diversification of solutions progresses, the change in the variance of the prominence of the solutions becomes smaller. For this reason, the information processing device 1 checks the state of change in the variance of the prominence to determine whether or not diverse solutions have been obtained, and terminates the optimization process when diverse solutions have been obtained.

[0094] In this embodiment, the information processing device 1 determines whether to terminate the optimization process based on the change in the prominence between generations or the change in the variance of the prominence between generations. However, the information processing device 1 may also determine whether to terminate the optimization process based on the change in the prominence between generations and the change in the variance of the prominence between generations. In other words, the information processing device 1 may be configured to terminate the optimization process when both the change in the prominence between generations and the change in the variance of the prominence between generations become small.

[0095] Thus, the information processing device 1 according to this embodiment can analyze the degree of prominence of each individual, thereby terminating the optimization process at a timing that takes into account either or both the convergence and diversity of the solution, and enabling efficient search for solutions.

[0096] Next, we will describe the hardware that implements the information processing device 1 described in each embodiment.

[0097] Figure 11 is a diagram showing an example of hardware that implements the information processing device 1 according to Embodiments 1 to 4. Figure 11 shows an example in which the information processing device 1 is implemented using a control circuit. The control circuit that implements the information processing device 1 includes an input circuit 91, a processor 92, a memory 93, and an output circuit 94.

[0098] The input circuit 91 receives signals from the outside. The output circuit 94 outputs signals from the control circuit to the outside. The processor 92 is, for example, a CPU (Central Processing Unit), central processing unit, processing unit, arithmetic unit, microprocessor, microcomputer, DSP (Digital Signal Processor), etc. The memory 93 is, for example, a non-volatile or volatile semiconductor memory such as RAM (Random Access Memory), ROM (Read Only Memory), flash memory, EPROM (Erasable Programmable Read Only Memory), EEPROM (Registered Trademark) (Electrically Erasable Programmable Read Only Memory), magnetic disk, flexible disk, optical disk, compact disk, minidisc, DVD (Digital Versatile Disk), etc.

[0099] When the information processing device 1 is implemented with the hardware shown in Figure 11, a program for operating as the initial solution setting unit 12, the optimization unit 20, and the simulation unit 16 of the information processing device 1 is stored in memory 93. The processor 92 reads and executes this program, thereby realizing the initial solution setting unit 12, the optimization unit 20, and the simulation unit 16. The above program stored in memory 93 may be provided to the user in the form of being written to a storage medium such as a CD (Compact Disc)-ROM or DVD-ROM, or it may be provided to the user via a network.

[0100] The information acquisition unit 11 and the output unit 17 of the information processing device 1 are implemented by the input circuit 91 and the output circuit 94 of the control circuit, respectively.

[0101] Furthermore, the information processing device 1 can also be implemented using dedicated hardware. Dedicated hardware for implementing the information processing device 1 may include, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or a combination thereof.

[0102] Alternatively, some components of the information processing device 1 may be implemented using dedicated hardware, while the remaining components may be implemented using the control circuit shown in Figure 11.

[0103] The configurations shown in the above embodiments are examples only, and it is possible to combine them with other known technologies, combine different embodiments, and omit or modify parts of the configuration without departing from the gist of the invention.

[0104] 1 Information processing device, 11 Information acquisition unit, 12 Initial solution setting unit, 13 First selection unit, 14 Second selection unit, 15 Gene manipulation unit, 16 Simulation unit, 17 Output unit, 20 Optimization unit, 101 Water treatment facility.

Claims

1. An information processing device that optimizes multiple objective functions using a genetic algorithm, comprising an optimization unit that, in at least one of a first selection process for selecting individuals to be used as parent individuals of the genetic algorithm and a second selection process for selecting individuals to be crossed over by the genetic algorithm, selects individuals using a degree of prominence that indicates how much each of the selected individuals protrudes in the direction in which an ideal solution exists compared to other individuals.

2. The information processing apparatus according to claim 1, characterized in that the optimization unit selects a predetermined number of individuals by combining the selection of individuals using the prominence with the selection of individuals by non-superiority sort.

3. The information processing apparatus according to claim 2, characterized in that the optimization unit selects individuals in order from those with the highest rank determined by the non-superiority sort, within a range in which the number of selected individuals does not exceed the required number, and further, for individuals of rank where the number of selected individuals exceeds the required number, it performs individual selection based on the degree of prominence until the number of selected individuals becomes the required number.

4. The information processing apparatus according to claim 2, characterized in that the optimization unit selects individuals in order from those with the highest rank determined by the non-superiority sort, within a range in which the number of selected individuals does not exceed the required number, and further selects individuals based on the degree of prominence, targeting individuals of the rank where the number of selected individuals exceeds the required number and individuals of the rank one level lower than that rank, until the number of selected individuals becomes the required number.

5. The information processing apparatus according to any one of claims 1 to 4, characterized in that the first selection process uses non-dominance sort and congestion sort to select the individual to be the parent individual, and the second selection process uses the prominence to select the individual to be crossed over.

6. The information processing apparatus according to any one of 1 to 5, characterized in that when the optimization unit calculates the degree of prominence of one of the selected individuals to be evaluated, it calculates the degree of prominence of the individual to be evaluated based on the largest norm among the norms of the vectors obtained by projecting the vectors from the reference point to each of the non-evaluated individuals (individuals other than the one to be evaluated) onto the vector from the reference point to the individual to be evaluated, and the norm of the vector from the reference point to the individual to be evaluated.

7. The information processing apparatus according to claim 6, characterized in that the reference point is the worst point, any point within a certain range including the worst point, the location of the individual with the lowest evaluation among all existing individuals, or the utopia point.

8. The information processing apparatus according to claim 6, characterized in that the reference point is set for each group of individuals with the same rank determined by the non-superiority sort.

9. The information processing apparatus according to any one of claims 1 to 8, characterized in that the optimization unit performs a transformation process by Pareto front modeling on the individuals to be selected, calculates the degree of protrusion of the individuals after transformation, and performs the selection using the calculated degree of protrusion.

10. The information processing apparatus according to claim 9, characterized in that the optimization unit, in the conversion process, converts the selected individual into an individual that forms an arc shape.

11. The information processing apparatus according to any one of claims 1 to 10, characterized in that the optimization unit performs the selection by considering that, among the individuals to be selected, the protrusion degree of the individuals at the endpoints is greater than the protrusion degree of the individuals at points other than the endpoints.

12. The information processing apparatus according to any one of claims 1 to 11, characterized in that when the optimization unit selects individuals to be subjected to the crossover processing of the genetic algorithm from among the individuals selected in the second selection process, it selects two individuals in descending order of their prominence.

13. The information processing apparatus according to any one of claims 1 to 12, characterized in that the optimization unit determines the timing for terminating the optimization process using the genetic algorithm based on the analysis results of the degree of prominence of the individual being optimized by the optimization process.

14. An information processing method comprising: an information processing device that optimizes multiple objective functions using a genetic algorithm, the first step of selecting individuals to be used as parent individuals of the genetic algorithm; and the second step of the information processing device selecting individuals to be crossed over by the genetic algorithm, wherein in at least one of the first step and the second step, the information processing device selects individuals using a degree of prominence that indicates how much each of the selected individuals protrudes in the direction in which an ideal solution exists compared to other individuals.

15. A control program for controlling an information processing device that optimizes multiple objective functions using a genetic algorithm, characterized in that the information processing device is made to perform the following steps: a first step of selecting individuals to be used as parent individuals for the genetic algorithm; a second step of selecting individuals to be crossed over by the genetic algorithm; and in at least one of the first and second steps, the information processing device is made to perform a process of selecting individuals using a degree of prominence that indicates how much each of the selected individuals protrudes in the direction in which an ideal solution exists compared to other individuals.

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