JP2007172306A - Multipurpose optimization apparatus, multipurpose optimization method and multipurpose optimization program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a multipurpose optimization apparatus capable of efficiently obtaining an appropriate Pareto optimum individual in a short time, a multipurpose optimization method and a multipurpose optimization program. <P>SOLUTION: A multipurpose evolutionary algorithm part 2 generates a plurality of slave individual candidates from first, second and third master individuals. Then, a fitness estimation module 30b calculates the estimated value of true fitness for all the master individuals and slave individual candidates. Further, the multipurpose evolutionary algorithm part 2 ranks all the master individuals and slave individual candidates, adds one slave individual candidate of a top rank to a master individual set, calculates a congestion degree, sorts the slave individual candidates in the descending order of the degree of the congestion, and selects a prescribed number of the slave individual candidates having the higher degree of the congestion as a slave individual set. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a multi-objective optimization device, a multi-objective optimization method, and a multi-objective optimization program that optimize parameters to be optimized.

  In this specification, the optimization means obtaining an optimum solution or a solution close to the optimum (suboptimal solution).

  Conventionally, there is a problem class called a multi-objective optimization problem. For example, when considering the problem of minimizing the cost of a product and maximizing performance, this becomes a multi-objective optimization problem of two objective functions. In this case, cost and performance are two objective functions. Generally, there is not a single solution for the multi-objective optimization problem because there is a trade-off relationship that lowering the cost degrades the performance and increasing the performance increases the cost.

FIG. 37 is a diagram showing an example in which the multi-objective optimization problem is applied to engine optimization. When the multi-objective optimization problem is applied to engine fuel efficiency and torque optimization, the fuel efficiency and torque are two objective functions f ₁ and f ₂ . In this case, the values of the objective functions f ₁ and f ₂ are optimized by adjusting parameters such as the fuel injection amount and the ignition timing.

  The solution A has better fuel efficiency than the solution B, but the torque is inferior to the solution B. As described above, since the engine fuel efficiency and the engine torque have a trade-off relationship, there are a plurality of optimum solutions. The user can select a solution suitable for the purpose from a plurality of optimum solutions. For example, the solution A is selected for an engine used for a motorcycle suitable for sports driving, and the solution B is selected for an engine used for a motorcycle suitable for long touring.

  In general, the multi-objective optimization problem is defined as a problem of minimizing the values of M objective functions for N parameters within the range of the constraint condition of each parameter. When maximizing the value of the objective function, a negative sign is added to the objective function to convert it into a problem that minimizes the value of the objective function.

  Such a multi-objective optimization problem generally does not have a single optimal solution, but has an optimal solution set defined by a concept called a Pareto optimal solution. Here, the Pareto optimal solution is a solution in which the value of at least one other objective function must be altered in order to improve the value of a certain objective function, and is defined as follows: (For example, refer nonpatent literature 1).

[Definition 1] For two solutions x1, x2εF of p objective functions f _k (k = 1,..., P), f _k (x1) ≦ f _k (x2) (∀k = 1 ,..., P) ∧f _k (x1) <f _k (x2) (∃k = 1,..., P), x1 is said to dominate x2. Here, F is a set of solutions.

  [Definition 2] When a solution x0 dominates all other solutions xεF, x0 is an optimal solution.

  [Definition 3] When there is no solution xεF superior to a solution x0, x0 is a Pareto optimal solution (or non-inferior solution).

  Obtaining the Pareto optimal solution set results in obtaining an optimal solution set with respect to the objective function trade-off.

FIG. 38 is a diagram for explaining the Pareto optimal solution. FIG. 38 shows an example of _two objective functions f ₁ and f ₂ . The value f ₁ of the objective function f ₁ for solution a (a) the value f ₁ of the objective function f ₁ for solutions b (b) less than, the value f ₂ of the objective function f ₂ for Solution a (a) Is smaller than the value f ₂ (b) of the objective function f ₂ for the solution b. Therefore, the solution a is superior to the solution b.

  Similarly, the solution a dominates the solutions c and d. There is no solution superior to solution a. Similarly, there is no solution superior to the solutions e and f. Accordingly, the solutions a, e, and f are Pareto optimal solutions.

  The solution g is a weak Pareto optimal solution. The weak Pareto optimal solution is a Pareto solution that is not superior to the Pareto optimal solution only for a certain objective function. The weak Pareto optimal solution is not a rational solution and is a solution that does not need to be originally obtained.

  Many solutions for multi-objective optimization problems have been proposed. Recently, there has been a multiple objective evolutionary algorithm (MOEAs).

  The biggest feature of this method is that the Pareto optimal solution set is obtained at a time using the multi-point search of the evolutionary algorithm. The obtained Pareto optimal solution set is used for decision making to find a solution that matches the purpose from among them, or for obtaining knowledge from the shape of the Pareto optimal solution set (Pareto boundary).

  There have been many studies on applying genetic algorithms (GA) as multi-objective optimization problems as evolutionary algorithms. Genetic algorithms are computational methods that mimic the adaptive evolution of organisms. In a genetic algorithm, a solution candidate is called an individual. The objective function is called an adaptive function, and the value of the fitness function is called fitness.

  This genetic algorithm is based on the process of natural evolution (chromosome selection, crossover and mutation) as a hint. This is an algorithm proposed by Holland. The design variable is regarded as a gene, an initial design individual set is randomly generated, and the fitness of each individual is evaluated. Parents are selected so that individuals with better fitness are more likely to be selected as parents. And offspring are created by crossover (gene replacement) and mutation (random change of gene). Furthermore, generations are repeated through evaluation, selection, crossover, and mutation to search for an optimal solution.

  Specifically, the Fonseca et al. MOGA (Multiple Objective Genetic Algorithm: see, for example, Non-Patent Document 1), Deb et al. NSGA-II (Non-Dominated Sorting Genetic Algorithm-II, see, for example, Non-Patent Document 2), Zitzler SPEA2 (Strength Pareto Evolutionary Algorithm 2: see, for example, Non-Patent Document 3) has been proposed. In particular, NSGA-II and SPEA2 are known as excellent multi-objective evolutionary algorithms.

In order to optimize the fitness function with uncertainties, MFEGA (Memory-based Fitness Estimation Genetic Algorithm) for estimating the true fitness using the search history has been proposed by Sano, Kita et al. ( For example, refer nonpatent literature 4). Here, in MFEGA, a sample value of the fitness of an individual obtained in the past is stored as a search history, and the true fitness is estimated with reference to the search history. MFEGA has been reported to have an excellent search performance in comparison with a method of sampling the fitness of the same individual multiple times and a normal genetic algorithm regarding a problem with uncertainty.
CMfonseca, pJFlemimg: genetic algorithms for multiobjective optimization: formation, discussion and generalization, of the 5th international conference on genetic algorithms, pp.416-423 (1993) K. Deb, S. Agrawal, A. Pratab, and T. Meyarivan: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II, KanGAL report 20001, Indian Institute of Technology, Kanpur, India (20OO ) E.Zitzler, M. Laumanns, L. Thiele: SPEA2: Improving the Performance of the Strength Pareto Evolutionary A1gorithm, Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001) Sano, Kita: Optimization of uncertain function by genetic algorithm using search history, Electrology C, Vol. 122, No. 6, PP-1001-1008 (2002) K.Ikeda, H.Kita, and S.Kobayashi: Failuer of Pareto-Based MOEAs, Does Non-Dominated Really Mean Near to Optimal? Congress on Evolutionary Computation, pp.957-962 (2001) MDBerg, et.al .: Computational Geometry: Algorithms and Applications, Springer-Verlag (1997) Hiroshi Imai, Keiko Imai, Computational Geometry, Information Mathematics Course 12, Kyoritsu Shuppan (1994) E.Zitzler, K.Deb, L, Thiele: Comparison of Mu1tiobjective Evo1utionary Algorithms: Empirical Results, Evolutionary Computation 8 (2), pp.173-195 (2000) Y. Jin, M. Olhofer, B. Sendhoff: On Evolutionary Optimization with Approximate Fitness Functions, Proc. Of GECCO2000, pp. 786-792 (2000)

  However, when performing simulation- or experiment-based optimization with large computational costs using normal single-purpose genetic algorithms and multi-objective genetic algorithms, the number of evaluations of fitness estimates to obtain suitable Pareto optimal individuals Is very large and takes a lot of time. Therefore, various methods for reducing the number of evaluations have been proposed.

  For example, Non-Patent Document 9 has a single purpose of generating a large number of child individuals, estimating fitness of those child individuals using a neural network, and evaluating only child individuals with high fitness estimates in a real environment. An evolutionary computation method has been proposed.

  On the other hand, in a multi-purpose genetic algorithm that uses ranking for evaluation of fitness estimates, if the Pareto optimal individuals that are more than the number of individuals that can be evaluated in the real environment are included in the child individual, it should be evaluated in the real environment The problem is how to select the offspring. However, in such a case, an effective method for selecting a child individual has not been proposed.

  Therefore, the Pareto optimal individual cannot be efficiently obtained in a short time using the conventional multi-purpose genetic algorithm.

  An object of the present invention is to provide a multi-objective optimization device, a multi-objective optimization method, and a multi-objective optimization program capable of efficiently obtaining an appropriate Pareto optimal individual in a short time.

  (1) The multi-objective optimization apparatus according to the first aspect of the present invention gives a set of individual parameters to an optimization target and receives from the optimization target a set of fitness for a plurality of fitness functions corresponding to a plurality of purposes. A multi-objective optimization device that generates a storage unit that stores a set of individual parameters and a fitness set output from the optimization target as a storage individual, and generates a new individual as an individual candidate for evaluation. A set of parameters of the individual selected as the evaluation individual among the evaluation individual candidates is given to the optimization target and the storage unit, and the evaluation individual set is evaluated according to the multi-objective evolutionary algorithm based on the fitness of multiple sets And an evaluation unit generated by the calculation unit based on a plurality of sets of fitness corresponding to a plurality of storage individuals stored in the storage unit. An estimation unit for obtaining a set of true fitness estimates corresponding to each individual included in the union of storage candidates stored in the body candidate and the storage unit, and the calculation unit includes a plurality of fitness functions. Compare the superiority or inferiority of the estimated values corresponding to a plurality of individuals included in the union for each, and rank each of the plurality of individuals included in the union based on the comparison result of the superiority or inferiority for each of the plurality of fitness functions. A distribution index representing the degree of sparseness in the distribution of storage individuals of the highest rank for each evaluation individual candidate of the highest rank is calculated, and a predetermined number of evaluation individual candidates are evaluated for evaluation based on the calculated distribution index. To choose as.

  In the multi-objective optimization apparatus, a set of individual parameters and a set of fitness values output from the optimization target are stored in the storage unit as storage objects. A new individual is generated as an evaluation individual candidate by the calculation unit, and a set of parameters of the individual selected by the estimation unit as the evaluation individual among the generated evaluation individual candidates is given to the optimization target and the storage unit. Further, the evaluation individual set is evaluated by the arithmetic unit according to the multi-objective evolutionary algorithm based on a plurality of sets of fitness. Thereby, the Pareto optimal individual set is obtained.

  When selecting the individual for evaluation, each of the evaluation candidate candidates and the union of the individual for storage is included based on a plurality of fitness values corresponding to the plurality of storage individuals stored in the storage unit. A set of true fitness estimates corresponding to the individual is obtained by the estimation unit. Then, the arithmetic unit compares the superiority or inferiority of the estimated values corresponding to the plurality of individuals included in the union for each of the plurality of fitness functions, and the union for each of the plurality of fitness functions is based on the comparison result of the superiority or inferiority. A plurality of contained individuals are ranked. Next, a distribution index representing the degree of sparseness in the distribution of the storage individuals of the highest rank is calculated for each evaluation individual candidate of the highest rank, and a predetermined number of evaluation individual candidates are evaluated based on the calculated distribution index. Selected as an individual.

  In this way, a plurality of evaluation individual candidates are generated, and a predetermined number of evaluation individual candidates are selected as evaluation individuals from the plurality of evaluation individual candidates at the highest rank based on the distribution index. The individual is actually evaluated. Thereby, the time for evaluating unnecessary individual candidates for evaluation is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

  (2) The multi-objective optimization apparatus according to the second invention provides a set of individual parameters to the optimization target, and optimizes a set of fitness sample values for a plurality of fitness functions corresponding to a plurality of objectives. A multi-purpose optimization device received from a target, wherein a storage unit stores a set of individual parameters and a set of fitness sample values output from the optimization target as a storage individual, and a plurality of storage units stored in the storage unit Based on a first estimator that obtains a set of estimated values of true fitness corresponding to the target individual based on a plurality of sets of sample values corresponding to the individual for storage, and an estimated value obtained by the first estimator A new individual is generated as an evaluation individual candidate, and a set of parameters of the individual selected as the evaluation individual among the generated evaluation individual candidates is given to the optimization target and the storage unit, and is obtained by the estimation unit. The A computing unit for obtaining a Pareto optimal individual set by evaluating the evaluation individual set according to a multi-objective evolutionary algorithm based on several sets of estimated values, and a plurality of sets of samples corresponding to a plurality of storage individuals stored in the storage unit A second set of a true fitness estimate corresponding to each individual included in the union of the individual for evaluation generated by the calculation unit and the storage individual stored in the storage unit, based on the value; An estimator, and the arithmetic unit compares the superiority or inferiority of the estimated values corresponding to the plurality of individuals included in the union for each of the plurality of fitness functions, and compares the superiority or inferiority for each of the plurality of fitness functions. Based on the ranking, multiple individuals included in the union are ranked, and a distribution index representing the degree of sparseness in the distribution of individuals for storage at the highest rank is calculated and calculated for each individual candidate for evaluation at the highest rank. And selects as the evaluation individuals for evaluation individual candidates of a predetermined number based on the distribution index is.

  In the multi-objective optimization apparatus, a set of individual parameters and a set of fitness sample values output from the optimization target are stored in the storage unit as storage individuals. Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, a set of true fitness estimation values corresponding to the target individual is obtained by the first estimation unit. Based on the estimated value, a new individual is generated as an evaluation individual candidate by the calculation unit, and the parameter set of the individual selected by the second estimation unit as the evaluation individual among the generated evaluation individual candidates is optimized. Given to the subject and storage. In addition, the evaluation individual set is evaluated by the calculation unit according to the multi-objective evolution type algorithm based on the obtained plural sets of estimated values. Thereby, the Pareto optimal individual set is obtained.

  When selecting the individual for evaluation, each of those included in the union of the candidate individual for evaluation and the individual for storage based on a plurality of sets of sample values corresponding to the plurality of storage individuals stored in the storage unit A set of true fitness estimation values corresponding to the individual is obtained by the second estimation unit. Then, the arithmetic unit compares the superiority or inferiority of the estimated values corresponding to the plurality of individuals included in the union for each of the plurality of fitness functions, and the union for each of the plurality of fitness functions is based on the comparison result of the superiority or inferiority. A plurality of contained individuals are ranked. Next, a distribution index representing the degree of sparseness in the distribution of the storage individuals of the highest rank is calculated for each evaluation individual candidate of the highest rank, and a predetermined number of evaluation individual candidates are evaluated based on the calculated distribution index. Selected as an individual.

  In this way, a plurality of evaluation individual candidates are generated, and a predetermined number of evaluation individual candidates are selected as evaluation individuals from the plurality of evaluation individual candidates at the highest rank based on the distribution index. The individual is actually evaluated. Thereby, the time for evaluating unnecessary individual candidates for evaluation is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

(3) the first estimation unit, a plurality of storage individuals stored in the storage unit and h _l, a set of sample values corresponding to the target individuals x and F (x), from the target individual with the parameter space When a set of sample values corresponding to individuals separated by a distance d _l is F (h _l ), k ′ is a coefficient, l = 1,..., H, and n is a natural number,

  A set f ′ (x) of estimated values of true fitness corresponding to the target individual x may be calculated using the estimation formula represented by:

  In this case, it is possible to obtain an estimated value with a smaller error from the true fitness in consideration of the distance between the target individual and other storage individuals in the parameter space.

(4) a second estimation unit, a plurality of storage individuals stored in the storage unit and h _l, the sample values corresponding to the storage individual spaced distance d _l from the evaluation individual candidate on the parameter space a set _Is F (h _l ), k ′ is a coefficient, l = 1,..., H, and n is a natural number,

  A set f ′ (x) of true fitness estimation values corresponding to the individual candidate for evaluation x may be calculated using the estimation formula represented by:

  In this case, an estimated value with a smaller error from the true fitness can be obtained in consideration of the distance between the individual for evaluation and the individual for storage in the parameter space.

  (5) n may be 1. In this case, in the calculation of the estimated value, the influence of the storage individual far from the evaluation individual candidate in the parameter space is reduced. Thereby, an estimated value with a sufficiently small error from the true fitness can be obtained.

  (6) n may be 3. In this case, in the calculation of the estimated value, the influence of the storage individual far from the evaluation individual candidate on the parameter space is greatly reduced. Thereby, it is possible to obtain an estimated value with a sufficiently small error from the true fitness.

  (7) The calculation unit detects two storage individuals adjacent to each evaluation individual candidate within the highest rank in the fitness function space, and mathematically calculates between the two storage individuals for each fitness function. The distance is calculated, the sum of mathematical distances in a plurality of fitness functions for each evaluation individual candidate is calculated as the distribution index, and a predetermined number of evaluations are performed in descending order of the distribution index calculated from the plurality of evaluation individual candidates. An individual candidate for use may be selected as an individual for evaluation.

  In this case, it is possible to easily generate a new evaluation individual in a region where the storage individual is sparse within the highest rank in the fitness function space. Thereby, a highly diverse Pareto optimal individual can be easily obtained.

  (8) The computing unit may display the Pareto optimal individual based on the set of estimated values obtained by the first estimating unit.

  In this case, since the user can visually recognize the Pareto optimal individual, various decision making can be easily performed.

  (9) The calculation unit may evaluate individuals in the evaluation individual set using a genetic algorithm as a multi-purpose evolutionary algorithm.

  In this case, an optimal Pareto optimal individual can be easily obtained by performing generation change based on a genetic algorithm.

  (10) The optimization target includes an evaluation system for evaluating a plurality of performances of the device, the set of parameters includes a set of control parameters for the evaluation system, and the plurality of fitness functions are included in the evaluation system. It is a plurality of performances obtained by evaluation, and the fitness set may be a plurality of performance values.

  In this case, a set of control parameters is given to the evaluation system. The evaluation system evaluates the performance of the device based on the set of control parameters, and outputs a set of sample values corresponding to a plurality of performances. According to this multi-objective optimization apparatus, an appropriate set of control parameter sets can be efficiently obtained in a short time as a Pareto optimal individual.

  (11) The device may be an engine. In this case, a set of engine control parameters is given to the evaluation system. The evaluation system evaluates engine performance based on a set of engine control parameters, and outputs a set of sample values corresponding to a plurality of performances. According to this multi-objective optimization apparatus, an appropriate set of engine control parameter sets can be efficiently obtained in a short time as a Pareto optimal individual.

  (12) The device may be a motor. In this case, a set of motor control parameters is given to the evaluation system. The evaluation system evaluates the performance of the motor based on the set of motor control parameters, and outputs a set of sample values corresponding to a plurality of performances. According to this multi-objective optimization apparatus, an appropriate set of motor control parameter sets can be efficiently obtained in a short time as a Pareto optimal individual.

  (13) The evaluation system may be a device evaluation device that controls a device based on a set of parameters and outputs a plurality of performance values generated by the operation of the device as sample values.

  In this case, a set of control parameters is given to the device evaluation apparatus. The device evaluation apparatus evaluates the performance of the device based on the control parameter set, and outputs a set of sample values corresponding to a plurality of performances. According to this multi-objective optimization apparatus, an appropriate set of control parameter sets can be efficiently obtained in a short time as a Pareto optimal individual.

  (14) The evaluation system may be a device simulator that evaluates a plurality of performances by simulating the operation of the device based on a set of parameters and outputs the evaluated values of the plurality of performances as a set of sample values. Good.

  In this case, a set of control parameters is given to the equipment simulator. A plurality of performances are evaluated by simulating the operation of the device based on the control parameter set by the device simulator, and a set of sample values corresponding to the evaluated plurality of performances is output. According to this multi-objective optimization apparatus, an appropriate set of control parameter sets can be efficiently obtained in a short time as a Pareto optimal individual.

  (15) In the multi-objective optimization method according to the third invention, a set of individual parameters is given to the optimization target, and the fitness of a plurality of fitness functions corresponding to the plurality of objectives output from the optimization target is determined. A multi-objective optimization method for optimizing parameters based on a set of sample values, and storing a set of individual parameters and a set of fitness sample values output from an optimization target as storage individuals in a storage unit Determining a set of true fitness estimates corresponding to the individual of interest based on a plurality of sets of sample values corresponding to a plurality of storage objects stored in the storage unit; and Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, and generating a new individual as an evaluation individual candidate based on Obtaining a set of true fitness estimates corresponding to each individual included in the union of stored individuals stored in the memory, and a plurality of individuals included in the union for each of a plurality of fitness functions Compares the superiority or inferiority of the estimated values corresponding to, ranks the multiple individuals included in the union based on the superiority / inferiority comparison results for each of the fitness functions, and evaluates each individual candidate for evaluation with the highest rank Calculating a distribution index representing a degree of sparseness in the distribution of the highest-ranking storage individuals, selecting a predetermined number of evaluation individual candidates as evaluation individuals based on the calculated distribution index, and the selected evaluation By providing a set of individual parameters for optimization to the optimization target and storage unit, and evaluating the individual set for evaluation according to the multi-objective evolutionary algorithm based on the obtained multiple sets of estimated values It is intended to include determining a rate optimal population of individuals.

  In the multi-objective optimization method, a set of individual parameters and a set of fitness sample values output from the optimization target are stored in the storage unit as storage individuals. Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, a set of estimated values of true fitness corresponding to the target individual is obtained.

  Next, a new individual is generated as an evaluation individual candidate based on the estimated value. Further, based on a plurality of sets of sample values corresponding to a plurality of storage individuals, a set of estimated values of true fitness corresponding to each individual included in the union of the individual for evaluation and the storage individual is obtained. . Then, for each of the plurality of fitness functions, the superiority or inferiority of the estimated values corresponding to the plurality of individuals included in the union is compared, and the plurality of fitness functions are included in the union based on the comparison result of the superiority or inferiority. The individuals are ranked. Next, a distribution index representing the degree of sparseness in the distribution of the storage individuals of the highest rank is calculated for each evaluation individual candidate of the highest rank, and a predetermined number of evaluation individual candidates are evaluated based on the calculated distribution index. Selected as an individual.

  Further, a set of parameters of the individual selected as the individual for evaluation is given to the optimization target and the storage unit. Further, the evaluation individual set is evaluated according to the multi-objective evolutionary algorithm based on the obtained plural sets of estimated values. Thereby, the Pareto optimal individual set is obtained.

  In this way, a plurality of evaluation individual candidates are generated, and a predetermined number of evaluation individual candidates are selected as evaluation individuals from the plurality of evaluation individual candidates at the highest rank based on the distribution index. The individual is actually evaluated. Thereby, the time for evaluating unnecessary individual candidates for evaluation is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

  (16) A multi-objective optimization program according to a fourth aspect of the present invention provides a set of individual parameters to an optimization target, and sets of fitness sample values for a plurality of corresponding fitness functions output from the optimization target Is a multi-objective optimization program that can be executed by a computer that optimizes parameters based on the parameters, and stores a set of individual parameters and a set of fitness sample values output from the optimization target as storage objects in the storage unit Processing for obtaining a set of true fitness estimates corresponding to the individual of interest based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, and the obtained estimated value Based on the process for generating new individuals as evaluation individual candidates and the generated evaluation based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit Included in the union for each of a plurality of fitness functions is a process for obtaining a set of true fitness estimates corresponding to each individual included in the union of individuals for storage and storage individuals stored in the storage unit Compares the superiority or inferiority of estimated values corresponding to multiple individuals, ranks multiple individuals included in the union based on the result of superiority or inferiority for each of multiple fitness functions, and evaluates each of the highest ranks A process of selecting a distribution index that represents the degree of sparseness in the distribution of storage individuals of the highest rank for individual candidates, and selecting a predetermined number of evaluation individual candidates as evaluation individuals based on the calculated distribution index and selection The set of parameters of the evaluated individual for evaluation is given to the optimization object and the storage unit, and the evaluation individual set is evaluated according to the multi-objective evolutionary algorithm based on the obtained multiple sets of estimated values. A process of obtaining the Pareto-optimal population of individuals by, those to be executed by a computer.

  In the multi-objective optimization program, a set of individual parameters and a set of fitness sample values output from the optimization target are stored in the storage unit as storage individuals. Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, a set of estimated values of true fitness corresponding to the target individual is obtained.

  Next, a new individual is generated as an evaluation individual candidate based on the estimated value. Further, based on a plurality of sets of sample values corresponding to a plurality of storage individuals, a set of estimated values of true fitness corresponding to each individual included in the union of the individual for evaluation and the storage individual is obtained. . Then, for each of the plurality of fitness functions, the superiority or inferiority of the estimated values corresponding to the plurality of individuals included in the union is compared, and the plurality of fitness functions are included in the union based on the comparison result of the superiority or inferiority. The individuals are ranked. Next, a distribution index representing the degree of sparseness in the distribution of the storage individuals of the highest rank is calculated for each evaluation individual candidate of the highest rank, and a predetermined number of evaluation individual candidates are evaluated based on the calculated distribution index. Selected as an individual.

  Further, a set of parameters of the individual selected as the individual for evaluation is given to the optimization target and the storage unit. Further, the evaluation individual set is evaluated according to the multi-objective evolutionary algorithm based on the obtained plural sets of estimated values. Thereby, the Pareto optimal individual set is obtained.

  In this way, a plurality of evaluation individual candidates are generated, and a predetermined number of evaluation individual candidates are selected as evaluation individuals from the plurality of evaluation individual candidates at the highest rank based on the distribution index. The individual is actually evaluated. Thereby, the time for evaluating unnecessary individual candidates for evaluation is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

  According to the present invention, a plurality of evaluation individual candidates are generated, and a predetermined number of evaluation individual candidates are selected as the evaluation individual based on the distribution index from the plurality of evaluation individual candidates at the highest rank. The evaluation individual is actually evaluated. Thereby, the time for evaluating unnecessary individual candidates for evaluation is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

(1) First Embodiment First, a multi-objective optimization apparatus according to a first embodiment of the present invention will be described with reference to FIG.

(A) Functional Configuration of Multi-Objective Optimization Device FIG. 1 is a block diagram showing a functional configuration of the multi-purpose optimization device according to the first embodiment of the present invention.

  The multi-objective optimization apparatus 1 in FIG. 1 calculates a Pareto optimal individual set of a multi-objective optimization problem using a multi-objective genetic algorithm (GA) as a multi-objective evolutionary algorithm. This multi-objective optimization apparatus 1 is connected to an optimization target 6.

  The optimization target 6 is an evaluation system that evaluates the performance of the device. The evaluation system is an evaluation device for evaluating an actual system or a simulator including a probability element. The actual system is, for example, an engine or a motor, and the evaluation device is, for example, an engine evaluation device or a motor evaluation device. The simulator is, for example, an engine simulator or a motor simulator. In the present embodiment, the optimization target 6 is an engine evaluation device.

  The multi-objective optimization apparatus 1 includes a multi-objective evolution type algorithm unit 2, a fitness estimation unit 3, an output interface 4 and an input interface 5. The fitness level estimation unit 3 includes fitness level estimation modules 30 a and 30 b and a search history storage device 31.

  The fitness estimation modules 30a and 30b of the multi-objective evolution type algorithm unit 2 and the fitness estimation unit 3 are realized by a CPU 101 (FIG. 2) described later executing a multi-objective optimization program. The search history storage device 31 is configured by an external storage device 106 (FIG. 2) described later.

The user 10 sets a plurality of fitness functions (objective functions) in the multipurpose evolution type algorithm unit 2. In the present embodiment, the plurality of fitness functions include fuel consumption, torque, and concentrations of components such as CO (carbon monoxide), HC (hydrocarbon), and NO _x (nitrogen oxide) contained in engine exhaust gas. Etc. are set.

Here, the trade-off relationship includes torque and fuel consumption, torque and CO concentration, torque and HC concentration, fuel consumption and NO _x concentration, CO concentration and NO _x concentration, HC concentration and NO _x concentration, and the like.

  An individual of the multi-objective genetic algorithm is a candidate for a solution of the multi-objective optimization problem, and has a plurality of parameter sets and a plurality of fitness values. A parameter is an adjustable value and is called a gene in the genetic algorithm. The parameters include fuel injection amount, fuel injection timing, ignition timing, throttle opening, and the like. The fitness is a value of the fitness function. Hereinafter, an individual of a multipurpose genetic algorithm is simply referred to as an individual.

  The multi-objective evolution type algorithm unit 2 receives the estimated value of the true fitness calculated by the fitness estimation modules 30a and 30b, which will be described later, and gives a set of individual parameters to the search history storage device 31 of the fitness estimation unit 3. At the same time, it is given to the optimization target 6 through the output interface 4. Hereinafter, the true fitness estimate is simply referred to as fitness estimate or estimate.

  The optimization target 6 outputs a set of fitness sample values based on the set of individual parameters given from the multipurpose optimization apparatus 1. Each sample value output from the optimization target 6 includes a true fitness and a noise component, as will be described later. Details of the sample value will be described later.

  A set of sample values output from the optimization target 6 is input to the search history storage device 31 of the fitness estimation unit 3 via the input interface 5. The search history storage device 31 stores a set of individual parameters and a set of sample values as a search history. Hereinafter, each set of individual parameters and sample values included in the search history is referred to as history data.

  The fitness estimation modules 30 a and 30 b calculate fitness value sets based on search history history data stored in the search history storage device 31, and provide the estimated value sets to the multi-objective evolution algorithm unit 2. . In particular, the fitness estimation module 30b is used to calculate an estimated fitness value of a child individual candidate when a child individual to be described later is selected. Details will be described later. The fitness estimation modules 30a and 30b may be configured by one fitness estimation module.

  The multi-objective evolution type algorithm unit 2 generates a plurality of individuals according to a genetic algorithm based on a plurality of sets of estimated values, performs a multipoint search, and evaluates the fitness function with the Pareto optimality, whereby the Pareto optimal individual Find a set at the same time. Further, the multi-objective evolution type algorithm unit 2 presents the obtained Pareto optimal individual set to the user 10.

  As described above, the multi-objective evolution type algorithm unit 2 and the fitness level estimation unit 3 optimize the parameters of the individual by working together.

  Detailed operations of the multi-objective evolution algorithm unit 2 and the fitness estimation unit 3 will be described later.

(B) Hardware configuration of multipurpose optimization apparatus FIG. 2 is a block diagram showing a hardware configuration of the multipurpose optimization apparatus 1 of FIG.

  The multi-objective optimization apparatus 1 includes a CPU (Central Processing Unit) 101, a ROM (Read Only Memory) 102, a RAM (Random Access Memory) 103, an input device 104, a display device 105, an external storage device 106, and a recording medium driving device 107. And an input / output interface 108.

  The input device 104 includes a keyboard, a mouse, and the like, and is used for inputting various commands and various data. The ROM 102 stores a system program. The recording medium driving device 107 includes a CD (compact disk) drive, a DVD (digital versatile disk) drive, a flexible disk drive, and the like, and reads / writes data from / to a recording medium 109 such as a CD, DVD, or flexible disk.

  A multipurpose optimization program is recorded on the recording medium 109. The external storage device 106 includes a hard disk device or the like, and stores a multipurpose optimization program and various data read from the recording medium 109 via the recording medium driving device 107. The CPU 101 executes the multipurpose optimization program stored in the external storage device 106 on the RAM 103.

  The display device 105 includes a liquid crystal display panel, a CRT (cathode ray tube), and the like, and displays various images such as a Pareto optimal individual set. The input / output interface 108 includes the output interface 4 and the input interface 5 of FIG. The optimization target 6 is connected to the input / output interface 108 by wireless communication or wired communication. The input / output interface 108 transfers a set of sample values output from the optimization target 6 to the external storage device 106 and provides the optimization target 6 with a set of individual parameters generated by the multi-objective optimization program.

  As the recording medium 109 for recording the multipurpose optimization program, various recording media such as a semiconductor memory such as a ROM and a hard disk can be used. Alternatively, the multipurpose optimization program may be downloaded to the external storage device 106 via a communication medium such as a communication line and executed on the RAM 103.

  Here, as long as the recording medium 109 is a computer-readable recording medium, the recording medium 109 includes an electronic reading method, a magnetic reading method, an optical reading method, or any other reading method. For example, in addition to the above-mentioned CD, DVD and flexible disk, optical reading type recording medium such as CDV (compact disk video), semiconductor recording medium such as RAM and ROM, magnetic recording type recording medium such as hard disk, MO (magneto-optical) A magnetic storage type / optical reading type recording medium such as a disk) can be used.

(C) Configuration of Optimization Target FIG. 3 is a block diagram showing an example of the configuration of the optimization target 6. The optimization target 6 in FIG. 3 is an engine evaluation device.

  The optimization target 6 includes an engine 61, an ECU (engine control unit) 62, an exhaust gas analyzer 63, a controller 64, a throttle unit 65, and a dynamo 66.

  The ECU 62 receives a set of parameters from the multipurpose optimization apparatus 1 by serial communication. In this example, the set of parameters is an ignition timing and a fuel injection timing. The ECU 62 controls the ignition timing and fuel injection timing of the engine 61 based on the parameter set. Engine information such as the rotational speed and the air-fuel ratio is given from the engine 61 to the controller 64.

  The controller 64 controls the throttle unit 65 and the dynamo 66 based on the engine information. The throttle unit 65 controls the output torque of the engine 61 by adjusting the intake air amount of the engine 61. The dynamo 66 controls the load torque.

The exhaust gas analyzer 63 analyzes the components in the exhaust gas from the engine 61 and outputs the HC concentration and the NO _x concentration as a set of sample values to the multipurpose optimization apparatus 1 by serial communication.

FIG. 4 is a graph showing the relationship between the HC concentration, NO _x concentration, CO concentration and air-fuel ratio.

If the fuel burns completely, the exhaust gas contains carbon dioxide and water. However, when the operating state changes, the combustion state also changes, and the exhaust gas contains CO, HC, and NO _x .

As shown in FIG. 4, when the air-fuel ratio is small, the HC concentration and the NO _x concentration are lowered. Concentration of NO _x is becomes maximum when the air-fuel ratio is slightly smaller than the stoichiometric air-fuel ratio (14.7), it decreases in the other region. In the vicinity of the theoretical air-fuel ratio, the HC concentration and the NO _x concentration have a trade-off relationship, and the CO concentration and the NO _x concentration have a trade-off relationship.

The optimization target 6 in FIG. 3 receives the ignition timing information indicating the ignition timing and the fuel injection timing information indicating the fuel injection timing as a set of individual parameters from the multi-purpose optimization apparatus 1, and receives the HC concentration and NO as a set of sample values. Output _x density.

(D) Overall Processing of Multipurpose Optimization Device FIGS. 5 and 6 are flowcharts showing the overall processing of the multipurpose optimization device 1 of FIG.

  As shown in FIG. 5, when the optimization process is started, the multi-objective evolution type algorithm unit 2 generates a parent individual set P as an initial individual set within a range determined by each parameter at random. The set P is initialized, and a set of parameters of each individual of the generated parent individual set P is sequentially given to the optimization target 6 (step S1). Thereby, a set of fitness sample values is sequentially output from the optimization target 6.

  When there is a Pareto optimal individual known as prior knowledge, the Pareto optimal individual may be used as part of the initial individual set. Thereby, the convergence of the search for the Pareto optimal individual is improved.

  The search history storage device 31 of the fitness estimator 3 acquires a set of sample values corresponding to each individual of the parent individual set P from the optimization target 6, and sets a set of parameters and a sample value of the parent individual set P. The search history is stored (step S2).

  Next, the fitness estimation module 30a of the fitness estimator 3 estimates fitness for each individual in the parent individual set P based on a set of sample values corresponding to a plurality of individuals stored in the search history storage device 31. A set of values is calculated (step S3). A method for calculating the fitness value will be described later.

  Next, the multi-objective evolution type algorithm unit 2 divides the parent individual set P into individual sets for each rank by superiority comparison and Pareto ranking based on the fitness value set (step S4). The Pareto ranking will be described later.

  Next, the multi-purpose evolution type algorithm unit 2 performs the congestion degree sort on the individual sets of each rank of the parent individual set P (step S5). Thereby, the individuals of each rank are arranged in descending order of the degree of congestion (congestion distance). The congestion degree sorting will be described later. Then, a predetermined number of individuals having a higher degree of congestion at a higher rank are selected, and other individuals are deleted.

  Furthermore, the multi-purpose evolution type algorithm unit 2 and the fitness estimation module 30b select one specific parent individual from the individual set of the highest rank (rank 1) of the parent individual set P, and randomly select 2 from the parent individual set P. One individual is selected, a total of three parent individuals are selected, and a child individual set C is generated by performing a crossover operation on the three parent individuals (step S6a). In this case, a large number of child individual candidates are generated, and a predetermined number of child individuals are selected from the child individual candidates by a method described later. Details of the generation process of the child individual set C will be described later.

  The multi-purpose evolution type algorithm unit 2 sequentially gives a set of parameters of each individual of the generated child individual set C to the optimization target 6 (step S6b). Thereby, a set of fitness sample values is sequentially output from the optimization target 6.

  Here, the crossover operation means generating a new individual by multiplying the genes of the individual. A method for selecting a specific parent individual will be described later.

  The search history storage device 31 of the fitness estimation unit 3 acquires a set of fitness sample values corresponding to each individual of the child individual set C output from the optimization target 6, and sets a parameter corresponding to each individual. The set of sample values is stored as a search history (step S7).

  Next, the multipurpose evolution type algorithm unit 2 generates an individual set F from the child individual set C and the parent individual set P (step S8).

  The fitness estimation module 30a of the fitness estimator 3 calculates a set of fitness estimation values corresponding to each individual in the population F based on a plurality of sample values stored in the search history storage device 31 ( Step S9).

  The multi-objective evolution type algorithm unit 2 divides the individual set F into individual sets for each rank by superiority or inferiority comparison and Pareto ranking based on a set of fitness estimates, and overlaps with individuals of the parent individual set P in the child individual set C The lowest rank is assigned to the individual (step S10).

  Next, the multi-purpose evolution type algorithm unit 2 generates a new parent individual set P by performing congestion degree sorting on the individual sets of each rank of the individual set F (step S11). Thereby, the individuals of each rank are arranged in descending order of the degree of congestion (congestion distance). The congestion degree sorting will be described later. Then, a predetermined number of individuals having a higher degree of congestion at a higher rank are selected, and other individuals are deleted.

  Thereafter, the multipurpose evolutionary algorithm unit 2 determines whether or not the number of generations has reached a predetermined end condition (step S12).

  Here, the generation includes a selection step for selecting a parent individual from an individual set, a crossover step for generating a new child individual by a crossover operation, and a generation change step for exchanging the parent individual and the child individual. If it is determined that the number of generations has not reached the predetermined end condition, the process proceeds to step S6a. When it is determined that the number of generations has reached a predetermined end condition, the multi-objective evolution algorithm unit 2 presents the parent individual set P generated in step S11 to the user 10 as a Pareto optimal individual set, and performs processing. finish.

(E) Specific Example of Each Process of Multipurpose Optimization Device FIGS. 7 to 12 are schematic diagrams illustrating specific examples of each process of the multipurpose optimization device 1.

7 to 12 show examples of two parameters x ₁ and x ₂ and two fitness functions f ₁ and f ₂ . In the case of the optimization target 6 in FIG. 3, the parameters x ₁ and x ₂ are the ignition timing and the fuel injection timing, and the fitness functions f ₁ and f ₂ are the HC concentration and the NO _x concentration.

(E-1) Initialization of parent individual set FIG. 7 is a schematic diagram showing a parent individual set generated by initialization, (a) shows a parent individual set in the fitness function space, and (b) shows parameters. Indicates the parent individual set in the space. In initialization, as shown in FIG. 7, a plurality of individuals are randomly generated in the fitness function space and the parameter space.

(E-2) Individual Evaluation Method In the multi-objective optimization problem, since individuals have fitness values corresponding to a plurality of fitness functions, it is not possible to compare the superiority or inferiority of individuals with simple values. In the present embodiment, an individual is evaluated using superiority / inferiority comparison, Pareto ranking, and congestion degree sorting described below.

(E-2-1) Superiority comparison In FIG. 5, the superiority comparison in step S4 of FIG. 5 and step S10 of FIG. 6 is demonstrated. For this superiority / inferiority comparison, the following α-domination strategy is used. Details of the α superiority strategy are described in Non-Patent Document 5, for example.

  FIG. 8 is a schematic diagram for explaining the α superiority strategy. Here, generally, α superiority is defined as follows.

G _k (x1, x2) represented by the following equation (8) is obtained for two solutions x1, x2∈F of a certain number of p objective functions f _k (k = 1,..., P). The solution x1 is α superior to the solution x2.

g _k (x1, x2) ≦ 0 (∀k = 1,..., p) ∧g _k (x1, x2) <0 (∃k = 1,..., p)

In the above equation, f _k (x1) and f _j (x1) are the values of the objective functions f _k and f _j corresponding to the solution x1, respectively, and f _k (x2) and f _j (x2) are the solutions x2, respectively. The values of the corresponding objective functions f _k and f _j . In the multi-objective genetic algorithm, the solutions x1 and x2 correspond to individuals, and the objective functions f _k and f _j correspond to fitness functions.

Here, attention is paid to the individual I3 in FIG. According to a general superiority comparison, a region where an individual I3 in a straight line L12 extending parallel from the line L11 and the individual I3 extending parallel to fitness functions f ₁ from the individual I3 in fitness function f ₂ is superior to other individuals Determined. That is, the individual I3 dominates the other individuals I6, I7, and I8 in the region above the straight line L11 and to the right of the straight line L12. Individuals I2 and I4 are not dominated by individual I3.

Individuals I2 is with respect to fitness functions f ₁ is slightly better than the two individual I3, are quite inferior individuals I3 respect fitness function f _2. Individuals I4 is with respect to fitness function f ₂ are slightly better than the individual I3, are quite inferior individuals I3 respect fitness function f _1. When the fitness of such individuals I2 and I4 has uncertainty (for example, noise), the individuals I2 and I4 may be dominated by the individual I3.

On the other hand, according to the α superiority strategy, the straight line L1 inclined so as to approach the axis of the fitness function f ₁ from the individual I3 and the straight line L2 inclined so as to approach the axis of the fitness function f ₂ from the individual I3. A region where the individual I3 is superior to other individuals is determined. That is, the individual I3 dominates the individuals I2, I4, I6, I7, and I8 in the region above the straight line L1 and to the right of the straight line L2. According to the α superiority / inferiority strategy, the individuals I2 and I4 are excluded from the Pareto optimal individuals.

  In the present embodiment, individual superiority or inferiority comparison is performed based on a weighted linear sum of a plurality of estimated values by an α superiority strategy. According to the α superiority strategy, if one fitness level of a certain individual gets worse by 1, the other fitness level becomes α worse. That is, in the superiority / inferiority comparison, superiority or inferiority of one fitness affects the superiority or inferiority of other fitness. As a result, it is possible to obtain a rational solution in consideration of the relationship between a plurality of fitness levels as follows.

  The weak Pareto optimal individual is a solution in which at least one of a plurality of fitnesses is not superior to another individual (that is, equal to a Pareto optimal solution having at least one fitness). Such weak Pareto optimal individuals have optimal solutions for certain fitness functions, but the remaining fitness functions are inferior to Pareto optimal individuals. Therefore, the weak Pareto optimal individual is not a reasonable solution, and is a solution that does not need to be obtained originally. Therefore, by introducing an α superiority strategy, weak Pareto optimal individuals can be deceived.

  Further, when the fitness is accompanied by uncertainty, a phenomenon occurs in which the weak Pareto optimal individual becomes a Pareto optimal individual due to the uncertainty. If a weak Pareto optimal individual is determined to be a Pareto optimal individual due to uncertainty, it will remain in the individual set without being deceived indefinitely, causing the Pareto optimal individual search to stagnate. Therefore, by introducing an α superiority strategy, it is possible to deceive such weak Pareto optimal individuals determined as Pareto optimal individuals.

  FIG. 9 is a schematic diagram for explaining individual superiority / inferiority comparison by the α superiority / inferiority strategy.

  In FIG. 9, the individual I3 dominates the individuals I2, I4, I5, I6, and I7, the individual I6 dominates the individual I8, and the individual I7 dominates the individual I8. There is no individual superior to individuals I1, I3, and I5. Therefore, the individuals I1, I3, and I5 are Pareto optimal individuals.

(E-2-2) Pareto Ranking Next, the Pareto ranking in step S4 in FIG. 5 and step S10 in FIG. 6 will be described. FIG. 10 is a diagram for explaining the Pareto ranking. In the Pareto ranking, a Pareto optimal individual set is obtained based on the ranking of each individual.

The rank r (x _i ) of the individual x _i that is superior to the p _i individuals is given by the following equation.

r (x _i ) = 1 + _pi
Here, rank 1 is the highest rank, and ranks of higher numerical values are lower ranks as the numerical values increase.

  In FIG. 10, individuals I1, I3, and I5 are not dominated by other individuals. Therefore, the rank of the individuals I1, I3, and I5 is 1. Individuals I2 and I4 are superior to one individual I3. Therefore, the ranks of the individuals I2 and I4 are 2. Similarly, the rank of the individual I6 is 6, the rank of the individual I7 is 5, and the rank of the individual I8 is 8.

(E-2-3) Congestion degree sort Next, the congestion degree sort in step S5 of FIG. 5 and step S11 of FIG. 6 will be described. FIG. 11 is a schematic diagram for explaining the congestion degree sorting.

  In the degree of congestion sort, for each target individual of the same rank, a rectangle whose diagonal is the line connecting two adjacent individuals is assumed, and the degree of congestion (congestion distance) is the sum of the lengths of the vertical and horizontal sides of the rectangle. Represents. The smaller the value of the degree of congestion, the more focused the individual is in the crowded area. Individuals at both ends of the same rank are given maximum congestion.

  In FIG. 11, the degree of congestion of the individual I3 is represented by the sum of the vertical and horizontal sides of the rectangle s1 formed by the adjacent individuals I1 and I5. The degree of congestion of the individual I1 is represented by the sum of the vertical and horizontal sides of the rectangle s2 created by the adjacent individuals I9 and I3. The congestion degree of the individual I5 is represented by the sum of the vertical and horizontal sides of the rectangle s3 formed by the adjacent individuals I3 and I10.

  FIG. 12 is a flowchart showing the congestion degree sorting process by the multipurpose evolutionary algorithm unit 2.

  First, the multipurpose evolutionary algorithm unit 2 sorts the individual set for each fitness function, and examines two individuals adjacent to each target individual within the same rank for each fitness function (step S31).

  Next, the multi-objective evolution type algorithm unit 2 calculates a mathematical distance between two individuals adjacent to each target individual for each fitness function, and sums the mathematical distances in a plurality of fitness functions for each target individual. Is calculated as the degree of congestion (step S32). Here, the Euclidean distance is used as the mathematical distance.

  Thereafter, the multi-purpose evolutionary algorithm unit 2 sorts the individuals in the individual set of each rank in descending order of the value of the degree of congestion (step S33).

(E-3) Calculation of Estimated Value Based on Search History Next, calculation of the estimated value in step S3 in FIG. 5 and step S9 in FIG. 6 will be described.

  FIG. 13 is a schematic diagram for explaining calculation of an estimated value by the fitness estimation module 30a of the fitness estimation unit 3.

In the search history storage device 31 of FIG. 1, a set of individual parameters given from the multi-objective evolution type algorithm unit 2 and a set of fitness sample values output from the optimization target 6 are sequentially stored as a search history HS. . In FIG. 13, a set of parameters x ₁ and x _{2 and} a set of sample values F ₁ and F ₂ are stored as a search history HS for each individual.

  The fitness estimation module 30a calculates the true fitness corresponding to each individual as an estimated value based on the search history HS. A set of parameters and a set of estimated values corresponding to each individual are stored in the search history storage device 31 of FIG.

As shown in FIG. 13, the search history storage device 31 stores a set of parameters x ₁ and x _{2 and} a set of estimated values f ₁ ′ and f ₂ ′ as estimation results E for each individual.

  Further, the fitness estimation module 30a can display the fitness function space and the Pareto optimal individual set on the parameter space on the screen of the display device 105 of FIG. 2 based on the parameter set and the set of estimated values of each individual. it can.

In FIG. 13, the Pareto optimal individual set is displayed on the fitness function space including the fitness functions f ₁ and f ₂ and on the parameter space including the parameters x ₁ and x ₂ . A boundary formed by the Pareto optimal population is called a Pareto boundary.

  A method for estimating the fitness of an individual using the search history HS stored in the search history storage device 31 is called a memory-based fitness estimated method (MFEM) (non-patent document). 5).

  When calculating the estimated value of the target individual, the target individual and the individual of the search history HS are generally different search points. In addition, in order to assume an uncertain environment, even if the same parameter set is given to the optimization target 6, a set of different sample values is output. Therefore, in order to calculate the set of estimated values of the individual of interest from the set of sample values of the search history HS, it is necessary to make some assumption on the nature of the fitness function. In MFEM, an uncertain environment is modeled on the assumption that the fitness function varies randomly according to the mathematical distance from the target individual.

  Let x be the target individual, and let f (x) be the true fitness of the target individual x. Consider the fitness f (h) of an individual h that is a distance d away from the target individual x in the parameter space. The expected value of the fitness f (h) is f (x), and a model that follows a normal distribution in which the variance of the fitness f (h) increases in proportion to the distance d is expressed by the following equation (1).

f (h) to N (f (x), kd) (1)
In the above equation (1), k is a positive constant that determines the weight based on distance, and N (f (x), kd) is a probability density function of a normal distribution with an average of f (x) and a variance of kd. Represents.

Here, it is assumed that noise δ according to a normal distribution having an average of 0 and a variance σ _E ² and independent of the position of the individual is added to the true fitness f (x). In this case, the sample value F (x) corresponding to the individual x is defined as follows:

F (x) = f (x) + δ (2)
FIG. 14 is a schematic diagram showing sample values with noise δ according to a normal distribution. Here, the sample value F (x) is a set of the sample value F ₁ (x) for the fitness function f ₁ and the sample value F ₂ (x) for the fitness function f ₂ , and the true fitness f ( x) is the set of true fitness f ₂ (x) of the true fitness f ₁ (x) and fitness function f ₂ for fitness functions f _1. Also, the noise [delta] is the noise [delta] ₂ of the set of the noise [delta] ₁ and a fitness function f ₂ for fitness functions f _1. Noise δ _i (i = 1, 2) is expressed by the following equation.

δ _{i to} N (0, σ _Ei ² ) (i = 1, 2)
In the above equation, N (0, σ _Ei ² ) represents a probability density function of a normal distribution with mean 0 and variance σ _E ² .

  The fitness estimating unit 3 obtains a Pareto optimal individual set that minimizes the expected value of the sample value F (x). At this time, the sample value F (h) corresponding to the individual h is modeled as the following equations (3.1) and (3.2).

F (h) to N (f (x), kd + σ _E ² ) (3.1)
d = | h−x | (3.2)
In the above equation (3.1), N (f (x), kd + σ _E ² ) represents a probability density function of a normal distribution having an average of f (x) and a variance of kd + σ _E ² .

  FIG. 15 is a schematic diagram showing a model of an uncertain fitness function. In this model, it is assumed that the sample value F (h) changes greatly and irregularly as the distance from the target individual x increases.

  Based on this model, an estimated value of the true fitness f (x) is calculated by the maximum likelihood method using the search history HS.

Individuals stored in the search history _{HS h l (l = 1,} ..., H), the distance d _{l (l} = 1 from the sample value F (h _l) and target individuals x individuals h _l to individuals h _l, ... , H), the probability of obtaining sample values F (h ₁ ),..., F (h _H ) can be expressed by the following equation.

Here, p (F (h _l ), d _l ) is a probability density function representing the probability that the sample value F (h _l ) is obtained, and can be represented by the following equation.

Here, k ′ = k / σ _E ² . In the present embodiment, the constant k ′ is obtained by a preliminary experiment. Non-Patent Document 4 proposes a method for estimating a constant k ′ during a search. The constant k ′ may be obtained by the proposed method.

The above equations (4) and (5) are considered as the likelihood of the true fitness f (x), and the maximum likelihood method is used. Thereby, the estimated value f ′ (x) of the true fitness f (x) can be expressed by a weighted average expression weighted by a function including the distance d _l as shown in the following expression (6). .

  FIG. 16 is a flowchart showing an estimated value calculation process by the fitness estimation module 30a of the fitness estimation unit 3.

  First, the fitness estimation module 30a confirms that the parent individual set P is initialized in the multi-objective evolution type algorithm unit 2 (step S41). Next, the fitness estimation module 30a clears all the search histories HS in the search history storage device 31 (step S42).

  Thereafter, the fitness estimation module 30a stores the set of sample values output from the optimization target 6 in the search history storage device 31 as the search history HS (step S43). Next, the fitness estimation module 30a calculates a set of true fitness estimation values corresponding to each individual from the above equation (6) based on the search history HS of the search history storage device 31 (step S44).

  The fitness estimation module 30a determines whether or not the processing of the multi-objective evolution type algorithm unit 2 has been completed (step S45).

  If the process of the multipurpose evolutionary algorithm unit 2 has not ended, the process returns to step S43 and the processes of steps S43 to S45 are repeated. When the process of the multipurpose evolution type algorithm unit 2 is finished, the calculation process of the estimated value is finished.

(E-4) Method from Selection of Parent Individual to Change of Generation Next, a method from selection of a specific parent individual in step S6a of FIG. 6 to change of generation in step S11 will be described. FIG. 17 is a schematic diagram for explaining a method from selection of a specific parent individual to generational change.

As shown in FIG. 17A, the parent individual set P is ranked by Pareto ranking. As shown in FIG. 17B, for the rank 1 individual set of the parent individual set P, the Euclidean distance between each two adjacent individuals in the fitness function space is calculated as a distribution index. In the present embodiment, the fitness function space includes two fitness functions f ₁ and f ₂ .

  One of the two individuals Ia and Ib having the maximum Euclidean distance is randomly selected as the first parent individual Ia with probability 1/2. Further, the second parent individual Ic and the third parent individual Id are selected from the parent individual set P by random selection.

  In the present embodiment, the Euclidean distance L of the distribution index is obtained by the following equation, assuming that two adjacent individuals are x and y, as shown in FIG.

L = [{f ₁ (x) −f ₁ (y)} ² + {f ₂ (x) −f ₂ (y)} ² ] ^1/2 (7)
Next, as shown in FIG. 17C, a plurality of child individual candidates are generated from the first, second, and third parent individuals Ia, Ic, Id, and a predetermined number is selected from the plurality of child individual candidates by a method described later. A child individual set C including the individual is generated. Further, as shown in FIG. 17 (d), an individual set F is generated from the child individual set C and the parent individual set P, and the Pareto ranking using the α superiority strategy is performed on the individual set F. At this time, if there is an individual that overlaps the individuals included in the parent individual set P in the child individual set C, the lowest rank is assigned to the individual.

  Thereafter, as shown in FIG. 17E, the degree of congestion is sorted into the individual set F, a predetermined number of individuals are selected based on the rank of the individuals and the degree of congestion within each rank, and the remaining individuals are deleted. Thereby, a new parent individual set P is generated. In this way, generational changes are made.

FIG. 18 is a schematic diagram for explaining generation processing of a child individual candidate. 18A shows a parent individual set P in the parameter space, and FIG. 18B shows a child individual candidate set in the parameter space. When the parameters x ₁ and x ₂ of the individual I 21 of the child candidate set coincide with the parameters x ₁ and x ₂ of the individual I 11 of the parent individual set P, the lowest rank is assigned to the individual I 21. Similarly, when the parameters x ₁ and x ₂ of the individual I 22 of the child individual candidate set coincide with the parameters x ₁ and x ₂ of the individual I 12 of the parent individual set P, the lowest rank is assigned to the individual I 22. .

  Note that the method for selecting a specific parent individual is not limited to the present embodiment, and the two individuals having the maximum Euclidean distance L from the rank 1 individual set are selected as the first and second parent individuals. Three parent individuals may be selected from the parent individual set P by a method such as random selection, roulette selection, or tournament selection.

  FIG. 19 is a flowchart showing a process of selecting a specific parent individual by the multipurpose evolution type algorithm unit 2.

  First, the multi-purpose evolutionary algorithm unit 2 sorts the rank-1 individual set selected from the parent individual set P for each fitness function (step S51).

  Next, the multipurpose evolutionary algorithm unit 2 calculates the Euclidean distance between two adjacent individuals in the rank-1 individual set (step S52).

  Furthermore, the multi-objective evolution type algorithm unit 2 randomly selects one of the two individuals giving the maximum Euclidean distance as the first parent individual with a probability of 1/2, and the second parent individual and the third A parent individual is selected from the parent individual set P by random selection (step S53).

  In the present embodiment, child individual candidates are generated from the first, second, and third parent individuals by a crossover operation. For example, UNDX (Unimodal Normal Distribution Crossover) is used as the crossover operation.

  FIG. 20 is a schematic diagram showing generation processing of a child individual candidate by UNDX. In UNDX, a child individual candidate C1 is generated in accordance with a normal distribution random number determined based on the positional relationship among the first parent individual P1, the second parent individual P2, and the third parent individual P3. In this case, since the child individual candidate C1 is generated according to the normal distribution around the axis AX connecting the first parent individual P1 and the second parent individual P2, the child individual candidate C1 is the first to third parent individuals. It is not generated at a position far away from P1 to P3.

(E-5) Generation Method of Child Individual Set C FIG. 21 is a flowchart showing generation processing of a child individual set C by the multi-purpose evolutionary algorithm unit 2 and the fitness estimation module 30b.

  First, the multipurpose evolutionary algorithm unit 2 generates a plurality of child individual candidates from the first, second, and third parent individuals by the above method (step S61).

  Next, the fitness estimation module 30b calculates true fitness estimation values for all parent individuals and child individual candidates (step S62).

The estimated value f ′ (x) of the true fitness f (x) for the child individual candidate is expressed by a weighted average expression weighted by a function including the distance d _l as shown in the following expression (6a). Can do.

  However, since the sample value corresponding to the child individual candidate is not obtained at this stage, the calculation formula of the estimated value f ′ (x) for the child individual candidate is different from the above formula (6), and the child individual candidate Sample value F (x) is not included.

  In addition to the above equation (6a), the estimated value is calculated by using polynomial regression, neural network, radial basis function, kriging, Gaussian process, local weighted regression, etc. This method can also be used.

  Further, the multipurpose evolution type algorithm unit 2 ranks all parent individuals and child individual candidates (step S63). For this ranking, the α superiority strategy of FIG. 8, the superiority comparison of FIG. 9, and the Pareto ranking of FIG. 10 are used.

  Next, the multi-purpose evolution type algorithm unit 2 calculates the degree of congestion by adding one child individual candidate with the highest rank to the parent individual set P (step S64). A method for calculating the degree of congestion will be described later.

  Next, the multi-purpose evolution type algorithm unit 2 determines whether or not the calculation of the degree of congestion of all the child individuals of the highest rank has been completed (step S65). If the calculation of the congestion level of all the child individual candidates of the highest rank has not been completed, the process returns to step S64.

  When the calculation of the congestion level of all the child individual candidates of the highest rank is completed, the child individual candidates are sorted in the order of good congestion level (step S66), and a predetermined number of child individual candidates having a better congestion level are selected. A child individual set C is selected (step S67).

  FIG. 22 is a schematic diagram showing the generation process of the child individual set C, where (a) shows a parent individual and a child individual candidate in the fitness function space, and (b) shows a calculation method of the congestion degree in the fitness space. .

  The method for calculating the degree of congestion of the child individual candidate is the same as the method for calculating the degree of congestion of the target individual shown in FIG.

  In the fitness function space of FIG. 22A, parent individuals Pa to Pd and generated child individual candidates C11 to C20 are shown. FIG. 22B shows parent individuals Pa to Pd and one child individual candidate C12 having the highest rank.

  As shown in FIG. 22A, a large number of child individual candidates are generated from the parent individual in the fitness function space.

  The calculation of the degree of congestion assumes that a candidate for a single child individual is a rectangle whose diagonal is a line connecting two adjacent parent individuals, and the degree of congestion (congestion distance) is the sum of the lengths of the vertical and horizontal sides of the rectangle. ). The smaller the congestion degree value, the more the child individual candidates are present in the congested area. The maximum degree of congestion is given to the child individual candidates at both ends of the same rank.

  In FIG. 22B, the degree of congestion of the child individual candidate C12 is represented by the sum of the vertical and horizontal sides of the rectangle created by the adjacent parent individuals Pb and Pc.

(F) Effects of the First Embodiment In the multi-objective optimization apparatus 1 according to the present embodiment, a large number of child individual candidates are generated, and a predetermined number of children in descending order of the degree of congestion from the plurality of child individual candidates at the highest rank. An individual candidate is selected as a child individual, and the selected child individual is actually evaluated. Thereby, time for evaluating unnecessary child individual candidates is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

  In addition, a set of sample values corresponding to each individual stored in the search history storage device 31 is weighted by the above equation (6), and the target individual is handled using a linear sum of a plurality of sets of weighted sample values. A set of fitness estimates is obtained.

  Since the weight of each individual is a function including the distance between the target individual and the individual in the parameter space, an estimated value with a sufficiently small error from the true fitness can be obtained. Therefore, even when the sample value output from the optimization target has uncertainty, an appropriate Pareto optimal individual set can be obtained.

  Further, the superiority or inferiority of the estimated values corresponding to a plurality of individuals in the individual set is compared for each of the plurality of fitness functions by the α superiority strategy, and the comparison result for each of the plurality of fitness functions is weighted. A plurality of individuals in the individual set are ranked based on a linear sum of a plurality of comparison results weighted with respect to the plurality of fitness functions. Thereby, even when the optimization target has uncertainty, it is possible to obtain a rational Pareto optimal individual considering the relationship between a plurality of fitness levels.

  Further, in the distribution of individuals of the highest rank in the fitness function space, a new child individual can be easily generated in a sparse region by using the distance between adjacent individuals as a distribution index. As a result, individuals with the highest rank can be generated so as to be distributed evenly over a wide area in the fitness function space. Therefore, Pareto optimal individuals having diversity can be easily obtained.

  Furthermore, when the generated new child individual overlaps with an individual in the parent individual set, the lowest rank is assigned to the new child individual. Thereby, bad individuals can be gradually reduced in the initial stage of searching for the Pareto optimal individual, and diversity of the Pareto optimal individual can be maintained in the latter stage of searching for the Pareto optimal individual.

  Further, the Pareto optimal individual is displayed on the screen of the display device 105 based on the set of estimated values calculated by the fitness estimating unit 3. As a result, the user can visually recognize the Pareto optimal individual and can easily make various decisions.

(2) Second Embodiment Next, a multi-objective optimization apparatus according to a second embodiment of the present invention will be described. The multipurpose optimization apparatus according to the present embodiment has the configuration shown in FIGS. Further, the overall processing of the multi-objective optimization apparatus according to the present embodiment is the same as the processing shown in FIGS.

  This embodiment is different from the first embodiment in the method of calculating the estimated value in step S3 of FIG. 5 and step S9 of FIG. 6 and the method of selecting a specific parent individual in step S6a of FIG.

(A) Calculation of Estimated Value In the present embodiment, the estimated value f ′ (x) of the true fitness f (x) is calculated by an improved estimation formula.

As shown in the above equation (9), the estimated value f ′ (x) is represented by a weighted average equation weighted by a function including the cube of the distance d _{1 in} the parameter space.

  According to the above equation (9), the shorter the distance from the target individual to the individual in the search history HS, the greater the weight. On the other hand, when the distance from the individual of interest to the individual in the search history HS increases, the weight becomes extremely small. Therefore, an individual away from the target individual hardly contributes to the calculation of the estimated value f ′ (x).

  FIG. 23 is a schematic diagram showing an individual search based on the search history stored in the search history storage device 31. FIG. 23A shows an individual set at the initial stage of search in single-objective optimization, FIG. 23B shows an individual set at the initial stage of search in multi-objective optimization, and FIG. 23C shows the latter stage of search in single-objective optimization. FIG. 23 (d) shows an individual set in the latter half of the search in multi-objective optimization.

23A and 23C, the vertical axis represents the fitness function f, and the horizontal axis represents the parameter x. 23B and 23D, the vertical axis indicates the fitness function f ₂ and the horizontal axis indicates the fitness function f ₁ .

  In the initial stage of the search, a plurality of individuals are dispersed as shown in FIGS. In the latter half of the search, in single-objective optimization, individuals are concentrated in the vicinity of a certain parameter value as shown in FIG. 23 (c), and in multi-objective optimization, a plurality of individuals are shown in FIG. 23 (d). Form a Pareto optimal population.

  In this way, in multi-objective optimization, individuals are dispersed over a wide range of the fitness function space. Therefore, the use of equation (9) reduces the contribution of individuals far away from the target individual, so that the accuracy of the estimated value can be reduced. Becomes higher.

(B) Method from Selection of Specific Parent Individual to Generation Change FIG. 24 is a schematic diagram for explaining a method from selection of a parent individual to generation change. In the present embodiment, examples of _three fitness functions f ₁ , f ₂ , and f ₃ are shown.

  As shown in FIG. 24A, the parent individual set P is ranked by Pareto ranking. As shown in FIG. 24B, the area of the triangle formed by each of the three adjacent individuals in the fitness function space is calculated as a distribution index for the rank 1 individual set of the parent individual set P.

  For the formation of the triangle, Delaunay Triangulation is used (see Non-Patent Document 6).

  Here, Delaunay triangulation will be briefly described. Delaunay triangulation is a dual figure of Voronoi Diagram, which is an important concept in computational geometry. Among the triangulation of a point set on a plane (space), it is known as an optimal triangulation in various meanings, and is also used for mesh generation in computer graphics or a finite element method. Delaunay triangulation is a division method for maximizing the minimum angle of a divided triangle, and examples include an algorithm using a sequential addition method, a division rule method, or a geometric transformation. The details of Delaunay triangulation are described in Non-Patent Document 7, for example.

  Any one of the three individuals IA, IB, and IC giving the maximum triangular area is selected at random with a probability of 1/3 as the first parent individual IA. Further, the second parent individual ID and the third parent individual IE are selected from the parent individual set P by random selection.

  Next, as shown in FIG. 24C, a plurality of child individual candidates are generated from the first, second, and third parent individuals IA, ID, IE, and a predetermined number of the plurality of child individual candidates is obtained by the above method. A child individual set C including the individual is generated. Further, as shown in FIG. 24 (d), an individual set F is generated from the child individual set C and the parent individual set P, and the Pareto ranking using the α superiority strategy is performed on the individual set F. At this time, if there is an individual that overlaps the individuals included in the parent individual set P in the child individual set C, the lowest rank is assigned to the individual.

  Thereafter, as shown in FIG. 24E, the degree of congestion is sorted into the individual set F, a predetermined number of individuals are selected based on the rank of the individuals and the rank within each rank, and the remaining individuals are deleted. Thereby, a new parent individual set P is generated. In this way, generational changes are made.

  Note that the method for selecting a specific parent individual is not limited to the present embodiment, and three individuals giving the largest triangular area may be selected as the first, second and third parent individuals, or Two of the three individuals giving the largest triangular area are selected as the first and second parent individuals, and the third parent individual is selected from the parent individual set P by a method such as random selection, roulette selection or tournament selection. You may choose.

  In addition, when there are three or more parameters, a cross-parent extended crossover method such as UNDX-m may be used.

  FIG. 25 is a flowchart showing a process of selecting a specific parent individual by the multipurpose evolution type algorithm unit 2.

First, multi-objective evolutionary algorithm unit 2 orthogonal projection of an individual set of rank 1 selected from the parent population of individuals P to f _i -f _j plane (step S61). Here, f _i and f _j are fitness functions. i, j = 1, 2, 3 and i ≠ j, and the combination thereof is changed for each generation.

  Next, the multi-objective evolution type algorithm unit 2 performs Delaunay triangulation of the orthogonally projected individual set (step S62).

Further, the multi-objective evolution type algorithm unit 2 gives a component of the fitness function f _k as a height component to the Delaunay triangulated rank 1 individual set, and develops a plurality of triangles in a three-dimensional space (step S63). . Here, k ≠ i, j.

  Next, the multi-objective evolution type algorithm unit 2 calculates the areas of a plurality of triangles developed in the three-dimensional space (step S64).

  One of the three individuals forming the triangle with the largest area is randomly selected as the first parent individual with a probability of 1/3, and two individuals from the parent individual set P are selected as the second parent individual and the third A parent individual is selected by random selection (step S65).

(C) Generation Method of Child Individual Set C The child individual set C generation process in the present embodiment is the same as the process shown in FIG.

  However, the estimated value f ′ (x) of the true fitness f (x) for the child individual candidate is calculated by the improved estimation formula.

As shown in the above equation (9a), the estimated value f ′ (x) is expressed by a weighted average equation weighted by a function including the cube of the distance d _{1 in} the parameter space.

  However, since the sample value corresponding to the child individual candidate is not obtained at this stage, the calculation formula of the estimated value f ′ (x) for the child individual candidate is different from the above formula (9), and the child individual candidate Sample value F (x) is not included.

(D) Effects of the Second Embodiment In the multi-objective optimization apparatus 1 according to the present embodiment, a large number of child individual candidates are generated, and a predetermined number of children in descending order of the degree of congestion from a plurality of top-ranked child individual candidates. An individual candidate is selected as a child individual, and the selected child individual is actually evaluated. Thereby, time for evaluating unnecessary child individual candidates is omitted. As a result, the speed of optimization is improved. Therefore, it is possible to efficiently obtain an appropriate Pareto optimal individual in a short time.

  Also, a set of sample values corresponding to each individual stored in the search history storage device 31 is weighted by the above equation (9), and the target individual is handled using a linear sum of a plurality of sets of weighted sample values. A set of fitness estimates is obtained.

  Since the weight of each individual is a function including the cube of the distance between the target individual and the individual in the parameter space, the influence of other individuals far away from the target individual in the parameter space is sufficiently small. Thereby, an estimated value with a sufficiently small error from the true fitness can be obtained. Therefore, even when the sample value output from the optimization target has uncertainty, an appropriate Pareto optimal individual set can be obtained.

  In addition, in the distribution of individuals with the highest rank in the fitness function space, a new child individual can be easily generated in a sparse region by using the area of a triangle with three adjacent individuals as vertices as a distribution index. can do. As a result, individuals with the highest rank can be generated so as to be distributed evenly over a wide area in the fitness function space. Therefore, Pareto optimal individuals having diversity can be easily obtained.

(3) Other Embodiments (a) Extended Estimation Formula When the above estimation expressions (4) and (9) are generalized, the following expression is obtained.

  In the above formula (10), n is an arbitrary natural number. The estimation formula (4) of the first embodiment shows a case where n = 1, and the estimation formula (9) of the second embodiment shows a case where n = 3. Although n = 3 is preferable, n may be another natural number.

  Thus, the estimated value of the true fitness of the individual of interest is calculated by the weighted linear sum of the estimated values of other individuals in the search history HS without using the fitness sample value having a noise component. Thereby, even when the sample value has uncertainty, the Pareto optimal individual can be searched stably.

  In addition, since a weight including a function of the nth power of the distance between the target individual and another individual is used in the parameter space, the estimation value is prevented from being greatly influenced by other individuals spreading over a wide range. Therefore, the estimated value can be calculated with high accuracy.

(B) Selection of parent individuals As shown in the first embodiment, in the two-purpose optimization problem, the distance between individuals is used as a distribution index for selecting a specific parent individual. Further, as shown in the second embodiment, in the three-purpose optimization problem, a triangular area formed by three individuals is used as a distribution index for selecting a specific parent individual.

  When the distribution index for selecting a specific parent individual is expanded to an m-objective optimization problem, the distribution index is the size of a simplex formed by m individuals adjacent in the fitness function space. . m is a natural number of 2 or more. The simple substance can be formed by Delaunay triangulation.

  FIG. 26 is a diagram showing a distribution index extended to the m-object optimization problem. As shown in FIG. 26, in the case of two objectives, the distribution index is the length of a straight line connecting two adjacent individuals. In the case of three objectives, the distribution index has three adjacent individuals as vertices. In the case of four purposes, the distribution index is the volume of a triangular pyramid having four adjacent individuals as vertices. The distribution index is a size of a four-dimensional simple substance, and is calculated by bottom volume × height ÷ 4. In the case of five purposes, the distribution index is the size of a five-dimensional simple substance, and is calculated by the following equation: bottom 4 dimensional area × height / 5. In the case of (m + 1) purpose, the distribution index is the size of a single m-dimension, and is calculated from the base (m−1) -dimensional area × height / m.

  In this way, by selecting a specific parent individual based on the distribution index, an active individual search is performed in a region where the distribution is sparse in the fitness function space. Thereby, since an individual is searched in a wide area, an estimated value can be calculated with high accuracy, and a Pareto optimal individual can be found equally in a wide area on the fitness function space.

(C) Extended estimation formula at the time of generation of a child individual set When the above estimation formulas (4a) and (9a) are generalized, the following formula is obtained.

  In the above formula (10a), n is an arbitrary natural number. The estimation formula (4a) of the first embodiment shows a case where n = 1, and the estimation formula (9a) of the second embodiment shows a case where n = 3. Although n = 3 is preferable, n may be another natural number.

  As an approximation model of the above equation (10a), other methods such as polynomial regression, neural network, radial basis function, kriging, Gaussian process, and locally weighted regression may be used. it can.

(D) Application Example to Engine Simulator FIG. 27 is a block diagram showing an example in which the multi-objective optimization apparatus is applied to an engine simulator.

  The optimization target 6a in FIG. 27 is an engine simulator. The engine simulator is composed of a personal computer, for example. The optimization target 6a simulates the operation of the engine based on a set of parameters given from the multipurpose optimization apparatus 1, and outputs a simulation result to the multipurpose optimization apparatus 1 as a set of fitness sample values.

In the present embodiment, the plurality of fitness functions include fuel consumption, torque, and concentrations of components such as CO (carbon monoxide), HC (hydrocarbon), and NO _x (nitrogen oxide) contained in engine exhaust gas. Etc. are set.

  The parameters include fuel injection amount, fuel injection timing, ignition timing, throttle opening, and the like.

  According to the multi-objective optimization apparatus 1 of FIG. 27, the Pareto optimal individual set can be efficiently obtained in a short time by setting the fitness function set and the parameter set.

(E) Application Example to Motor Evaluation Device FIG. 28 is a block diagram showing an example in which the multi-objective optimization device is applied to a motor evaluation device.

  The optimization target 6b in FIG. 28 is a motor evaluation device. The motor evaluation device includes a motor, a control circuit, and various detection circuits. The optimization target 6b controls the motor based on a set of individual parameters given from the multi-purpose optimization apparatus 1, measures a plurality of performance items of the motor, and uses the measurement results as a set of fitness sample values. Output to the optimization device 1.

  As the plurality of fitness functions, a plurality of functions such as rise time, settling time, overshoot amount, and current consumption are set.

  The parameters include PID (Proportional Integral Derivative) gain, drive current, and the like.

  Here, the trade-off relationship includes rise time and overshoot amount, rise time and current consumption, settling time and overshoot amount, and the like.

  According to the multi-objective optimization apparatus 1 of FIG. 28, the Pareto optimal individual set can be efficiently obtained in a short time by setting the fitness function set and the parameter set.

  It is also possible to perform real-time control of the motor in accordance with the actual environment by calculating the Pareto optimal population in real time.

(F) Application Example to Motor Simulator FIG. 29 is a block diagram showing an example in which the multi-purpose optimization device is applied to a motor simulator.

  The optimization target 6c in FIG. 29 is a motor simulator. The motor simulator is composed of a personal computer, for example. The optimization target 6c performs a simulation of motor operation based on a set of parameters given from the multipurpose optimization apparatus 1, and outputs a simulation result to the multipurpose optimization apparatus 1 as a set of fitness sample values.

  As the plurality of fitness functions, a plurality of functions such as rise time, settling time, overshoot amount, and current consumption are set. The parameters include PID gain, drive current, and the like.

  According to the multi-objective optimization apparatus 1 of FIG. 29, the Pareto optimal individual set can be efficiently obtained in a short time by setting the fitness function set and the parameter set.

(G) Other examples of multi-objective evolutionary algorithm In the above embodiment, the genetic algorithm (GA) is used as the multi-objective evolutionary algorithm. However, the present invention is not limited to this, and instead of the genetic algorithm, an evolution strategy ( A calculation method based on a similar idea such as ES (Evolution Strategy) may be used.

  Note that calculation methods such as GA and ES are collectively referred to as evolutionary algorithms (EAs) or evolutionary computation (Evolutionary Computation).

(H) Application to four or more objectives In the above embodiment, the optimization of two objectives and three objectives has been described as an example, but the present invention is similarly applied to optimization of four or more objectives. be able to. In this case, four or more fitness functions having a trade-off relationship are set.

(I) Generation change method In step S10 of FIG. 6 described above, a new parent individual set P is obtained by replacing an individual that does not overlap with an individual of the parent individual set P in the child individual set C with an individual lower in the parent individual set P. May be generated.

  In this case, in the initial stage of searching for the Pareto optimal individual, it is possible to reduce the number of bad individuals gradually and maintain the diversity of the Pareto optimal individual in the latter stage of searching for the Pareto optimal individual.

(J) Re-evaluation of parent individual In the above embodiment, a parent individual is re-evaluated. However, if there is a limit on the number of individual evaluations in a real system or large-scale simulation, only a child individual is re-evaluated. May be. Thereby, the number of evaluations can be reduced.

(K) Restriction on Acquisition of Sample Values Acquisition of sample values in the search history storage device 31 may be terminated when the amount of sample values stored in the search history storage device 31 reaches a predetermined storage capacity. As a result, the estimated value is calculated based on the search history HS stored in the search history storage device 31 and the search for the Pareto optimal individual can proceed based on the calculated estimated value.

(L) Ranking In the above embodiment, a plurality of individuals are ranked by Pareto ranking, but the present invention is not limited to this, and a plurality of individuals are ranked using other methods such as non-dominant sorting. May be.

(M) Application to a multi-objective optimization apparatus that does not consider the uncertainty of the optimization target In the above embodiment, Pareto optimal individuals having diversity even when the optimization target 6 has uncertainty such as observation noise. Although the multi-objective optimization apparatus 1 that can be obtained in a short time has been described, the present invention can also be applied to a multi-objective optimization apparatus that does not consider uncertainties such as observation noise to be optimized. Also in this case, the time for evaluating unnecessary child individual candidates is omitted. As a result, the speed of optimization is improved.

(N) Method of Realizing Each Unit In the above embodiment, the multi-objective evolution algorithm unit 2, the fitness estimation modules 30a and 30b, and the search history storage unit 31 are realized by the CPU 101 and the program. A part or all of the fitness estimation module 30 and the search history storage unit 31 may be realized by hardware such as an electronic circuit.

(4) Examples and Comparative Examples In the following examples, the benchmark problem was executed by the multi-objective optimization apparatus according to the first and second embodiments. In the comparative example, the benchmark problem is executed by a multi-objective optimization device similar to the multi-objective optimization devices according to the first and second embodiments except for the method for generating the child individual set C.

  FIG. 30 is a diagram showing conditions for multi-objective optimization of the example and the comparative example. FIG. 31 shows a benchmark problem executed in the example and the comparative example.

  As shown in FIG. 31, the number of evaluations was 1500, and the example and the comparative example were compared. For reference, the comparative example was evaluated up to 3000 times. In the examples and comparative examples, the population size is 100. In the example, three child individuals were selected from 100 child individual candidates by the method for generating a child individual set of the second embodiment, and three child individuals and two parent individuals were evaluated. On the other hand, in the comparative example, 8 child individuals were generated from a specific parent individual, and 8 child individuals and 2 parent individuals were evaluated. This is to confirm that good results can be obtained even when the number of evaluations of the example is half that of the comparative example.

  In the examples and comparative examples, UNDX is used as the crossover operator, and the selection method of the first and second embodiments (the method of selecting a specific parent individual shown in FIGS. 17 and 24) is used as the selection operator. It was. Further, the generation change method shown in FIGS. 17 and 24 was used. Furthermore, Pareto ranking was used as a method for determining the highest rank.

  Here, the number of evaluations is obtained by (number of generations × number of child individuals + number of individuals in the initial individual set).

  In Examples and Comparative Examples, test functions ZDT1, ZDT2, and DTLZ2 shown in FIG. 31 were used as benchmark problems (see Non-Patent Document 8).

  The test function ZDT1 is a two-objective optimization problem in which the Pareto optimal solution set has a convex Pareto boundary. The test function ZDT2 is a two-objective optimization problem in which the Pareto optimal solution set has a concave Pareto boundary. Here, the test function ZDT1 and the test function ZDT2 are set as the minimization problem of the two-variable two-objective function. Note that the test function ZDT1 and the test function ZDT2 have weak Pareto optimal solutions. Appropriate noise is added to each objective function.

  The test function DTLZ2 is a three-objective optimization problem in which the Pareto optimal solution set has a concave Pareto boundary. Here, the test function DTLZ2 is a minimization problem of a three-variable three-objective function. Appropriate noise is added to each objective function.

Constants k _i ′ (i = 1, 2) of the test function ZDT1 and the test function ZDT2 ) Was determined in a preliminary experiment and k _i ′ = 310000. The constant k _i ′ (i = 1, 2, 3) of the test function DTLZ2 was determined in a preliminary experiment, and k _i ′ = 31000. Also, α _ij (i = 1,... N; j = 1,..., N; i ≠ j) in the α superiority strategy was set to 0.1. Here, n is the target number.

Here, in the examples and comparative examples, the average absolute error A _error and the average estimation error E _error were calculated.

The following equation is a formula for calculating the average absolute error A _error in the test function ZDT1 and the test function ZDT2.

The following equation is a formula for calculating the average absolute error A _error in the test function DTLZ2.

In the above formulas (11) and (12), | P | indicates the number of parent individual sets P, m indicates the number of parameters (decision variables), and x _ij indicates the parameters. In the examples and comparative examples, the average estimation error E _error was calculated by the following equation.

In the above equation (13), | P | represents the number of parent individual sets P, n represents the number of fitness functions (objective functions), f _j (x _i ) represents the true fitness value, f ′ _j (x _i ) represents an estimated value of true fitness.

In the examples and comparative examples, the average absolute error A _error and the average estimation error E _error were evaluated in 30 trials.

FIG. 32A is a schematic diagram showing the concept of the average absolute error A _error in the test function ZDT1 and the test function ZDT2, and FIG. 32B is a schematic diagram showing the concept of the average absolute error A _error in the test function DTLZ2.

In FIG. 32A, when there is no noise component, the individuals i101, i102, i103 exist on the straight line of x ₂ = 0 in the parameter space. The average absolute error A _error in the test function ZDT1 and the test function ZDT2 is obtained by calculating the average value of the distances between the individuals I101, I102, I103 obtained by optimization and the individuals i101, i102, i103 when there is no noise component. can get.

In FIG. 32B, when there is no noise component, the individual i111, i112, i113 exists on the plane of x ₃ = 0.5 in the parameter space. The average absolute error A _error in the test function DTLZ2 is obtained by calculating the average value of the distances between the individuals I111, I112, I113 obtained by optimization and the individuals i111, i112, i113 when there is no noise component.

FIG. 33 is a schematic diagram showing the concept of the average absolute error A _error in the case of two purposes.

  In FIG. 33, the true fitness values f (xa), f (xb), f (xc) and the true fitness estimates f ′ (xa), f ′ (xb), f ′ ( xc) is shown.

The sum of the distance for the fitness function f _{1 and} the distance for the fitness function f ₂ between the true fitness f (xa) and the estimated value f ′ (xa), the true fitness f (xb) and The sum of the distance for the fitness function f _{1 and} the distance for the fitness function f ₂ between the estimated value f ′ (xb) and the true fitness f (xc) and the estimated value f ′ (xc) The average absolute error A _error is obtained by calculating the sum of the distance for the fitness function f _{1 and} the distance for the fitness function f ₂ and calculating the average of these sums.

  FIG. 34 is a diagram showing calculation results of the average absolute error and the average estimation error in the example and the comparative example.

  In FIG. 34, in addition to the average absolute error and the average estimation error, the standard deviation of the absolute error and the standard deviation of the estimation error are shown for reference. For reference, the calculation results of the average absolute error and the average estimation error when the number of evaluations is 3000 are also shown for the comparative example.

  As shown in FIG. 34, the average absolute error of the example in the test function ZDT1, the test function ZDT2, and the test function DTLZ2 is smaller than that of the comparative example, and even when the number of evaluations of the comparative example is 3000. It has become smaller.

  Further, the average estimation error of the example in the test function ZDT1 and the test function ZDT2 is smaller than that of the comparative example, and is smaller than that in the case where the number of evaluations of the comparative example is 3000.

  This is considered to be because in the embodiment, the distribution of the Pareto optimal individuals is difficult to spread, and thus the search can easily proceed in a region where the Pareto optimal individuals are present. Note that only the average estimation error of the example in the test function DTLZ2 was larger than that of the comparative example. It seems that the reason why the average estimation error of the test function DTLZ2 is bad is that individuals in the search history exist unevenly.

  FIG. 35 is a diagram showing the relationship between the average absolute error and the number of evaluations in the examples and comparative examples. The relationship of FIG. 35 shows the calculation result when the test function ZDT1 is used.

  As shown in FIG. 35, it can be seen that, in the example, the average absolute error decreases at a speed two to three times that of the comparative example.

  FIG. 36 is a diagram showing the relationship between the average estimation error and the number of evaluations in the examples and comparative examples. The relationship of FIG. 36 shows the calculation result when the test function ZDT1 is used.

  As shown in FIG. 36, it can be seen that in the example, higher estimation accuracy can be obtained from the initial stage of evaluation than in the comparative example.

  From the examples and comparative examples, it has been found that the multi-objective optimization apparatus according to the first and second embodiments can reduce the number of evaluations.

(5) Correspondence between Claim Component and Each Part of Embodiment The following describes an example of correspondence between each component of the claim and each part of the embodiment, but the present invention is not limited to the following example. .

  In the above embodiment, the search history storage device 31 corresponds to a storage unit, the fitness estimation module 30a corresponds to a first estimation unit, the fitness estimation module 30b corresponds to a second estimation unit, and multipurpose evolution. The type algorithm unit 2 corresponds to a calculation unit.

  Further, the parent individual corresponds to the storage individual, the child individual candidate corresponds to the evaluation individual candidate, and the child individual corresponds to the evaluation individual.

  Note that the fitness obtained from the simulation by the real system may be directly used without using the first estimation unit.

  The present invention is used for optimizing various optimization targets such as parameters to be optimized for real systems or simulations with uncertainty, optimization targets for simulations without uncertainty, etc. Can do.

It is a block diagram which shows the functional structure of the multi-objective optimization apparatus which concerns on the 1st Embodiment of this invention. It is a block diagram which shows the hardware constitutions of the multi-objective optimization apparatus of FIG. It is a block diagram which shows an example of a structure of the optimization object. HC concentration, is a diagram showing a relationship between concentration of NO _x and CO concentration and the air-fuel ratio. It is a flowchart which shows the whole process of the multi-objective optimization apparatus of FIG. It is a flowchart which shows the whole process of the multi-objective optimization apparatus of FIG. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram which shows the specific example of each process of a multipurpose optimization apparatus. It is a schematic diagram for demonstrating calculation of the estimated value by the fitness estimation module of a fitness estimation part. It is a schematic diagram which shows the sample value with the noise according to normal distribution. It is a schematic diagram which shows the model of an uncertain fitness function. It is a flowchart which shows the calculation process of the estimated value by the fitness estimation module of a fitness estimation part. It is a schematic diagram for demonstrating the method from selection of a specific parent individual to generational change. It is a schematic diagram for demonstrating the production | generation process of a child individual candidate. It is a flowchart which shows the selection process of the specific parent individual by a multipurpose evolution type algorithm part. It is a schematic diagram which shows the production | generation process of the child individual candidate by UNDX. It is a flowchart which shows the production | generation process of the child individual set by a multipurpose evolution type algorithm part and a fitness estimation module. It is a schematic diagram which shows the production | generation process of a child individual set. It is a schematic diagram which shows the search of the individual based on the search history memorize | stored in the search history memory | storage device. It is a schematic diagram for demonstrating the method from selection of a parent individual to generational change. It is a flowchart which shows the selection process of the specific parent individual by a multipurpose evolution type algorithm part. It is a figure which shows the distribution parameter | index extended to the m objective optimization problem. It is a block diagram which shows the example which applied the multipurpose optimization apparatus to the engine simulator. It is a block diagram which shows the example which applied the multipurpose optimization apparatus to the motor evaluation apparatus. It is a block diagram which shows the example which applied the multipurpose optimization apparatus to the motor simulator. It is a figure which shows the conditions of the multipurpose optimization of an Example and a comparative example. It is a figure which shows the benchmark problem performed in an Example and a comparative example. FIG. 4 is a schematic diagram showing a concept of average absolute error in test function ZDT1 and test function ZDT2, and a schematic diagram showing a concept of average absolute error in test function DTLZ2. It is a schematic diagram which shows the concept of the average absolute error in the case of 2 objectives. It is a figure which shows the calculation result of the average absolute error and average estimation error in an Example and a comparative example. It is a figure which shows the relationship between the average absolute error and the frequency | count of evaluation in an Example and a comparative example. It is a figure which shows the relationship between the average estimation error and the frequency | count of evaluation in an Example and a comparative example. It is a figure which shows the example which applied the multi-objective optimization problem to engine optimization. It is a figure for demonstrating a Pareto optimal solution.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Multi-objective optimization apparatus 2 Multi-objective evolution type algorithm part 3 Fitness estimation part 4 Output interface 5 Input interface 6 Optimization object 10 User 30a, 30b Fitness estimation module 31 Search history storage device 61 Engine 62 ECU (engine control unit)
63 Exhaust gas analyzer 64 Controller 65 Throttle unit 66 Dynamo 101 CPU (Central processing unit)
102 ROM (read only memory)
103 RAM (Random Access Memory)
104 Input Device 105 Display Device 106 External Storage Device 107 Recording Medium Drive Device 108 Input / Output Interface 109 Recording Medium C Child Individual Set d _l Distance f ₁ , f ₂ Fitness Function F Individual Set HS Search History I1, I2, I3, I4 , I5, I6, I7, I8, I9, I10, I11, I12, I21, I22 Individual L1, L2, L11, L12 Straight line P Parent individual set P1 First parent individual P2 Second parent individual P3 Third parent Individual s1, s2, s3 rectangle x ₁ , x ₂ parameters

Claims (16)

A multi-objective optimization apparatus that gives a set of individual parameters to an optimization target, and receives a set of fitness for a plurality of fitness functions corresponding to a plurality of objectives from the optimization target,
A storage unit for storing a set of individual parameters and a set of fitness output from the optimization target as an individual for storage;
A new individual is generated as an evaluation individual candidate, and a set of parameters of the individual selected as the evaluation individual among the generated evaluation individual candidates is given to the optimization target and the storage unit, and a plurality of sets are applied. A computing unit for obtaining a Pareto optimal individual set by evaluating the evaluation individual set according to a multi-objective evolutionary algorithm based on the degree;
Based on a plurality of sets of fitness corresponding to a plurality of storage individuals stored in the storage unit, the union of the evaluation individual candidates generated by the calculation unit and the storage individual stored in the storage unit An estimation unit that obtains a set of true fitness estimates corresponding to each individual included,
The arithmetic unit compares superiority or inferiority of estimated values corresponding to a plurality of individuals included in the union for each of the plurality of fitness functions, and based on a result of comparison of superiority or inferiority for each of the plurality of fitness functions. The distribution is calculated by ranking a plurality of individuals included in the union, calculating a distribution index representing the degree of sparseness in the distribution of individuals for storage of the highest rank for each candidate for evaluation of the highest rank A multi-objective optimization device, wherein a predetermined number of evaluation individual candidates are selected as evaluation individuals based on an index. A multi-objective optimization apparatus that gives a set of individual parameters to an optimization target and receives a set of fitness sample values for a plurality of fitness functions corresponding to a plurality of objectives from the optimization target,
A storage unit for storing a set of individual parameters and a set of fitness sample values output from the optimization target as an individual for storage;
A first estimation unit for obtaining a set of true fitness estimation values corresponding to an individual of interest based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit;
A new individual is generated as an evaluation individual candidate based on the estimated value obtained by the first estimation unit, and the parameter set of the individual selected as the evaluation individual among the generated evaluation individual candidates is An arithmetic unit that obtains a Pareto optimal individual set by giving an optimization object and the storage unit and evaluating an evaluation individual set according to a multi-objective evolution type algorithm based on a plurality of sets of estimation values obtained by the estimation unit;
Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, an evaluation individual candidate generated by the arithmetic unit and a union of storage individuals stored in the storage unit A second estimation unit for obtaining a set of true fitness estimates corresponding to each individual included,
The arithmetic unit compares superiority or inferiority of estimated values corresponding to a plurality of individuals included in the union for each of the plurality of fitness functions, and based on a result of comparison of superiority or inferiority for each of the plurality of fitness functions. The distribution is calculated by ranking a plurality of individuals included in the union, calculating a distribution index representing the degree of sparseness in the distribution of individuals for storage of the highest rank for each candidate for evaluation of the highest rank A multi-objective optimization device, wherein a predetermined number of evaluation individual candidates are selected as evaluation individuals based on an index. Wherein the first estimation unit, a plurality of storage individuals stored in the storage unit and h _l, a set of sample values corresponding to the target individuals x and F (x), the distance from the target individual with the parameter space When a set of sample values corresponding to storage _objects separated by d _l is F (h _l ), k ′ is a coefficient, l = 1,..., H, and n is a natural number,

The multi-objective optimization apparatus according to claim 1, wherein a set f ′ (x) of estimated values of true fitness corresponding to the target individual x is calculated by an estimation formula represented by: The second estimation unit, a plurality of storage individuals stored in the storage unit and h _l, a set of sample values corresponding to the storage individual spaced distance d _l from the evaluation individual candidate parameter space When F (h _l ), k ′ is a coefficient, l = 1,..., H and n is a natural number,

The multi-objective optimum according to any one of claims 1 to 3, wherein a set f ′ (x) of estimated values of true fitness corresponding to the individual candidate for evaluation x is calculated by an estimation formula represented by: Device. 5. The multi-objective optimization apparatus according to claim 3, wherein n is 1. The multi-objective optimization apparatus according to claim 3 or 4, wherein n is 3. The arithmetic unit detects two storage individuals adjacent to each evaluation individual candidate within the highest rank in the fitness function space, and calculates a mathematical distance between the two storage individuals for each fitness function. And calculating a sum of mathematical distances in a plurality of fitness functions for each evaluation individual candidate as the distribution index, and a predetermined number of evaluation individuals in descending order of the distribution index calculated from the plurality of evaluation individual candidates The multi-objective optimization apparatus according to claim 1, wherein a candidate is selected as an individual for evaluation. The multipurpose optimization apparatus according to claim 1, wherein the arithmetic unit displays the Pareto optimal individual based on a set of estimated values obtained by the first estimating unit. The multipurpose optimization apparatus according to any one of claims 1 to 8, wherein the arithmetic unit evaluates individuals of the evaluation individual set using a genetic algorithm as the multipurpose evolutionary algorithm. The optimization target includes an evaluation system for evaluating a plurality of performances of the device, the set of parameters includes a set of control parameters for the evaluation system, and the plurality of fitness functions are the evaluation functions The multi-objective optimization apparatus according to claim 1, wherein the plurality of performances are obtained by system evaluation, and the set of fitness values is a value of the plurality of performances. The optimization device according to claim 10, wherein the device is an engine. The optimization device according to claim 10, wherein the device is a motor. The apparatus according to claim 10, wherein the evaluation system is an apparatus evaluation apparatus that controls the apparatus based on the set of parameters and outputs a plurality of performance values generated by the operation of the apparatus as sample values. The equipment optimization device described. The evaluation system is a device simulator that evaluates a plurality of performances by simulating the operation of the device based on the set of parameters, and outputs a plurality of evaluated performance values as a set of sample values. The device optimizing device according to claim 10, wherein Multi-objective optimization that gives a set of individual parameters to an optimization target and optimizes parameters based on a set of fitness sample values for a plurality of fitness functions corresponding to the plurality of objectives output from the optimization target A method of
Storing a set of individual parameters and a set of fitness sample values output from the optimization target as storage objects in a storage unit;
Determining a set of true fitness estimates corresponding to the individual of interest based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit;
Generating a new individual as a candidate for evaluation based on the obtained estimated value;
Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, each of the generated evaluation candidate individuals and the union of storage individuals stored in the storage unit Obtaining a set of true fitness estimates corresponding to the individual;
For each of the plurality of fitness functions, the superiority and inferiority of the estimated values corresponding to a plurality of individuals included in the union are compared, and each of the plurality of fitness functions is included in the union based on a comparison result of superiority or inferiority A distribution index that represents the degree of sparseness in the distribution of storage individuals with the highest rank for each candidate for evaluation with the highest rank, and predetermined based on the calculated distribution index Selecting a number of evaluation candidate individuals as evaluation individuals;
Pareto by giving a set of parameters of the selected individual for evaluation to the optimization target and the storage unit, and evaluating the individual set for evaluation according to a multi-objective evolution type algorithm based on the obtained plural sets of estimated values A multi-objective optimization method comprising: obtaining an optimal individual set. A multipurpose that can be executed by a computer that provides a set of individual parameters to an optimization target and optimizes the parameters based on a set of fitness sample values for a plurality of corresponding fitness functions output from the optimization target An optimization program,
A process of storing a set of individual parameters and a set of fitness sample values output from the optimization target as storage objects in a storage unit;
Processing for obtaining a set of estimated values of true fitness corresponding to an individual of interest based on a plurality of sets of sample values corresponding to a plurality of individuals for storage stored in the storage unit;
A process of generating a new individual as an individual candidate for evaluation based on the obtained estimated value;
Based on a plurality of sets of sample values corresponding to a plurality of storage individuals stored in the storage unit, each of the generated evaluation candidate individuals and the union of storage individuals stored in the storage unit A process for obtaining a set of true fitness estimates corresponding to individuals,
For each of the plurality of fitness functions, the superiority and inferiority of the estimated values corresponding to a plurality of individuals included in the union are compared, and each of the plurality of fitness functions is included in the union based on a comparison result of superiority or inferiority A distribution index that represents the degree of sparseness in the distribution of storage individuals with the highest rank for each candidate for evaluation with the highest rank, and predetermined based on the calculated distribution index A process of selecting a number of individual individuals for evaluation as evaluation individuals,
Pareto by giving a set of parameters of the selected individual for evaluation to the optimization target and the storage unit, and evaluating the individual set for evaluation according to a multi-objective evolution type algorithm based on the obtained plural sets of estimated values A multi-objective optimization program characterized by causing a computer to execute processing for obtaining an optimal individual set.

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