JPH09325949A - Method for optimizing genetic algorithm and system for analyzing genetic algorithm - Google Patents

Abstract

PROBLEM TO BE SOLVED: To search an optimum solution in a short time by optimizing parameters such as the copy rate, cross rate and mutation rate of genetic algorithm. SOLUTION: The genetic group of an initial generation is generated (step S210), the degree of adaptivity is respectively evaluated for each gene belonging to this initial generation (step S130), the hamming distance of respective genes of the genes belonging to this generation and having the highest degree of adaptivity is calculated (step S140) and concerning the genetic group of this generation, the distribution of frequency is found on the plane with two axes of the hamming distance and the degree of adaptivity (step S150). Corresponding to this frequency distribution, the parameter of the genetic algorithm is optimized (step S160) and by using the genetic algorithm specified by this parameter, the genetic group of the next generation is generated (step S170).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for optimizing a genetic algorithm for obtaining an optimal solution by a genetic operation inspired by the evolution process of living things.

[0002]

2. Description of the Related Art A genetic algorithm is an algorithm inspired by Darwinian evolution based on mutation and selection and can be considered as a method of probabilistic search / learning / optimization.

A suitable problem for applying a genetic algorithm is a problem that an algorithm for obtaining an optimum solution cannot be described in a formula, but the solution can be evaluated. In other words, in the real world, the optimal solution is basically unknown and the solution method has not been established, or the method for obtaining the optimal solution is very inefficient and unpractical. There are many problems that can be performed by a relatively simple calculation process, such as a knapsack problem, a traveling salesman problem, a circuit layout problem, and a linear programming problem.

In addition, it is possible to manufacture a device for evaluating an arbitrary solution and experimentally evaluate a solution candidate,
For example, there are hydrodynamic shape optimization problems, engine control optimization problems, and the like.

For such a problem, the optimization target is coded to be associated with a gene, and this gene is subjected to genetic operations such as selection, crossover, and mutation to successively generate new generation genes. There is a method to search for an optimal solution by
It is called a genetic algorithm.

Next, FIG. 11 shows the configuration of a blade shape optimizing device as an example of a conventional optimizing device using a genetic algorithm. An optimizing device 101 shown in the figure includes a variable blade device 121 provided in a wind tunnel, and a mechanical device 12 incorporated in the variable blade device 121 and capable of arbitrarily changing its cross-sectional shape.
3, a resistance coefficient measuring device 125 for measuring the resistance coefficient of the variable blade device 121, and a calculation device for advancing optimization using a genetic algorithm described later.

As shown in FIG. 12, the variable blade device 121 includes a tip bar 131 that forms the tip of the blade, a thin plate of spring steel 155 that forms the upper surface of the blade, and an outer frame that forms the lower and side surfaces of the blade. 151, a packing 145 for keeping airtight between the outer frame and the thin plate, six shafts 133 arranged in parallel with the length direction of the blade, and six adjusting screws 143 corresponding to each shaft 133. , And is assembled as a main component with the beam 137 attached to each shaft 133.

Each shaft 133 is provided with a thread groove, and after being screwed into the threaded holes of the corresponding beam 137, a wedge 139 is driven into the groove provided in the shaft 133 and the beam 137 and fixed to each other. ing. As a result, the shaft 133 and the beam 137 are integrated, and a camshaft structure is formed in which the beam 137 lifts the thin plate 155 on the upper surface of the blade in accordance with the rotation angle of the shaft 133.

A bevel gear 14 is provided at one end of each shaft 133.
1 is provided, meshes with a bevel gear provided at the upper end of the corresponding adjusting screw 143, and the lower end of the adjusting screw 143 is rotated from the lower surface of the blade, whereby each shaft 1
The rotation angle of 33, that is, the position of the upper surface of the blade above the shaft can be adjusted.

The computing device comprises an input device 103, a console 119, a genetic algorithm execution device 109, a random number generator 111, an output device 113, an auxiliary storage device 115, and a printer 117. There is.
The input device 103 is a device for inputting the resistance count value from the resistance coefficient measuring device 125 to the calculation device, and the console 119 includes a CRT and a keyboard, and the operator gives instructions to the calculation device and the whole optimization device. Or a device for monitoring the condition.

The genetic algorithm execution device 109 is a device that searches for an optimal solution of a problem by a genetic algorithm, and a general-purpose computer or a dedicated computer is used. The random number generator 111 is a device for generating pseudo-random numbers mathematically or logically, and generates genes in the early generation, selects gene pairs to be crossed, selects crossover positions, selects genes causing mutation, and suddenly. It gives various random numbers necessary for executing a genetic algorithm such as selection of mutation occurrence position.

The output device 113 converts a gene, which is a solution candidate obtained by the genetic algorithm, into a wing shape, which is its phenotype (converting a gene to its phenotype is called decoding). Machinery 123
It is an interface to output to.

The auxiliary storage device 115 stores a program for executing the genetic algorithm, parameters of the genetic algorithm, etc., and is read out to the internal storage of the genetic algorithm execution device 109 as necessary.
The printer 117 is for printing the execution result of the genetic algorithm.

FIG. 13 shows a genetic algorithm executing device 1.
It is a flowchart which shows the processing procedure of the optimization method by the conventional genetic algorithm performed by 09.

In the figure, first, a target problem is encoded into a character string so as to be associated with a gene (step S910). In the following description, it is assumed that the six movable positions of the variable blade device can be displaced up and down by 2 and 4 mm from the blade base shape (the shape on which optimization is performed).

First, as shown in FIG. 14, the vertical displacement of each movable position on the variable vane device, -4 mm,
-2 mm, 2 mm, and 4 mm are 2-bit numerical values,
Expressed as 00, 01, 10, 11. This correspondence is shown in Table 1.

[0017]

[Table 1] Then, the numerical values corresponding to the displacements of the above-mentioned 6 movable positions are concatenated to make a total of 12 bits, and this is made a gene indicating an optimization target. Thus, a gene is expressed as a code string (one-dimensional array), and the length of this gene (called the gene length) is 12, which is the same as the bit length.

When the definition of this gene is input to the computer, the random number generator then generates an early generation gene group (step S920). The genetic algorithm execution device uses the random numbers obtained from the random number generator to generate N 12-bit genes (population size: N), respectively, and stores them as an early generation gene group.

Next, based on the mutation rate, which is one of the parameters of the genetic algorithm, a certain percentage of genes among N genes are randomly selected, and one randomly selected gene on that gene is selected. The gene is mutated by inverting the value of the bit corresponding to the locus (step S930).

Next, based on the crossover rate, which is one of the parameters of the genetic algorithm, a certain number of gene pairs in N are randomly selected, and one randomly selected gene locus on the gene is selected. To one end of the gene are exchanged with each other (called simple crossover or one-point crossover) to cause crossover (step S94).
0).

Next, the fitness of each of the N genes is determined (step S950). In this case, the goodness of fit means a small resistance coefficient when each gene is converted into a phenotype, and conversion of a gene into a phenotype is called decoding. To determine the fitness of a gene, the 12-bit value of the gene is divided into 2 bits, and the position of each movable part is changed by the amount of displacement indicated by this value. The drag force received by the variable wing device is measured by and the resistance coefficient (Cd value) is calculated. This Cd value is fed back to the genetic algorithm execution device via the input device as the fitness of this gene.

In this way, when all the genes belonging to this generation are evaluated, the convergence condition (the evaluated fitness reaches a predetermined state, or a certain number of generation alternations are completed) is satisfied. It is determined whether or not (step S
960), if the convergence condition is satisfied, the optimum solution is output (step S980) and the process ends.

If the convergence condition is not satisfied, the gene having the highest fitness (the smallest Cd value) is increased according to the replication rate, which is one of the parameters of the genetic algorithm,
The same number of genes having a small fitness are removed (selected) (step S970), and the process returns to the mutation step (S930). By repeating this, the shape of the variable wing device having the minimum Cd value, that is, the optimum solution is obtained. The parameters of each genetic algorithm are as follows: gene length L = 12, population size N = 3, mutation rate αM = 2/3, crossover rate αC =
FIG. 15 shows a situation where the ratio is 2/3 and the copy rate is 1/3.

The above-mentioned genetic algorithm shows an example of a conventional genetic algorithm or evolutionary algorithm. For example, the order of crossover, mutation, and duplication is arbitrary, and duplication and mutation Some of them differ in how they are made, some differ in the method of crossover such as two-point crossover for exchanging genes between two points, and some have neither crossover nor mutation.

[0025]

By the way, if the problem of applying the genetic algorithm is different, the duplication rate, crossover rate,
Optimal values of the parameters of the genetic algorithm itself, such as the mutation rate, change. For example, in the optimization of the blade shape, the optimum parameter value of the genetic algorithm is different when the blade base shape is different or when the wind speed when obtaining the resistance coefficient is different.

However, in the conventional optimization method using the genetic algorithm, a method for optimizing these parameters according to the problem has not been established, and these parameters have been set by trial and error. Therefore, there is a problem that it takes a very long time to obtain an optimum solution or an approximate solution of the problem by the genetic algorithm, or the search may fail due to falling into a local solution.

Further, since a method for optimizing these parameters according to the problem has not been established, the parameters are set depending on the personal craftsmanship (intuition) of the user of the genetic algorithm. There is a problem that it requires considerable experience to apply the genetic algorithm to the real problem.

In view of the above problems, a first object of the present invention is to provide a method for optimizing a genetic algorithm that can automate parameter optimization without depending on the problem to be applied.

A second object of the present invention is to provide a method for optimizing a genetic algorithm that can be used by anyone regardless of their experience.

[0030]

In order to solve the above problems, the present invention has the following constitution. That is, the invention according to claim 1 manipulates a gene associated with a target,
A method of optimizing a genetic algorithm for optimizing parameters of a genetic algorithm for searching an optimal solution or an approximate solution of a target, comprising: a first process of generating a gene group of an early generation; A second step of evaluating the goodness of fit for each gene belonging to any generation after the second generation, and a third step of calculating the Hamming distance of each gene with respect to the gene having the highest goodness of fit of the generation, A fourth step of obtaining a frequency distribution on a plane stretched by two axes of the Hamming distance and the goodness of fit for the generational gene group, and a fifth step of changing the parameters of the genetic algorithm according to the frequency distribution. The outline of the process is

Further, the invention according to claim 2 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching for an optimal solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, A third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness in the generation, and the frequency distribution on the plane extending on the two axes of the Hamming distance and the fitness for the gene group of the generation And the frequency distribution shows a distribution in which an optimal solution cannot be obtained by the genetic algorithm, the association between the optimization target and the gene is changed to A fifth step of returning to the second step, depending on the frequency distribution, and summarized in that comprising: a sixth step of changing the parameters of the genetic algorithm, the.

Further, the invention according to claim 3 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, The third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness of the generation and the difference in fitness between the genes belonging to the generation, which is larger than the minimum value of the fitness, divides the gene group. Alternatively, the gene group is divided by a Hamming distance step difference that is larger than the minimum value of the Hamming distance difference between the genes belonging to the generation, and the generation's inheritance is divided for each division. Fourth to determine the frequency distribution for a population
And the fifth step of changing the parameters of the genetic algorithm according to the frequency distribution.

Further, the invention according to claim 4 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize a parameter of the genetic algorithm for searching an optimal solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, At least one of the third step of calculating the Hamming distance of each gene with respect to the elite, which is the gene having the highest fitness in the generation, and the gene having the maximum Hamming distance, or both, The fourth process of creating mutant genes, and the fitness of these mutant genes and the Hamming distance of each gene to the elite, respectively. And a sixth step of obtaining a frequency distribution on a plane stretched by two axes of the Hamming distance and the fitness for the gene of these mutants and the gene of the generation, and the frequency. A seventh step of changing the parameters of the genetic algorithm according to the distribution,
The summary is that

Further, the invention according to claim 5 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, A third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness in the generation, and the frequency distribution on the plane extending on the two axes of the Hamming distance and the fitness for the gene group of the generation And a fifth step of dividing the Hamming distance into a plurality of sections and dividing the generational gene group into at least each section to form a plurality of groups. And a sixth process of expressing the existence probability of each group by a simultaneous differential equation or simultaneous differential equation using a crossover constant that does not depend on gene length, and the simultaneous differential equation or simultaneous differential equation with the frequency distribution as an initial condition. Based on the seventh step of predicting the behavior of the genetic algorithm by solving the equation and the prediction,
An eighth step of changing the parameters of the genetic algorithm is provided.

Further, the invention according to claim 6 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimum solution or an approximate solution of the object. A first step of generating a gene group of an early generation, a second step of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the generation A third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness of the group, and the frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation. A fourth step of obtaining and a fifth step of dividing the Hamming distance into a plurality of sections and dividing the gene group of the generation into at least each section to form a plurality of groups , A sixth step of expressing the existence probability of each group by a simultaneous differential equation or a simultaneous difference equation with the number of variables not more than three times the gene length using a crossover constant that does not depend on the gene length, and the frequency distribution A seventh step of predicting the behavior of the genetic algorithm by solving the simultaneous differential equations or simultaneous differential equations as an initial condition; and an eighth step of changing the parameters of the genetic algorithm based on the prediction. The summary is that

Further, the invention according to claim 7 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, A third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness in the generation, and the frequency distribution on the plane extending on the two axes of the Hamming distance and the fitness for the gene group of the generation And a fifth step of dividing the Hamming distance into a plurality of sections and dividing the generational gene group into at least each section to form a plurality of groups. And a sixth step of expressing the existence probability of each group by a simultaneous differential equation or simultaneous differential equation using a crossover constant depending on either or both of the gene length and the gene population size, and the frequency distribution A seventh step of predicting the behavior of the genetic algorithm by solving the simultaneous differential equations or the simultaneous difference equations by using as an initial condition, and an eighth step of changing the parameters of the genetic algorithm based on the prediction. The summary is that

Further, the invention according to claim 8 is an optimization of a genetic algorithm for manipulating a gene associated with an object to optimize a parameter of the genetic algorithm for searching an optimum solution or an approximate solution of the object. A first step of generating a gene group of an early generation, and a second step of evaluating the fitness of each gene belonging to an arbitrary generation of the initial generation or the second and subsequent generations, A third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness in the generation, and the frequency distribution on the plane extending on the two axes of the Hamming distance and the fitness for the gene group of the generation And a fifth step of dividing the Hamming distance into a plurality of sections and dividing the generational gene group into at least each section to form a plurality of groups. And a crossover constant depending on either or both of the gene length and the gene population size, the existence probability of each group is determined by a simultaneous differential equation or simultaneous difference equation with the number of variables that is 3 times or less the gene length. A sixth step of expressing, a seventh step of predicting the behavior of the genetic algorithm by solving the simultaneous differential equations or simultaneous differential equations with the frequency distribution as an initial condition, and a genetic step based on the prediction. An eighth step of changing the parameters of the algorithm is provided.

Further, the invention according to claim 9 is the method for optimizing a genetic algorithm according to any one of claims 1 to 8, wherein the size of the gene population of the n-th (n is a natural number) generation is The gist is that the size is made larger than the size of the n + 1th generation gene group that follows.

The invention according to claim 10 is the same as claim 1
10. The method for optimizing a genetic algorithm according to any one of claims 9 to 9, wherein the parameter is in accordance with the length of the gene associated with the optimization target, the size of the gene group, and the fitness of the gene. The gist is that it includes one parameter arbitrarily selected from the replication rate, the crossover rate, and the mutation rate, or any combination thereof.

The invention according to claim 11 uses the genetic algorithm that can be changed according to the parameter for the gene associated with the optimization target, which is an industrial or technical resource, to change generations. Is a method for optimizing a genetic algorithm for obtaining an optimal solution or an approximate solution thereof, which belongs to a first process of generating a gene group of an early generation and an arbitrary generation after the initial generation or the second generation. A second step of evaluating the fitness for each gene, a third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness belonging to the generation, and the Hamming distance for the gene group of the generation. A fourth step of obtaining a frequency distribution on a plane stretched by two axes with the goodness of fit and parameters of the genetic algorithm are changed according to the frequency distribution. Comprising the steps of 5 a method of optimizing the genetic algorithm which summarized as further comprising a.

Further, the invention according to claim 12 is a genetic algorithm analysis system for operating a gene associated with an object to analyze the behavior of the genetic algorithm for retrieving an optimum solution or an approximate solution of the object. And a fitness evaluation means for evaluating the fitness for each of the genes,
A Hamming distance calculating means for calculating a Hamming distance of each gene with respect to a gene having the highest fitness among genes belonging to a certain gene group, and a plane stretched by two axes of the Hamming distance and the fitness for the gene group. And a display unit for displaying the frequency distribution, the frequency distribution of the gene at the stage of associating the gene with the target or at any stage of the execution of the genetic algorithm. This is a genetic algorithm analysis system whose gist is that the distribution can be displayed on the display means.

Further, the invention according to claim 13 is a genetic algorithm analysis system for operating a gene associated with an object to analyze the behavior of the genetic algorithm for retrieving an optimum solution or an approximate solution of the object. And a fitness evaluation means for evaluating the fitness for each of the genes,
A Hamming distance calculating means for calculating the Hamming distance of each gene with respect to the gene having the highest fitness among genes belonging to a certain gene group, and the gene having the highest fitness is the highest layer, and another gene is set for each Hamming distance. And a gene phylogenetic tree for creating a gene phylogenetic tree in which genes having different Hamming distances of 1 are related to each other by genes having different signs indicating each locus by 1 And a display means for displaying, which is capable of displaying the gene phylogenetic tree on the display means at a stage of associating a gene with a target or at any stage of execution of a genetic algorithm. Is a genetic algorithm analysis system.

[0043]

As described above, according to the first aspect of the present invention, a plane stretched by two axes of the Hamming distance and the fitness for each gene belonging to the initial generation or any generation after the second generation. By obtaining the frequency distribution on (hereinafter referred to as the Hamming distance-fitness plane) and changing the parameters of the genetic algorithm according to this frequency distribution, the parameter optimization of the genetic algorithm is automated and the genetic algorithm is optimized. This has the effect of shortening the search time for the optimum solution. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the second aspect of the invention, the frequency distribution on the Hamming distance-fitness plane is obtained for each gene belonging to the initial generation or any generation after the second generation, and this frequency distribution is genetic. If the algorithm shows a distribution for which an optimal solution cannot be obtained, by changing the correspondence between the optimization target and the gene and generating the early generation gene group or returning to the evaluation of the fitness for each gene, the genetic It is said that it is possible to eliminate unnecessary processing time due to the correspondence between optimization objects and genes that are inappropriate for the algorithm, automate the parameter optimization of the genetic algorithm, and shorten the search time for the optimal solution by the genetic algorithm. Produce an effect. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the third aspect of the present invention, the Hamming distance and the fitness are calculated for each gene belonging to the initial generation or any generation from the second generation onward, and the fitness between the genes belonging to this generation is calculated. This fitness group is created by dividing this gene group by a difference in fitness that is greater than the minimum difference, or a Hamming distance that is greater than the minimum difference in Hamming distance between genes that belong to this generation. Since the frequency distribution is determined for each gene group of this generation for each generation, even when the frequency distribution includes many small peaks and valleys, small peaks and valleys on the frequency distribution that do not affect the value of the optimization parameter are removed. , Extracting the macroscopic peak-valley shape of the frequency distribution that shows the basic nature of the problem,
Since it can be associated with the optimum value of the parameter, the parameter optimization can be automated, and the search time for the optimum solution by the genetic algorithm can be shortened. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

Further, according to the invention of claim 4, whichever of the gene having the highest fitness, elit, which belongs to any generation from the initial generation or the second generation onward, and the gene whose Hamming distance is farthest from this elite, At least one mutant gene is prepared from one or both of them, and the frequency distribution on the Hamming distance-fitness plane is obtained for the genes of these mutants and the genes of this generation, and the genetic algorithm is calculated according to this frequency distribution. By changing the parameters of, it is possible to supplement the frequency distribution of the part with a small number of genes on the Hamming distance-fitness plane, and more accurately automate the parameter optimization of the genetic algorithm, This has the effect of shortening the search time for a solution. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

Further, by determining the fitness of the elite variant, it becomes easy to determine whether or not the optimum solution (or a solution equivalent thereto) is stable, and the stability of the calculated optimum solution against disturbances is improved. Is effective.

With respect to the stability of the optimum solution against disturbance, for example, when manufacturing an optimum blade shape, an error within a predetermined accuracy occurs due to manufacturing tolerances. In addition, the wing shape may change due to the actual use environment (for example, change in load during flight). Therefore, it is not desirable that a subtle change in shape from the optimum blade shape causes a significant increase in the resistance coefficient. Therefore, there is an effect that the stability evaluation of the optimum solution, which is important depending on the nature of the problem to be applied, can be presented together.

According to the invention of claim 5, the frequency distribution on the Hamming distance-fitness plane is determined for each gene belonging to the initial generation or any generation after the second generation, and the genes on this plane are identified. The behavior of the genetic algorithm is divided into multiple groups and the simultaneous differential equations or simultaneous differential equations indicating the existence probabilities of these groups are solved by using the crossover constant that does not depend on the gene length, with the frequency distribution as the initial condition. Can be predicted.

By changing the parameters of the genetic algorithm based on this prediction, the optimization of the parameters of the genetic algorithm can be automated, and the search time for the optimal solution by the genetic algorithm can be shortened. Play. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the sixth aspect of the present invention, the frequency distribution on the Hamming distance-fitness plane is obtained for each gene belonging to the initial generation or any generation from the second generation onward, and the genes on this plane are hummed. By dividing into a plurality of groups according to the distance and using a crossover constant that does not depend on the gene length, simultaneous differential equations or simultaneous difference equations with the number of variables less than or equal to 3 times the gene length indicating the existence probability of each group are described above. The behavior of the genetic algorithm can be predicted by solving the frequency distribution as an initial condition.

By changing the parameters of the genetic algorithm based on this prediction, it is possible to automate the parameter optimization of the genetic algorithm and shorten the search time for the optimal solution by the genetic algorithm. Play. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

Further, according to the invention of claim 7, the frequency distribution on the Hamming distance-fitness plane is obtained for each gene belonging to the initial generation or any generation after the second generation, and the genes on this plane are identified. Divide into multiple groups, and use a crossover constant that depends on either or both of the gene length and the gene population size to create a simultaneous differential equation or simultaneous differential equation that indicates the existence probability of each of these groups. By solving as a condition, the behavior of the genetic algorithm can be predicted.

By changing the parameters of the genetic algorithm based on this prediction, it is possible to automate the optimization of the parameters of the genetic algorithm and shorten the search time for the optimal solution by the genetic algorithm. Play. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the invention of claim 8, a frequency distribution on the Hamming distance-fitness plane is obtained for each gene belonging to the initial generation or any generation from the second generation onward, and the genes on this plane are identified. A variable which is divided into a plurality of groups according to the Hamming distance, and which indicates the existence probability of each of these groups by using a crossover constant depending on one or both of the gene length and the gene population size The behavior of the genetic algorithm can be predicted by solving a number of simultaneous differential equations or simultaneous differential equations with the frequency distribution as an initial condition.

By changing the parameters of the genetic algorithm based on this prediction, it is possible to automate the parameter optimization of the genetic algorithm and shorten the search time for the optimal solution by the genetic algorithm. Play. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the invention of claim 9, the n-th
By making the size of the gene group of the generation larger than the size of the gene group of the subsequent n + 1 generation, by obtaining the frequency distribution on the Hamming distance-fitness plane for the gene group of the nth generation having a large number of samples, Further, it is possible to obtain the frequency distribution that represents the nature of the problem even more accurately. Further, it has an effect of increasing the search density in the initial stage of the execution of the genetic algorithm and improving the convergence to the optimum solution.

According to the tenth aspect of the invention, the parameters are the length of the gene associated with the optimization target, the size of the gene group, the replication rate according to the fitness of the gene, and the crossover rate. And by including one parameter arbitrarily selected from the mutation rates or any combination thereof, the parameter optimization of the genetic algorithm is automated, and the search time for the optimal solution by the genetic algorithm is shortened. There is an effect that can be. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the invention of claim 11, the frequency distribution on the Hamming distance-fitness plane is obtained for each gene belonging to the initial generation or any generation from the second generation onward, and the frequency distribution is determined according to this frequency distribution. By changing the parameters of the genetic algorithm, it is possible to automate the parameter optimization of the genetic algorithm and shorten the search time of the optimum solution that optimizes the industrial or technical resources by the genetic algorithm. Play. In addition, it is possible to make the optimization method of the genetic algorithm available to anyone without any experience.

According to the twelfth aspect of the present invention, a plane stretched by two axes of the Hamming distance and the goodness of fit at the stage of associating the gene with the object or at any stage of execution of the genetic algorithm. Find the frequency distribution of the above genes,
By displaying on the display means, it is possible to determine the compatibility between the optimization target and the genetic algorithm, and to observe the macroscopic behavior of the genetic algorithm.

According to the thirteenth aspect of the present invention, at the stage of associating a gene with an object or at any stage of executing a genetic algorithm, another Hamming distance from the gene having the highest fitness is changed. Genes are hierarchically classified, and a gene phylogenetic tree in which genes having different Hamming distances of 1 and different signs of each locus are associated with each other is created and displayed. The effect of being able to determine the compatibility with the genetic algorithm and observing the macroscopic behavior of the genetic algorithm is obtained.

[0062]

Embodiments of the present invention will now be described in detail with reference to the drawings. FIG. 1 is a block diagram showing the configuration of an apparatus that executes the method for optimizing a genetic algorithm according to the present invention. In FIG. 1, the genetic algorithm optimizing device 1 optimizes various parameters of the genetic algorithm based on the input device 103, the gene distribution calculating device 5 for obtaining the gene distribution, and the calculation result of the gene distribution calculating device 5. Parameter setting device 7 to be converted, genetic algorithm execution device 9, random number generation device 111, output device 113, auxiliary storage device 115, and printer 117.
And a console 119, a variable blade device 121, a mechanical device 123 incorporated in the variable blade device 121, and a resistance coefficient measuring device 125.

The genetic algorithm optimizing apparatus 1 is configured by adding a gene distribution calculating apparatus 5 and a parameter setting apparatus 7 to the conventional genetic algorithm optimizing apparatus 101 shown in FIG. The components of
Since it is the same as the constituent element of the conventional example shown in FIG. 11, the same reference numerals are given and duplicate description is omitted.

First, consider a population of all possible genes (2 powers of 2) expressed in binary with length L (L = 12). Then, the gene of the optimum shape (Cd = 0.88)
2), each gene is classified into a hierarchy according to the Hamming distance from the code: 111100001010 indicating the optimum species).
The distribution is as shown in. Since L = 12, the Hamming distance from the optimal species (hereinafter, the Hamming distance from the optimal species is simply referred to as the Hamming distance unless otherwise specified) is 0 to the optimal species gene, which indicates the optimal species itself. The number of genes classified into the hierarchy of each Hamming distance i is 12, which is a combination of 12 i, that is, C (12, i).

The distribution shape for each layer has a Hamming distance of 0.
There is one gene in each of 1 and 12, and it becomes a diamond with the maximum number C (12,6) at the Hamming distance of 6 (= L / 2). Within each layer composed of genes with equal Hamming distances, there is no one with the same numerical sequence, but there may be one with the same goodness of fit. Therefore, a frequency distribution (this is referred to as a degenerate structure) on a plane (hereinafter, referred to as a Hamming distance-fitness plane) in which all possible powers of 2 L genes are stretched on two axes of the Hamming distance and the fitness. ), The distribution is as shown in FIG. 3, for example.

The shape of this frequency distribution is determined according to the method of coding the solution candidate of the problem in a gene and the phenotypic fitness function (evaluation function) decoded from this gene. That is, the shape of this frequency distribution does not depend on the parameters of the genetic algorithm such as the size of the gene group, the replication rate according to the fitness of the gene, the crossover rate, and the mutation rate, and the nature of the problem is objective. It is also a quantitative measure. However, investigating the distribution of all 2 L power genes, that is, finding all the solutions, does not need to use a genetic algorithm.

Therefore, assuming that the population size of the genes of the genetic algorithm in the initial generation is N (0 << N << 2L), the Hamming distance-for N genes generated by random numbers
Frequency distribution on the fitness plane (this is called the initial degenerate structure)
Ask for. If N is large to some extent, according to the law of large numbers,
It can be expected that the shape of the frequency distribution of this early generation is close to the shape obtained by compressing the distribution shape of FIG. 3 to N / 2L in the frequency axis direction (similar to the distribution shape of FIG. 3). From this, using the initial degenerate structure, we consider the optimization of the parameters of the genetic algorithm as shown below.

The initial degenerate structure of N genes in this early generation population gives the landscape of the genetic algorithm when the problem is associated with genes. As a result, the initial degenerate structure is determined by each parameter of the genetic algorithm, crossover rate αC, mutation rate αM, replication rate, gene length L,
The respective optimum values of the population size N have a one-to-one correspondence or have a strength correlation. This explanation is given in Reference 1 (Four-Group Equ) by the present inventor.
ation of Genetic Algorithm
m, JSME International Jour
nal, Series C, Vol. 38, no. 2, 1
995).

Next, it will be considered to optimize the parameters of the genetic algorithm by utilizing this correspondence relationship with respect to an arbitrary problem. Therefore, regarding various problems in advance,
Hamming distance-Fitness distribution Frequency distribution on the plane and various values of the parameter are used to actually execute the genetic algorithm to find the optimum parameter, and the correspondence table (map) between the initial degenerate structure and the optimum value of the parameter Is created and stored in the parameter setting device 7, the auxiliary storage device 115, or the like.

Then, when a problem to be solved is given by the genetic algorithm, the initial degenerate structure of this problem is obtained by the gene distribution calculation device 5 and the above correspondence table is searched to obtain optimum parameters. Next, using this parameter, the genetic algorithm execution device 9
By executing the genetic algorithm, the optimal solution can be obtained in a short time, and the execution time can be shortened.

An operator who has no experience of using the genetic algorithm can execute the genetic algorithm by using the optimum parameters. Further, the means for obtaining the initial degenerate structure and the initial degenerate structure-parameter optimum value correspondence By linking with the search means of the table, the parameter optimization of the genetic algorithm can be automated without human intervention.

Further, the conditions for evaluating the conformity (for example, the wind speed for obtaining the resistance coefficient, the conformity evaluation function, etc.) are changed, and independent optimization can be performed according to various unexpected environmental changes.

FIG. 4 is a flow chart showing the first embodiment of the method for optimizing a genetic algorithm according to the present invention. In the flowchart of FIG. 4, the parameters of the genetic algorithm are determined according to the frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness of each gene with respect to the gene having the highest fitness for the gene group of the early generation. The procedure for changing the is shown.

First, the target problem is encoded into a character string so as to be associated with a gene (step S110).
Next, an early generation gene group having a population size N is generated (step S120). A random number obtained from the random number generator 111 may be used for the generation of this early generation gene group, or a Lorentz model for heat convection or a spring.
A numerical value obtained from a non-linear equation expressing the vibration of the mass system may be used as the value of the gene group of the early generation. Of course, any value can be used as the gene group of the early generation.

Next, the fitness of each gene belonging to this early generation is evaluated (step S130). In the gene compatibility evaluation, each gene is decoded, and a variable wing device control signal is output from the output device 113 to the mechanical device 123 to change the wing shape, which is the phenotype of the gene. The resistance force of the variable blade device 121 whose shape has changed is measured by the resistance coefficient measuring device 125 in the wind tunnel, and the resistance coefficient (Cd value) is calculated from this resistance force. The Cd value corresponding to each gene is returned to the genetic algorithm execution device 9 via the input device 103.

When the evaluation of the fitness of all the genes belonging to the initial generation is completed, the gene distribution calculator 5 calculates the initial degenerate structure of the genes. In this calculation, first, with reference to the sign of the gene with the highest fitness among the genes of this early generation, the number of different signs of the corresponding loci of each gene is counted to obtain the Hamming distance (step S140). The definition of the Hamming distance is the same as the Hamming distance used in general code theory.

Next, all the genes belonging to this generation are plotted on the plane stretched by the two axes of the Hamming distance and the goodness of fit to obtain the frequency distribution (step S150). This frequency distribution (initial degenerate structure) shows the macroscopic behavior of this gene group in the genetic algorithm.

Next, the parameter setting device 7 optimizes the parameters of the genetic algorithm, for example, the duplication rate, the crossover rate, the mutation rate, etc., according to this frequency distribution (step S160). Then, using these optimized parameters, the genetic algorithm execution device 9 performs processing such as mutation, crossover, selection, and duplication to generate a next-generation gene group (step S170). Next, with respect to this gene group, the fitness is evaluated for each gene as in step S130 (step S180).

Next, it is determined whether or not the convergence condition is satisfied (step S190). If the convergence condition is satisfied, the optimum solution is output (step S200) and the process ends.

If the convergence condition is not satisfied, the process returns to step S170 to continue the execution of the genetic algorithm.

In the present embodiment, the frequency distribution on the Hamming distance-fitness plane is obtained for the gene group of the initial generation, but the Hamming distance-adaptation is not limited to the gene group of any generation, not limited to the initial generation. The frequency distribution on the frequency plane may be obtained, and the parameters of the genetic algorithm may be optimized according to this frequency distribution.

FIG. 5 is a flow chart showing the second embodiment of the method for optimizing a genetic algorithm according to the present invention. In the flowchart of FIG. 5, for a gene group of the early generation, a frequency distribution on a plane stretched by two axes of the Hamming distance and the fitness of each gene with respect to the gene having the highest fitness is obtained, and this frequency distribution is genetic. The procedure for changing the correspondence between the optimization target and the gene is shown when the distribution is such that the optimal solution cannot be obtained by the algorithm. Note that the same step numbers are given to the same steps as those in the first embodiment of the optimization method shown in FIG. 4, and duplicate description will be omitted.

In FIG. 5, steps S110 to S150 are the same as those in the first embodiment shown in FIG. Next, the shape of the frequency distribution of the genes on the Hamming distance-fitness plane is determined, and it is determined by the genetic algorithm whether or not the distribution yields the optimum solution (step S1).
52). When the shape of this frequency distribution is steep, it is considered that the optimal solution cannot be obtained by the genetic algorithm, and the association between the optimization target and the gene performed in the previous step S110 is changed ( Step S154), and the process returns to step S120 or step S130.

This change is, for example, to change the correspondence between the optimization target and the gene shown in Table 1 described in the section of the prior art to the correspondence shown in Table 2 or Table 3 below.

[0085]

[Table 2]

[Table 3] In the determination of step S152, no matter how the correspondence between the optimization target and the gene is changed, if the initial degenerate structure is such that the optimum solution cannot be obtained, this is a problem unsuitable for the genetic algorithm. It will be canceled by the appropriate termination condition.

If it is determined in step S152 that the distribution obtains the optimum solution by the genetic algorithm, then the procedure from step S160 onward is executed as in FIG.

FIG. 6 is a flow chart showing the third embodiment of the genetic algorithm optimizing method according to the present invention. In the flowchart of FIG. 6, the frequency distribution on the plane extended by two axes of the Hamming distance and the fitness of each gene with respect to the gene having the highest fitness is calculated in the early generation gene group, and the frequency distribution is very high. If there are many peaks and the map cannot find the correspondence between the initial degenerate structure and the optimum value of each parameter of the genetic algorithm, a procedure using a macroscopic frequency distribution on the Hamming distance-fitness plane is shown. ing. Note that the same step numbers are given to the same steps as those in the first embodiment of the optimization method shown in FIG. 4, and duplicate description will be omitted.

In FIG. 6, steps S110 to S150 are the same as those in the first embodiment shown in FIG. Next, the shape of the frequency distribution of genes on the Hamming distance-fitness plane is determined, and it is determined whether or not there are many peaks and valleys (step S156). When this frequency distribution has a large number of peaks and valleys, the number of patterns becomes huge, and the shape of the frequency distribution and the map of the optimum parameter cannot be used. Therefore, either the Hamming distance or the goodness of fit, or Both division range (hereinafter,
The window is enlarged) to obtain a macroscopic frequency distribution (step S158).

Since the nature of the problem that affects the optimization process of the genetic algorithm is the large peaks and valleys of this degenerate structure, the distribution shape obtained by taking a relatively large window for obtaining the frequency. Is sufficient, and the parameters of the genetic algorithm are optimized using this macroscopic frequency distribution. The process thereafter is step S16 in FIG.
This is the same as the processing of 0 or less.

As an example of the window size, the Hamming distance is 6
The fitness of each gene is 1.0, 0.95, 0.91, 0.72, 0.6
In the case of 6,0.65,0.65,0.33,0.31, the smallest difference of goodness of fit is 0.01. At this time, the frequency distribution when the width for measuring the frequency in the goodness-of-fit direction (fitness difference) is set to 0.01 and the frequency distribution when the width for measuring the frequency in the goodness-of-fit direction is set to 0.10.
Shown in (a) and (b). In FIG. 7A, there are five mountains, and FIG.
In FIG. 7B, the number of peaks is three, and the small peak-valley shape does not affect the value of the optimization parameter. Therefore, the distribution of FIG. 7B is used as the initial degenerate structure.

FIG. 8 is a flow chart showing the fourth embodiment of the genetic algorithm optimizing method according to the present invention. In the flowchart of FIG. 8, a gene having the highest fitness (hereinafter referred to as an elite) and a gene having the longest Hamming distance from this elite are generated for the gene group of the early generation, and the genes of the early generation and these are generated. A procedure for obtaining a frequency distribution by combining with mutant genes is shown. Note that the same step numbers are given to the same steps as those in the first embodiment of the optimization method shown in FIG. 4, and duplicate description will be omitted.

In FIG. 8, steps S110 to S140 are the same as those in the first embodiment shown in FIG. Then, the gene with the highest fitness is set as the elite,
At least one mutant of this elite and at least one mutant of the gene with the longest Hamming distance from the elite (hereinafter referred to as opposite species) are prepared (step S1).
42).

The elite and its mutant can supplement the frequency distribution of the gene in the portion with a small Hamming distance, and the opposite species and its mutant can supplement the frequency distribution of the gene in the portion with a large Hamming distance. As a result, it is possible to correct that the frequency distribution of the gene group of the early generation largely deviates from the distribution shape of all possible genes, and to approximate the distribution shape of a similar shape.

Then, the goodness of fit and the Hamming distance of these mutants are obtained (step S144), and the frequency distribution on the Hamming distance-fitness plane is obtained for the initial generation and the mutants (step S146). The subsequent processing is shown in FIG.
This is the same as the processing from step S160 onward.

FIG. 9 is a flow chart showing the fifth embodiment of the method for optimizing a genetic algorithm according to the present invention. In the flowchart of FIG. 9, the frequency distribution on the Hamming distance-fitness plane is obtained for the gene group of the early generation, and simultaneous differential equations or simultaneous differential equations indicating the existence probabilities for each group of genes divided according to the Hamming distance are calculated. A procedure is described for standing, solving the simultaneous equations to predict the behavior of the genetic algorithm, and optimizing the parameters of the genetic algorithm based on this prediction. Note that the same step numbers are given to the same steps as those in the first embodiment of the optimization method shown in FIG. 4, and duplicate description will be omitted.

Further, the existence probability of each group can be considered not as a continuous function on the time axis but as a function of the number of generations as a discrete value, when attention is paid to the generational alternation of the gene group. Although it is expressed by a difference equation, it will be called a differential equation for the sake of simplicity.

In FIG. 9, steps S110 to S150 are the same as those in the first embodiment shown in FIG. Then, the Hamming distance is divided into a plurality of sections, and the genes are grouped according to the sections (step S16).
2).

Next, the existence probability of the gene group for each group is expressed by a simultaneous differential equation as shown in equation (1) (step S164).

[0099]

[Equation 1] In Expression (1), xi (t) is the existence probability of the genes of group i at time t. αC, αM is, _their respective crossover rate, is a mutation rate. Ci, jk, Bi, _{jk ,} Mi,
_{j, is,} when each _Re its Re group j and the group k was crossing, the ratio of the group i is increased, when the group j has been replicated to the group k, is the probability that a group i increases. Incidentally, Ci, jk assumes that depend on one or both of the _gene length and gene cluster size.

Then, using the initial degenerate structure, which is this frequency distribution, as an initial condition, the simultaneous differential equations shown in equation (1) are solved, and the change in the existence probability with respect to the passage of time for each gene group is obtained to obtain the genetic The behavior of the algorithm is predicted (step S166).

This group division method includes a method of dividing genes into four groups according to the Hamming distance. That is, the group A is the optimum species with the highest fitness, the group B is a group from Hamming distance 1 to Lc (for example, Lc = L / 8), the group C is all the remaining species, and the group B is the group B1. And group B2.
In the frequency distribution in the goodness-of-fit direction of the B-group, if the peak value of the frequency is fB2, the B1 group is any one species having a goodness-of-fit value of fB2 to 1.0, and the other species are the B2 group. To do.

The time change of the existence probability of each group shows the behavior of the genetic algorithm, and if the time for solving the simultaneous differential equations is sufficiently shorter than the time for executing the genetic algorithm, the parameters of the genetic algorithm are set. Can be obtained by trial and error without executing the genetic algorithm.

According to the research by the inventor, when the physical evaluation process is not included, the execution time of the genetic algorithm and the operation time for solving the simultaneous differential equations showing this macroscopic behavior are the same number of generations. By comparison, the latter has a CPU time of a few tenths or less of the former (using computer: CRY YM
P-1) was found to be completed (Reference 2: Ken Naito,
Genetic Algorithm's macroscopic equation,
Proceedings of 4th Works
op on Complex System, Kyot
o, 1995).

Thus, the optimum parameter value of the genetic algorithm is obtained by solving the equation (1) using various parameters with the initial degenerate structure as the initial condition (step S168). Next, using this optimum value, the process proceeds to the execution of the genetic algorithm from step S170.

[0105] Next, as a modification of the fifth embodiment, when the group j and group k are cross, Ci group i is an increasing proportion, a jk, as does not depend on the _gene length or population size Good.

As a modification of the fifth embodiment, if the number of groups into which the gene group is divided is increased, the variables are increased in accordance with the increased number of groups, and the simultaneous differential equations are increased, the behavior of the genetic algorithm can be predicted. Accuracy improves. However, in a multivariable system with a gene length of three times or more, the time for solving simultaneous differential equations cannot be said to be smaller than the time for executing a genetic algorithm, and the number of variables is three times the gene length. Is the limit.

Next, as a sixth embodiment, an example in which the gene group size of the nth (n is a natural number) generation is made larger than the gene group size of the (n + 1) th generation and thereafter will be described. When the frequency distribution on the Hamming distance-fitness plane is obtained from the gene group of a certain generation and the behavior of the genetic algorithm is inferred from the degenerate structure indicated by this frequency distribution, the larger the gene group size is, the more accurate the frequency becomes. Distribution is obtained. Therefore, the gene population size of the generation for which the frequency distribution is to be determined is set to, for example, 2N and 3N, and is made larger than the population size N of this generation and thereafter. Other processes are the same as those in the other embodiments. This makes it possible to more accurately predict the behavior of the genetic algorithm. The generation for which the frequency distribution is obtained depends on the gene generation method, but the initial generation is generally preferable.

Next, an example in which the present invention is applied to optimization of fuel injection of a gasoline engine will be described with reference to FIG. The genetic algorithm optimizing device 11 of FIG.
Instead of the variable wing device 121 of the genetic algorithm optimization device 1 of FIG. 1, an engine test device 51 is connected,
The fuel injection conditions that minimize pollutants in the exhaust gas are sought.

The engine test apparatus 51 is equipped with an engine control C
PU53, air flow meter 55, and air cleaner 5
7, a fuel pump 59, a speedometer 61, a throttle sensor 63, an injector 65, and a spark plug 6
7, an ignition coil 69, and a water temperature sensor 71
A knock sensor 73, an O2 sensor 75, a distributor 77 having an engine speed detection function, an exhaust gas measuring device 79, a muffler 81, and a three-way catalytic converter 83.

The engine control CPU 53 has an intake air amount signal from the air flow meter 55 and a throttle sensor 63.
From the throttle opening signal, from the water temperature sensor 71 to the cooling water temperature signal, from the knock sensor to the knocking detection signal, from the O2 sensor 75 to the oxygen concentration signal in the exhaust gas, and from the distributor 77 as the engine speed. Further, the engine control CPU 53 outputs a fuel injection signal to the injector 65 for each cylinder and an ignition timing signal to the ignition coil 69, respectively.

Since the optimizing device 11 of the present embodiment seeks the fuel injection condition that minimizes the pollutants in the exhaust gas, the compatibility is determined by the exhaust gas measuring device 79 such as CO, NOx, etc. Either the exhaust gas concentration or the exhaust gas amount, the oxygen concentration obtained from the O2 sensor 75, the engine speed obtained from the distributor 77, or any combination thereof. The measured value of the exhaust gas measuring device 79, the measured value of the O2 sensor 75, and the engine speed obtained from the distributor 77 are taken into the gene distribution calculation device 5 and the genetic algorithm execution device 9 via the input device 13, respectively.

The fuel injection amount, fuel injection timing, and ignition timing to be optimized are, for example, changed from the conventional standard fuel injection control map in the range of -8% to + 7% in steps of 1%. Adjust the stages. For this reason, a locus of 4 bits is assigned to each of the control amounts of the fuel injection amount, the fuel injection timing, and the ignition timing to make a gene of 12 bits in total.

Genes output from the genetic algorithm execution unit 9 to the phenotype for decoding are output from the output unit 15.
The engine control CPU 53 is instructed to change each control amount via. The engine control CPU, from the conventional standard fuel injection control map, by the control amount instructed by the output device 15,
The fuel injection amount, the fuel injection timing, and the ignition timing are changed. Then, in this engine rotating state, the exhaust gas measuring device 79, the O2 sensor ₇ 5, distributor 7
7, or an evaluation value of engine performance obtained from any combination thereof as the degree of conformity to the input device 13
Taken from.

This genetic algorithm optimizing device 11
The parameter optimization procedure according to step 1 may use any of the embodiments of the optimization method described above. The optimized fuel injection control map is obtained in a short time by the genetic algorithm using the parameters of the optimized genetic algorithm. After that, the ROM in which this map is written is mounted on a commercial vehicle to contribute to the reduction of air pollution.

Although the preferred embodiments have been described above, these do not limit the present invention. For example, in the embodiment, the behavior of the genetic algorithm is predicted by obtaining the frequency distribution on the Hamming distance-fitness plane for the gene group of the early generation, but even if the frequency distribution is obtained for the gene group of the second generation and thereafter. Good.

In the embodiment, the decoding of the gene into the phenotype includes a physical model and a physicochemical model of the variable wing device, the engine test device, etc. However, depending on the problem to be applied, the numerical calculation or the It is obvious that the present invention can also be applied to the case where the degree of compatibility can be obtained by arithmetic processing such as logical operation.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a genetic algorithm optimizing apparatus according to the present invention.

FIG. 2 is a diagram showing a gene phylogenetic tree in a genetic algorithm.

FIG. 3 is a diagram showing frequency distributions of all species on a Hamming distance-fitness plane.

FIG. 4 is a flowchart showing a first embodiment of a method for optimizing a genetic algorithm according to the present invention.

FIG. 5 is a flowchart showing a second embodiment of a genetic algorithm optimizing method according to the present invention.

FIG. 6 is a flowchart showing a third embodiment of a genetic algorithm optimizing method according to the present invention.

FIG. 7 is a diagram showing an example of gene frequency distribution in a cross section with a Hamming distance of 6;

FIG. 8 is a flowchart showing a fourth embodiment of a genetic algorithm optimizing method according to the present invention.

FIG. 9 is a flowchart showing a fifth embodiment of the method for optimizing a genetic algorithm according to the present invention.

FIG. 10 is a block diagram showing a device configuration when the genetic algorithm optimization method according to the present invention is applied to engine control optimization.

FIG. 11 is a block diagram showing a configuration of an optimizing apparatus using a conventional genetic algorithm.

FIG. 12 is a partial cross-sectional perspective view showing the structure of a variable blade device.

FIG. 13 is a flowchart showing an example of a conventional genetic algorithm.

FIG. 14 is a diagram illustrating gene expression information of a wing shape.

FIG. 15 is a diagram illustrating a genetic algorithm.

[Explanation of symbols]

1 ... Genetic algorithm optimizing device, 5 ... Gene distribution calculating device, 7 ... Parameter setting device, 9 ... Genetic algorithm executing device, 103 ... Input device, 111 ... Random number generating device, 113 ... Output device, 115 ... Auxiliary Storage device, 11
7 ... Printer, 119 ... Console, 121 ... Variable wing device, 123 ... Mechanical device, 125 ... Resistance coefficient measuring device.

Claims (13)

[Claims] 1. A method for optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimum solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to the gene, and a fourth step of obtaining a frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, A fifth step of changing a parameter of a genetic algorithm according to the frequency distribution, and a method of optimizing a genetic algorithm. 2. A method for optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: A second step of evaluating the fitness for each gene belonging to the generation or any generation after the second generation, and a third step of calculating the Hamming distance of each gene with respect to the gene having the highest fitness belonging to the generation. And a fourth step of obtaining a frequency distribution on a plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, and the frequency distribution cannot obtain an optimum solution by a genetic algorithm. A fifth step of changing the correspondence between the optimization target and the gene and returning to the first or second step when showing a distribution; and a genetic algorithm according to the frequency distribution. Optimization method of the genetic algorithm, characterized in that the steps of the sixth, with the changing parameters of the beam. 3. A genetic algorithm optimization method for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. The third step of calculating the Hamming distance of each gene with respect to the gene, and dividing the gene group by the fitness difference which is larger than the minimum value of the fitness difference between the genes belonging to the generation, or the genes belonging to the generation The gene group is divided by a Hamming distance difference that is greater than the minimum value of the Hamming distance difference between And Mel fourth step, depending on the frequency distribution, a method of optimizing the genetic algorithm, characterized in that it comprises a fifth step of changing the parameters of the genetic algorithm, the. 4. A method for optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to an elite that is a gene, and a fourth step of producing at least one mutant gene from either or both of the elite and the gene having the largest Hamming distance. And the fifth step of calculating the fitness and the Hamming distance of each gene with respect to the elite for the genes of these mutants, respectively. A sixth step of obtaining a frequency distribution on a plane stretched by two axes of the Hamming distance and the fitness for the genes of these mutants and the genes of the generation, and a genetic algorithm according to the frequency distribution. A seventh step of changing parameters, and a method of optimizing a genetic algorithm, comprising: 5. A genetic algorithm optimization method for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to the gene, and a fourth step of obtaining a frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, A fifth step of dividing the Hamming distance into a plurality of sections and dividing the gene group of the generation into at least each section to form a plurality of groups; A sixth step of expressing the existence probability of each group by a simultaneous differential equation or simultaneous differential equation using a crossover constant, and solving the simultaneous differential equation or simultaneous differential equation with the frequency distribution as an initial condition, 7. A method for optimizing a genetic algorithm, comprising: a seventh step of predicting the behavior of the genetic algorithm; and an eighth step of changing the parameters of the genetic algorithm based on the prediction. 6. A method for optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to the gene, and a fourth step of obtaining a frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, A fifth step of dividing the Hamming distance into a plurality of sections and dividing the gene group of the generation into at least each section to form a plurality of groups; A sixth step of expressing the existence probability of each group by a simultaneous differential equation or simultaneous differential equation with the number of variables less than or equal to three times the gene length using a crossover constant; and the simultaneous distribution with the frequency distribution as an initial condition. A seventh step of predicting the behavior of the genetic algorithm by solving a differential equation or a simultaneous difference equation; and an eighth step of changing the parameters of the genetic algorithm based on the prediction. A characteristic genetic algorithm optimization method. 7. A method for optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to the gene, and a fourth step of obtaining a frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, A fifth step of dividing the Hamming distance into a plurality of sections and dividing a gene group of the generation into at least each section to form a plurality of groups; A sixth step of expressing the existence probability of each group by a simultaneous differential equation or a simultaneous difference equation using a crossover constant depending on either or both of the group size, and the simultaneous distribution with the frequency distribution as an initial condition. A seventh step of predicting the behavior of the genetic algorithm by solving a differential equation or a simultaneous difference equation; and an eighth step of changing the parameters of the genetic algorithm based on the prediction. A characteristic genetic algorithm optimization method. 8. A method of optimizing a genetic algorithm for manipulating a gene associated with an object to optimize parameters of the genetic algorithm for searching an optimal solution or an approximate solution of the object, the method comprising: The first process of generating the gene population of, and the second process of evaluating the fitness for each gene belonging to the initial generation or any generation after the second generation, and the highest fitness belonging to the generation. A third step of calculating a Hamming distance of each gene with respect to the gene, and a fourth step of obtaining a frequency distribution on the plane stretched by two axes of the Hamming distance and the fitness for the gene group of the generation, A fifth step of dividing the Hamming distance into a plurality of sections and dividing a gene group of the generation into at least each section to form a plurality of groups; A sixth step of expressing the existence probability of each group by a simultaneous differential equation or a simultaneous difference equation with the number of variables not more than 3 times the gene length, using a crossover constant depending on either or both of the group size And a seventh step of predicting the behavior of the genetic algorithm by solving the simultaneous differential equations or simultaneous differential equations with the frequency distribution as an initial condition, and changing the parameters of the genetic algorithm based on the prediction. An eighth method, and a method for optimizing a genetic algorithm, comprising: 9. The method according to claim 1, wherein when n is a natural number, the size of the n-th generation gene group is larger than the size of the subsequent n + 1-th generation gene group. 1. A method for optimizing a genetic algorithm according to item 1. 10. The parameter is arbitrarily selected from a length of a gene associated with an optimization target, a size of a gene group, a replication rate according to the fitness of a gene, a crossover rate, and a mutation rate. The method for optimizing a genetic algorithm according to any one of claims 1 to 9, further comprising one parameter or any combination thereof. 11. A genetic method for manipulating a gene associated with an optimization target, which is an industrial or technical resource, to optimize parameters of a genetic algorithm for searching an optimum solution or an approximate solution of this target. An algorithm optimization method, which is a first step of generating a gene group of an early generation, and a second step of evaluating a fitness for each gene belonging to an arbitrary generation from the initial generation or the second generation and thereafter. And a third step of calculating a Hamming distance of each gene with respect to a gene having the highest fitness of the generation, and a plane stretched by two axes of the Hamming distance and the fitness of the gene group of the generation. And a fifth step of changing the parameters of the genetic algorithm in accordance with the frequency distribution. How to optimize rugorism. 12. A genetic algorithm analysis system for operating a gene associated with an object to analyze the behavior of a genetic algorithm for searching for an optimal solution or an approximate solution of the object, wherein Goodness-of-fit evaluation means for respectively evaluating goodness-of-fit, Hamming distance calculation means for calculating the Hamming distance of each gene with respect to the gene having the highest fitness among genes belonging to a certain gene group, and the Hamming distance and the A frequency distribution calculation means for obtaining a frequency distribution on a plane stretched by two axes with the goodness of fit, and a display means for displaying the frequency distribution, and a step of associating a gene with a target, or genetic The genetic distribution characterized in that the frequency distribution of genes can be displayed on the display means at any stage of execution of the algorithm. Algorithm analysis system. 13. A genetic algorithm analysis system for manipulating a gene associated with an object to analyze the behavior of a genetic algorithm for retrieving an optimum solution or an approximate solution of the object, wherein: The fitness evaluation means for evaluating the fitness, the Hamming distance calculation means for calculating the Hamming distance of each gene with respect to the gene having the highest fitness among the genes belonging to a certain gene group, and the gene having the highest fitness And other genes are hierarchically classified according to the Hamming distance, and a gene phylogenetic tree is created in which genes that differ from each other in the Hamming distance by 1 are associated with genes that differ from each other by only one code indicating each locus. A gene phylogenetic tree creating means, and a display means for displaying the gene phylogenetic tree, a step of associating a gene with a target, In any stage of the execution of the genetic algorithm, the analysis system of the genetic algorithm, characterized in that capable of displaying the gene phylogenetic tree on the display means.