JPH07200516A - Optimizing method and optimizing device - Google Patents

Abstract

PURPOSE:To shorten the time needed for calculating a satisfactory solution of the optimization problem by providing a constitution where a certain parent genetic code replaces by itself the value of the genes of two or more parent genetic codes with the value of the genes of the parts corresponding to the value of the genes of the parent genetic codes. CONSTITUTION:In a crossing process of a genetic algorithm, three or more parent genetic codes are selected decisively or in terms of probability as the crossing objects based on some rule. Then a certain parent genetic code replaces the value of the genes of the different parts of two or more other parent genetic codes with the value of its own genes of the parts corresponding to those genetic codes. For instance, the gene d1 of the first parent genetic code is replaced with the gene d2 of the second parent genetic code, the gene d2 is replaced with the gene d3 of the third parent genetic code, and the gene d3 is replaced with the gene d1 respectively among these three genetic codes. Thus various genetic codes are acquired.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optimization method and an optimization device.

[0002]

2. Description of the Related Art A combinatorial optimization problem such as a traveling salesman problem, a scheduling problem, a knapsack problem, an LSI optimal wiring problem, or a discrete optimization problem is an evaluation function (or a cost) having a parameter as a variable. Function) and find the parameter set where those values are maximum (or minimum).
Generally, these evaluation functions (or cost functions) are multi-peaked (or multi-valleyed), and when this is solved by a conventional non-linear optimization method such as a gradient method, a maximum point, that is, a local optimum point (or a minimum point). ), The optimization ends, and there is a drawback that an unsatisfactory solution is obtained as a solution of the optimization problem.

[0003]

The drawbacks of the conventional optimization method as shown above are that the optimization problem has been held for many years.
This is due to the problem of both searching widely for the solution space and focusing on the search. The genetic algorithm, which is a multipoint parallel search algorithm, is expected as one of the solving methods for it, but in order to obtain a solution that is sufficiently satisfactory as a solution of an optimization problem, the calculation time is required. It had the problem of becoming very large.

The optimization method and the optimization apparatus of the present invention have been made in view of such a problem, and an object thereof is to achieve both wide area search and concentrated search of the solution space of the optimization problem. (EN) Provided are an optimization method and an optimization device capable of reducing the probability that optimization ends with a local optimal solution and shortening the calculation time until a sufficiently satisfactory solution is obtained as a solution of an optimization problem. is there.

[0005]

In order to achieve the above object, the optimization method of the present invention is such that one parent genetic code is two or more other parent genetic codes in the process of crossover in a genetic algorithm. The child genetic code is generated by substituting the values of the genes of the above for the values of the genes of the part corresponding to them.

Further, the optimizing device of the present invention is provided with a plurality of processors, each processor is assigned one of the contents of the parent genetic code to be crossed, and relates to another parent genetic code from another processor. In an optimizer that receives genetic information and executes a genetic algorithm that performs crossover based on it, in the process of crossover,
Each processor receives genetic information about other parental genetic codes from two or more other processors and performs crossover based on it.

[0007]

That is, in the optimization method of the present invention, when a child genetic code is generated in the process of crossing over in a genetic algorithm, a certain parent genetic code uses the gene values of two or more other parent genetic codes by itself. The values of the genes corresponding to those of are replaced.

Further, in the optimizing device of the present invention, each processor of the plurality of processors is assigned one by one the contents of the parent genetic code to be crossed over, and the genes relating to other parent genetic codes from other processors are assigned. In executing a genetic algorithm that receives information and performs crossover based on it, in the process of crossover, each processor receives genetic information about another parent genetic code from two or more other processors and performs crossover based on it. To do.

[0009]

Embodiments of the present invention will now be described in detail with reference to the drawings.

First, a genetic algorithm to which the optimization method according to the first embodiment of the present invention is applied will be described. First,
For a given optimization problem, a series of symbols (hereinafter referred to as genes) that determine the variable set, that is, the rules for generating a genetic code, and the fitness corresponding to each genetic code, Is defined so that the larger the value of, the higher the evaluation function value of the original optimization problem (or the lower cost function) of the variable set corresponding to the genetic code.

FIG. 1 is a diagram showing a logical configuration of one genetic code for explaining the outline of the present embodiment, and
An is a gene that constitutes it. First, multiple genetic codes are prepared, and these are used as parent genetic codes.

(1) First, in the selection process, the same genetic code as the parent genetic code is stochastically or deterministically duplicated according to the fitness of the parent genetic code. For example, the number of expected values serving as the function value of the fitness of the parent genetic code is stochastically or deterministically replicated at the rate of serving as the function value of the fitness. Specifically, a genetic code having a high fitness is stochastically increased, and a genetic code having a low fitness is replicated less. Alternatively, the highly adaptable genetic code is always duplicated. Alternatively, it is conceivable that a genetic code having a low fitness is not replicated at all, but various models have been conventionally proposed as a replication method according to the fitness, and this embodiment is limited to a specific method. is not.

(2) In the next crossover process, three or more parental genetic codes are deterministically selected from the parental genetic codes that have undergone the selection process and are selected according to some rule to be the target of the crossover. Here, the crossover process of the present embodiment is an extension of the concept of crossover itself from that between two parent genetic codes which has been conventionally performed.

That is, a certain genetic code includes the conventional method in which the value of a gene of only one other parent genetic code is used as the value of a gene of its own portion.
The crossover is to replace the gene values of different parts of one or more other parental genetic codes with the gene values of the part corresponding to them. This also includes adding the values of genes of other parental genetic codes having different numbers of genes included in the genetic code, that is, having different lengths, to the part where the gene does not posses itself.

In the following examples, all gene replacements are described definitely, but it is assumed that gene replacements of specific or all parts are stochastically carried out and other parts are definitely replaced. Can also be considered.

Therefore, the crossover in this embodiment is conventionally
This is an extended concept including the concept of crossover used in a genetic algorithm, that is, the values of some of the genes of two parent genetic codes are exchanged with each other to obtain a child genetic code. Also, in the case of a crossover between two conventional parental genetic codes,
If the positions of the genes to be exchanged in the genetic code are determined, the number of child genetic codes to be created will be the same as the number of parent genetic codes, 2
However, according to the crossover between three or more parent genetic codes according to the present embodiment, the number of child genetic codes can be combined and made larger than the number of parent genetic codes.

A more specific description will be given below with reference to actual examples. FIG. 2 shows the parental genetic code to be crossed. The genetic codes 01, 02, 03, 04 are parent genetic codes that are the targets of crossover. Gene a1
-H1, a2-h2, a3-h3, and a4-h4 are genes showing the contents of genetic codes 01, 02, 03, 04, respectively.

In this figure, all the parent genetic codes have the same length, but the genetic codes need not have the same length as long as the following operations are possible. In this example, for example, three parental genetic codes 01, 02,
As an example of crossover between 03, as shown in FIG. 3, d1 of the parent genetic code 01 is changed to d2 and d of the parent genetic code 02 is changed.
2 is replaced with d3 and d3 of the parental genetic code 03 is replaced with d1 as the child genetic code.

Further, as another example of the crossover between the three parent genetic codes, as shown in FIG.
1, c1 to b2 and c2, f1 to f3, parent genetic code 02 b2 and c2 to b3 and c3, f2 to f1, parent genetic code 03 b3 and c3 to b1 and c1, f3 to f2
It is possible to replace it with.

Further, as shown in FIG. 5, b1 and c1 of parental genetic code 01 are set to b3 and c3, f1 is set to f2, b2 and c2 of parental genetic code 02 are set to b1 and c1, and f2 is set to f3.
, B3, c3 of parental genetic code 03 into b2, c2, f
It is conceivable that 3 is replaced with f1.

Further, as shown in FIG. 6, b1, c1 of parental genetic code 01 is set to b2, c2, b2, c2 of parental genetic code 02 is set to b1, c1, f2 is set to f3, and parental genetic code 03 is set. It is possible to replace f3 with f2.

Each or all of the above-mentioned genetic codes shown in FIGS. 4, 5 and 6 are parental genetic codes 01, 0.
It can be used as a child genetic code by crossing between 2003 and 03.

Further, in one crossover, it is possible to select a plurality of sets of positions in the genetic code of the gene to be rewritten, and all the genetic codes of FIGS. 3, 4, 5, and 6 are set to three. It is also possible to use the child genetic code by crossing over the parent genetic codes 01, 02, 03.

The four parent genetic codes 01, 02, 0
As an example of crossover by 3, 04, as shown in FIG. 7, b1 of parental genetic code 01, b2, g1 to g3
, D2, e2 of parental genetic code 02 to d3, e3, g
2 to g4, b3 of parental genetic code 03 to b2, d3
e3 to d2, e2, g3 to g1, parental genetic code 04
The child genetic code can be obtained by replacing b4 with b3 and g4 with g2. Further, as an example of crossover between parent genetic codes having different lengths, for the parent genetic codes 11, 12, 13 composed of genes α1 to ε1, α2 to η2, and α3 to ε3 as shown in FIG. As shown in FIG. 9, γ1 of the parent genetic code 11 is replaced with γ3, ζ2 and η2 are added, and the parent genetic code 1
It is considered that the γ2 of 2 is replaced by γ1 and the γ3 of the parental genetic code 13 is replaced by γ2, and ζ2 and η2 are added as the child genetic code.

The above-described child genetic codes of FIGS. 4, 5, 6, 7, and 9 can generate a child genetic code that cannot be obtained by crossing two conventional parent genetic codes. It has the effect of being able to.

Further, which of the child genetic codes which can be combined in combination is selected as the final child genetic code is selected based on its fitness or the adaptation of its parent genetic code. An example is conceivable in which the number of child genetic codes to be created is determined according to the degree.

(3) In the next mutation process, a gene at a specific site determined probabilistically or in accordance with some rule for each child's genetic code is replaced with another code value with a predetermined probability. . These are the parental genetic codes for the next generation.

The above procedures (1) to (3) are repeated a predetermined number of times, and the genetic code of the maximum fitness obtained up to that point is taken as the solution.

As described above, according to the first embodiment described above, whether or not a plurality of sets of positions in the genetic code of a rewritten gene are permitted in one crossover, and the length of the genetic code to be crossed over is determined. Irrespective of whether or not they match, it is possible to obtain a far more diverse child genetic code including the child genetic code obtained by the crossover between two parent genetic codes that has been conventionally performed. They include a child genetic code that inherits a gene from three or more highly adaptable parent genetic codes that could never be obtained by crossover between two conventional parent genetic codes.
When the procedure from (3) to (3) is repeated the same times and compared with the conventional genetic algorithm using crossover, it is expected that the value of the maximum fitness finally obtained will be increased. That is,
It is possible to shorten the calculation time for obtaining a sufficiently satisfactory solution as the solution of the optimization problem. At the same time, it is possible to reduce the probability that the optimization will end with the local optimum solution.

An optimizing apparatus according to the second embodiment of the present invention will be described below. In the second embodiment of the present invention, when the genetic algorithm is executed by a parallel computer having a plurality of processors, each parent genetic code to be crossed is assigned to one processor. In this embodiment, when the crossover process as shown in the first embodiment is executed after the selection process, each parent genetic code 21, 22, 23, 24 is assigned as shown in FIG. Each processor 201, 202, 203,
The processor 204 receives the genetic information of the parent genetic code other than the parent genetic code assigned to each processor through the two-way communication paths 312, 313, 314, 323, 324, 334 that directly connect the respective processors. .

The rearrangement of the genetic code in each processor is such that when the genetic information of another parent genetic code required by the parent genetic code assigned to that processor is obtained, that is, those other parent genetic codes are If the selection process is completed, it may be performed immediately, and does not necessarily have to be executed synchronously. As a result, it is possible to make the messages for gene information exchange asynchronous so as to prevent message collision. For example, parental genetic code 21, 2
2 and 23 have completed the selection process, but not 24, and the parental genetic code 21 at the crossover
This is the case where only the genetic information of the parent genetic codes 22 and 23 is needed.

The child genetic code generated through the above process is stored in the memory 40, and is redistributed to each processor during the next mutation process. This memory may be provided in a distributed manner.

As described above, according to the second embodiment described above, the advantage that the calculation speed is improved by executing the genetic algorithm which is essentially suitable for parallel calculation on the parallel computer is used, and then the crossover is performed once. Whether to allow multiple sets of positions in the genetic code of the rewriting gene in
Includes a child genetic code obtained by crossover between two parental genetic codes that has been conventionally performed, regardless of whether or not the lengths of the genetic codes to be crossed are the same. You will get the code.
They include a child genetic code that inherits a gene from three or more highly adaptable parent genetic codes that could never be obtained by crossover between two conventional parent genetic codes. When the procedures of (1) to (3) are repeated and the conventional genetic algorithm using crossover is compared with the one executed on the same parallel computer, a sufficiently satisfactory solution is obtained as a solution of the optimization problem. It is possible to shorten the calculation time of.

At the same time, it is possible to reduce the probability that the optimization will end with the local optimum solution.

Needless to say, the present invention is not limited to the first and second embodiments described above, and various modifications and variations can be considered without departing from the gist of the present invention.

[0036]

As described above, according to the present invention, it is possible to obtain much more diverse child genetic codes than the child genetic codes obtained by crossover in the conventional genetic algorithm, and to solve the optimization problem. As a result, it is possible to reduce the calculation time required to obtain a sufficiently satisfactory solution.

At the same time, it is possible to reduce the probability that the optimization will end with the local optimum solution.

[Brief description of drawings]

FIG. 1 is a logical configuration diagram of a parent genetic code for explaining the outline of an example of the present invention.

FIG. 2 is a diagram showing a parent genetic code which is a target of crossover.

FIG. 3 is a diagram showing a structure of a child genetic code according to the first embodiment of the present invention.

FIG. 4 is a diagram showing another structure of the child genetic code according to the first embodiment of the present invention.

FIG. 5 is a diagram showing another configuration of the child genetic code according to the first embodiment of the present invention.

FIG. 6 is a diagram showing another configuration of a child genetic code according to the first embodiment of the present invention.

FIG. 7 is a diagram showing another configuration of a child genetic code according to the first embodiment of the present invention.

FIG. 8 is a diagram showing another configuration of the parent genetic code according to the first example of the present invention.

FIG. 9 is a diagram showing another configuration of the child genetic code according to the first example of the present invention.

FIG. 10 is a diagram showing a configuration of a parallel computer according to a second embodiment of the present invention.

[Explanation of symbols]

01, 02, 03, 04, 11, 12, 13, 21, 2
2, 23 ... Genetic code, A1 to An, a1 to h1, a2
~ H2, a3 to h3, a4 to h4, α1 to ε1, α2
η2, α3 to ε31 ... Gene, 201, 202, 20
3, 204 ... Processor, 312, 313, 314, 3
23, 324, 334 ... Communication paths.

Claims (3)

[Claims] 1. In a process of crossover in a genetic algorithm, a parent genetic code replaces a gene value of two or more other parent genetic codes with a gene value of its corresponding portion. An optimization method characterized by generating a genetic code. 2. The optimization method according to claim 1, wherein the gene value is replaced at two or more positions. 3. A plurality of processors, each processor being assigned one of the contents of the parent genetic code to be crossed over, receiving genetic information relating to the other parent genetic code from another processor, and based on that In an optimizing device for executing a genetic algorithm for performing crossover, each processor receives genetic information regarding another parent genetic code from two or more other processors in the process of crossover, and performs crossover based on the genetic information. And the optimization device.