JP2003196635A - Problem solution operation device and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reach a solution wherein a generation value has a large fitness value in a small step even to a large-scale complex problem by using a genetic algorithm. <P>SOLUTION: Assuming that a part between two crossover points of a parent chromosome is gc, genes of the parent chromosome are rearranged so that the gc parts of two parent chromosomes are constituted from the genes having the same value, and, while preserving the order of genes other than the gc part of the parent chromosome, the gc parts are crossed over, to thereby generate a child chromosome. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a solution method of a combinatorial optimization problem such as a traveling salesman problem, and more particularly to a problem solving arithmetic unit and method for searching for an optimum solution.

[0002]

2. Description of the Related Art A problem solving arithmetic unit targeted by the present invention is a device for obtaining a solution to a so-called mathematical programming problem. The target mathematical programming problem is traffic control, especially the optimal transmission path of packets in communication networks,
Or control of distribution route of power network, determination of distribution route in transportation system, schedule problem such as train schedule, bus schedule, flight schedule, load balancing method between parallel processors, and routing of connection network between processors There are controls, etc.

Among these mathematical programming problems, for the traveling salesman problem of "turning N cities in the shortest distance without allowing duplication", all combinations are searched for optimum solutions. When the method is applied, the calculation time increases exponentially as the number of cities N increases. Such problems are so-called NP-hard (non-deterministic
It is already known that there is no algorithm that finds the optimal solution within the so-called polynomial time.

From the viewpoint of strictness, that is, the optimality of the obtained solution, the conventional optimization method for obtaining the optimum solution of such a mathematical programming problem is an exact solution method as a method for obtaining an exact solution, and an approximation. It is roughly classified into an approximate solution method for obtaining the highest solution at high speed.

From the viewpoint of a solution search method,
The optimization method uses an exact enumeration or an enumeration common method for obtaining an exact optimal solution by an equalization enumeration, a rule for generating an optimal solution, or an approximate solution.
Heuristics as a method of heuristically narrowing down one solution, and an intermediate method between and, which is an exploratory method as a method for finding an approximate optimal solution by searching a partial region of the solution space. being classified.

A genetic algorithm (GA) as one of such optimization methods is a method classified into the above-mentioned and, and generates an initial population consisting of a plurality of individuals having random genes. After that, basically, the search for the optimal solution is repeated until the search end condition is satisfied, using three types of genetic manipulations such as reproduction (reproduction), crossover (crossover), and mutation (mutation). .

Here, reproduction is a process of randomly selecting some of the individuals of the previous generation to determine the individuals of the current generation, and the resulting individuals are subjected to the next crossover process. . Crossover is the process of exchanging a part of an individual, that is, by partially exchanging the genotypes of two individuals with each other to produce a new individual as a progeny, and mutation is a process of gene generation in each progeny. This is a process of exchanging or mutating a part of alleles, and in the conventional genetic algorithm, these three gene manipulations were repeatedly performed until the termination condition of the optimum solution search was satisfied.

[0008]

For such a mathematical programming problem, in order to apply a genetic algorithm to search for an optimal solution, generation alternation is repeated, and when the generation value becomes large, the generation value becomes large. There is a problem that the rate of increase of the fitness value as the evaluation value of the solution to the increase decreases, that is, the growth rate of the fitness value slows down.

This problem is particularly important when the problem for which a solution is to be searched is large and complicated, and it is possible to search for a solution that satisfies a practical fitness value within a realistic time. There was a problem that it was difficult.

The present invention, using the GA algorithm, makes it possible to reach a solution having a good evaluation value or a large fitness value at a small generation value stage even for a large-scale complex problem. The purpose is to do.

[0011]

FIG. 1 is a block diagram showing the principle of the present invention. FIG. 1 is a block diagram showing the principle configuration of a problem-solving arithmetic unit in which the concept of state transition is introduced in order to search a search space of a solution for a mathematical programming problem or the like to find an optimal solution for the purpose of solving the problem. .

In FIG. 1, a plurality of optimum solution searching means 1 are generally provided, and an optimum solution is searched for in a state in which a combination of one or more optimum solution searching methods is used. Here, the optimum solution search method is, for example, the above-mentioned reproduction, crossover, and mutation methods in a genetic algorithm, and also includes a search method other than the genetic algorithm.

The search process observation and state transition means 2 observes the search process of the optimum solution by one of the optimum solution search means 1,
When a predetermined condition is satisfied in the process of the search, the state is transited to the search by another one of the plurality of optimum solution search means 1.

Further, another problem solving arithmetic unit according to the present invention comprises a memory, a cross processing means, and an optimum solution searching means, and searches a search space of a solution for a problem to obtain an optimum solution.

The memory stores a group of chromosomes which are solution candidates for the problem. The crossover processing means includes first and second
In the parent chromosome of, the part between the two crossover points is the copy part, the copy of the first parent chromosome is the third parent chromosome, and the copy part of the third parent chromosome is the copy part of the second parent chromosome. The genes of the third parent chromosome are rearranged so that they are composed of genes having the same value as the included gene, and the order of the genes other than the copy part of the third parent chromosome is the order of the corresponding genes of the first parent chromosome. Make it the same, copy the gene of the copy part of the second parent chromosome to the copy part of the child chromosome, and copy the gene of the part other than the copy part of the third parent chromosome to the part other than the copy part of the child chromosome. By doing so, a child chromosome is generated on the memory. The optimum solution searching means searches for an optimum solution using the generated child chromosome as a solution candidate.

[0016]

In the present invention, the search for the optimum solution is performed in a state where a combination of one or more optimum solution search methods is used.
As this optimal solution search method, a combination of several methods in the genetic algorithm as described above and optimization methods other than the genetic algorithm is used.
When the same method is used in a plurality of optimum solution search means, different values may be used as search parameters, for example.

When an optimum solution search is performed by one optimum solution search means 1 in a combination state of a certain optimum solution search method, the search process is observed, and, for example, the growth rate of the fitness value of the solution is below a specified value. When a predetermined condition such as, for example, is achieved, the search for the optimal solution in that state is stopped, and the search in the state using another combination of optimal solution search methods (or a change in the search parameter) is performed. This is performed by another optimum solution searching means 1. That is, the transition of the search state of the solution is performed.

As described above, according to the present invention, each 1
The state transition of the search is performed among the plurality of optimum solution searching means 1 that searches for the optimum solution in the state using the combination of one or more optimum solution searching methods, and the effect of the search by the certain optimum solution searching means 1 is reduced. Sometimes, another optimum solution searching means 1 continues the optimum solution search.

[0019]

FIG. 2 is a block diagram showing the basic arrangement of a problem solving arithmetic unit according to the present invention. In the figure, the arithmetic unit is roughly composed of a search module 11 and a control module 12, and a plurality of search states 16-1, 16 are provided in the search module 11.
-, 16-3, ..., 16-M is provided with a search unit 13, and the control module 12 is provided with an observation unit 14 and a transition control unit 15.

The search module 11 outputs an optimum solution to the input of the problem, and a plurality of search states 16-1, which the search unit 13 in the search module 11 can take ,.
.., 16-M correspond to the optimum solution searching means 1 in FIG. 1, and are a state in which one or more optimum solution searching methods are combined. This optimal solution search method includes search methods other than the genetic algorithm method.

The control module 12 is the search module 11
The optimal solution search process is observed, and the search unit 13 in the search module 11 is caused to transit to the optimal solution search state based on the observation result. The observation unit 14 has a function of observing the rate of increase of the evaluation value (or fitness value) of the searched solution, that is, the rate of change of the fitness value with respect to the change of the generation value, the variance of the fitness value within the population of individuals in one generation, etc. It includes the function of observing, the function of observing the number of search executions, and the function of observing other evaluation criteria in the genetic algorithm. When it is determined that the effect of the search by the search unit 13 in one state has decreased, the search unit 13 changes to the search in another state, that is, the search state transitions.

To further explain the operation of each block in FIG. 2, the search module 11 outputs and controls the state of the population for each generation, such as the maximum fitness value and the variance, during the processing using the genetic algorithm. Module 1
The observation unit 14 inside 2 observes the output of the search module 11, compares the observation result with the state transition condition, and instructs the transition control unit 15 to perform the state transition according to the comparison result. Output. The transition control unit 1 that has received the instruction
By switching the search state of the search unit 13,
The search for the optimum solution by the search module 11 is continued.
The operation is repeated until the search termination condition is satisfied.

FIG. 3 is an explanatory diagram of the state transition of the optimum solution search state in the present invention. In the same figure, as the search state for searching the optimum value for a given problem,
Optimum value search state 21 to fifth optimum value search state 5 of 5
In each optimum value search state, the optimum value is generally searched in a state in which a combination of a plurality of optimum value search methods is used.

Between the optimum value search states, the transition conditions 12, 23, 25, 31, 34, for the state transition are set.
43, 51 and 54 are set corresponding to the possibility of improving the search effect. For example, from the first optimum value search state 21 to the second optimum value search state 22, the transition condition 12
Is set, and from the fifth optimum value search state 25, the transition condition 51 for the first optimum value search state 21
The transition condition 54 for the optimum value search state 24 of is set.

Next, an embodiment of the present invention will be described using the traveling salesman problem described above as a specific example. 4 and 5 are examples of city arrangement in the traveling salesman problem. FIG. 5 shows the X and Y coordinates of each city whose arrangement is shown in FIG. The traveling salesman problem is the problem of finding a solution that allows the 100 cities shown here to travel the shortest distance without allowing duplication.

In the method of solving the traveling salesman problem using a genetic algorithm, first, a traveling route that is a solution candidate is coded as a chromosome. In the present embodiment, a coding method is adopted in which a chromosome is formed by arranging city names in the order in which a salesman makes a tour using genes as city names.
FIG. 6 is an example of the coating results of solution candidates. In the figure, the first to 100th city names are coded using the numbers of each city, and 1
One solution candidate is represented as a chromosome. The total of the distances corresponding to such a traveling route corresponds to the cost of the solution, and the traveling salesman problem is to minimize the cost.

The fitness function f (x), which is the evaluation function of the solution x in the traveling salesman problem, is expressed by the following equation, for example.

[0028]

[Equation 1]

Where d _i (x) is i−1 at solution x
It is the distance between the th city and the i th city, and n is the number of cities (n = 100 in FIG. 4). However, d
₁ (x) is the distance from the starting point to the first city,
d _n (x) is the n-1th (second from the last) city and n
It shall be the distance between the second city (which is the last city and the starting point at the same time). Bias K is the product of the diameter of the circle (maximum distance between cities) obtained by connecting adjacent cities in FIG. 4 and the number n of cities.

The outside 1 on the right side of the equation (1) represents the cost of the solution x in this problem.

[0031]

[Outer 1]

The smaller the strike, the fitness function f
It can be seen that the value of (x) becomes large. FIG. 7 is an explanatory diagram of state transitions for the traveling salesman problem as an example. As shown in the figure, the optimum solution search process in this embodiment is executed by performing state transition among four states of state 0 to state 3 according to transition conditions 01, 12, 23, 31. .

FIG. 8 is an example of a combination of operations of the genetic algorithm in each state in FIG. In the same figure, in state 0, a search for an optimum solution is performed by a combination of three operations of the excellent individuals from the previous generation: splicing, reproduction (reproduction, R), and crossover (crossover, C). For the first generation,
Outstanding individuals are taken from the population of early individuals instead of the previous generation. This state 0 is a state in which initial processing is performed.

In the state 1, the operation of mutation (mutation, M) is combined with the three operations in the state 0, and the search process for the optimum solution is performed. In the present embodiment, as will be described later, processing is performed with the same operation in state 0 and state 1, for example, a parameter in the next operation of excellent individuals from the previous generation, that is, the ratio of excellent individuals attracted to the next generation is constant. However, it is naturally possible to change this parameter between state 0 and state 1. It should be noted that this state 1 is a state in which normal genetic algorithm processing is performed.

In the state 2, in addition to the four operations in the state 1, a neighborhood search is further performed, and this neighborhood search is intensively performed. In this neighborhood search, some individuals are selected from the one having a larger fitness value in the population of one generation, and the same process as the mutation is intensively repeated for each individual. In the neighborhood search, the actual change of the chromosome pattern is performed only when the fitness value is improved. The main parameter value in this neighborhood search is 1 as the number of iterations of the neighborhood search.
The number of generations per individual is 1 or more, and the range of the neighborhood search, that is, the ratio of the number of individuals to be subjected to the neighborhood search to the total number of individuals in the group is 0.0 or more and 1.0 or less.

FIG. 9 shows the concept of neighborhood search. In FIG. 9, it can be seen that a solution (chromosome) that increases the fitness value is searched for by changing the pattern of the chromosome.

The state 3 is a state in which an optimal solution is searched for by a combination of two operations, that is, the operation of excelling individuals from the previous generation and the acceptance of new individuals, and is the state of accepting a new group. The ratio of new individuals in the population as a parameter for acceptance of this new individual is 0.0
It is set between 1 and 1.0.

FIG. 10 shows the concept of acceptance (recruitment) of a new individual. In FIG. 10, it can be seen that new individuals are randomly generated, and thus the pattern of their chromosomes is widely dispersed.

Next, the parameters commonly set for each operation in the states 0 to 3 will be described. First, the total number of chromosomes in one generation, that is, the size of the population, which is the total number of individuals, is set to 10, and the proportion of successive individuals from the previous generation, that is, the generation overlap rate (the opposite concept of the generation gap rate) As a result, 40% of the people who were excellent were operated to attract the next generation. Also, mutations, ie the exchange of the values of a set of genes on one chromosome, FIG.
So one set of city name exchanges is 0.01, or 1%
Was done with a frequency of. In the mutation operation for this problem, the gene positions are pointed one by one from the left end of the chromosome, and the content of the pointed position is exchanged with the content of any other position with a probability of 1%. .

The transition condition between the states in FIG. 7 was set as a combination of the following three conditions. The first condition (Condition 1) is that the sum of the standard deviations of the genes in the 10 chromosomes as the population is below the specified value.

FIG. 11 is an explanatory diagram of this first condition.
In the same figure, for each of the n slots, the average value and standard deviation of the values (city number) of each gene in the m chromosomes are obtained. Furthermore, the sum of the standard deviations is calculated from the standard deviations for each slot, and if the sum is less than the specified value, it is assumed that the first condition is satisfied. That is, the first condition is that each chromosome is regarded as a point in the n-dimensional space, and the standard deviation with respect to the n coordinates (city number) representing the point is less than or equal to a specified value, which results in variation of the chromosome in the n-dimensional space. Means smaller.

The second condition (condition 2) is that the number of times the search process is executed exceeds a predetermined value. The third condition (condition 3) is that the growth rate of the fitness value is lower than the specified value. This is the function f that represents the fitness value.
It is determined by substituting the value of d _i (x) of the chromosome as a solution candidate into (x), calculating the fitness value for each generation, and obtaining the rate of change of the fitness value.

FIG. 12 is an explanatory diagram of the rate of change of the fitness value under the third condition. In FIG. 12, the largest value among the fitness values of a plurality of individuals belonging to each generation is plotted. As shown in the figure, the change rate of the fitness value is calculated by the following equation.

[0044]

[Equation 2]

When the inheritance operation is performed, the individual having the maximum fitness value of the previous generation is always succeeded to the next generation, so the maximum value of the fitness value in each generation does not fall below the maximum value in the previous generation. . Therefore, the maximum fitness value monotonically increases as the generation progresses.

In FIG. 7, the problem solving arithmetic unit in the embodiment searches for an optimum solution in the state 0 at the beginning, and shifts to the search in the state 1 when the transition condition 01 is satisfied. After that, the state transition of state 1 → state 2 → state 3 → state 1 → ... is repeated until, for example, the maximum execution time is reached.

In this embodiment, transition conditions 01, 12 and 23
Are all the same, and the state transition is performed when the first condition ∪ (the second condition ∩ the third condition) (3) is satisfied.

That is, in this embodiment, the second condition and the third condition are
When the above conditions are satisfied at the same time, or only the first condition is satisfied, the state transition from the state 0 to the state 1, the state 1 to the state 2, and the state 2 to the state 3 is performed. Moreover, the transition condition 31 from the state 3 to the state 1 is assumed to match the first condition. Here, the logical structure of each transition condition is the same, and different values of parameters such as threshold values can be used.

FIG. 13 shows the basic structure of the problem solving arithmetic unit shown in FIG. 2 in more detail in response to the above description. 2, the control module 12 and the search module 11 of FIG. 2 are included in a cell 30, which has an input unit 31 for receiving an input signal, an output unit 32 for outputting a solution,
A memory 33 for storing input data and a solution candidate in the search process, a fitness value calculation processing unit 34 for calculating a fitness value of a solution, a duplication / crossover processing unit 35 for performing duplication and crossover operations in a genetic algorithm, suddenly It is composed of a mutation processing unit 36 that executes a mutation operation and a neighborhood search processing unit 37 that performs the neighborhood search described above.

By combining the processing by the fitness value calculation processing unit 34, the duplication / crossover processing unit 35, the mutation processing unit 36, and the neighborhood search processing unit 37, the cell 3
0 can be set to any of the M search states 16-1 to 16-M shown in FIG.

The evaluation observation processing unit 38 corresponding to the observation unit 14 in FIG.
The transition control unit 15 is supported based on the measure, the generation gap measure that is the generation gap ratio, the growth rate measure that is the prescribed value of the growth rate of the fitness value, and the termination measure that is the maximum limit value of the number of executions. It gives necessary instructions to the GA operation transition control processing unit 39. The GA operation transition control processing unit 39 is a duplication / crossover processing unit 35,
It outputs control signals to the mutation processing unit 36 and the neighborhood search processing unit 37.

For example, the generation gap rate defined by the generation gap measure is a parameter when performing the operation of handing over excellent individuals from the previous generation. This represents the ratio of the number of individuals to be inherited to the number of individuals included in one population, and the operation of inheritance as the GA algorithm is executed according to this parameter.

By providing a plurality of cells as shown in FIG. 13,
If parallel processing is performed such that each independently searches for an optimum solution, the search efficiency is further improved. FIG. 14 is a configuration diagram of a problem solving calculation device of the present invention in which a plurality of cells to which the hill climbing method can be applied are connected in parallel. 14
In, the cells 41-1 to 41-N are connected to the migration value distribution processing unit 56 and the parallel processing control unit 57, respectively, and perform processing in parallel. Parallel processing further increases the speed of solution growth.

Each cell includes a condition 1 processing unit 52, a condition 2 processing unit 53, a condition 3 processing unit 54, a GA operation transition control processing unit 55, an input unit 42, a memory 43, an output unit 44, a fitness value calculation processing unit 45. Duplication / crossover processing unit 46,
Mutation processing unit 47, neighborhood search processing unit 48, inversion processing unit 49, recruitment processing unit 50, hill climbing processing unit 51.
Equipped with. Of these, the functions of the input unit 42, the memory 43, the output unit 44, the fitness value calculation processing unit 45, the duplication / crossover processing unit 46, the mutation processing unit 47, and the neighborhood search processing unit 48 are respectively the input unit 31 of FIG. , Memory 33, output unit 32, fitness value calculation processing unit 34, duplication / crossover processing unit 35, mutation processing unit 36, and neighborhood search processing unit 37.

The inversion processing unit 49 of FIG. 14 performs an operation of inverting the order of a part of the genes of the chromosome, and the recruitment processing unit 50 performs an operation of accepting a new individual. Further, the mountain climbing processing unit 51 performs a search by a mountain climbing method similar to the neighborhood search. The fitness value calculation processing unit 45 calculates the sum of standard deviations, the number of processing executions in each generation, and the growth rate of the fitness value, and sends them to the condition 1 processing unit 52, the condition 2 processing unit 53, and the condition 3 processing unit 54, respectively. .

The condition 1 processing unit 52, the condition 2 processing unit 53, and the condition 3 processing unit 54 compare these values with their respective prescribed values to determine whether Condition 1, Condition 2, and Condition 3 are satisfied. G
A operation transition control processing unit 55 is notified. The GA operation transition control processing unit 55 uses the transition condition 0 of FIG.
It is determined whether or not 1, 12, 23, and 31 are established, and the fitness value calculation processing unit 45, the duplication / crossover processing unit 46, the mutation processing unit 47, and the neighborhood search are performed according to the transition flag s set as a result. The processing unit 48, the inversion processing unit 49, the recruitment processing unit 50, and the hill climbing processing unit 51 are controlled.

The migration value distribution processing unit 56 collects the pattern of the chromosome having the highest fitness value from the memory 43 of each cell, and distributes the collected chromosome having the best fitness value to each cell.

The parallel processing control unit 57 synchronizes the start and stop of the processing of each cell and causes them to perform the parallel processing. In addition, the parallel processing control unit 57 controls the parallel processing and also controls the migration value distribution processing unit 56.

FIGS. 15 and 16 are flowcharts of the search process for the optimum solution by each cell of the problem solving arithmetic unit of FIG. When the process is started in FIG. 15, first, an initialization operation is performed in each cell (step S
1). By this operation, the problem and the parameter are read from the input section 42 of each cell, and the initial population is generated on the memory 43. Further, the value of the bias K of the fitness function is determined according to the read question.

Next, the GA operation transition control processing unit 55 sets the transition flag s to 0 and generates a control signal for performing the search processing in the state 0. As a result, the replication / crossover processing unit 46 continuously performs the takeover, reproduction, and crossover processes, and the hill-climbing processing unit 51 continuously performs the search process (step S2).

When the transition condition to the state 1 represented by the equation (3) is satisfied, the GA operation transition control processing unit 5
5 sets the transition flag s to 1 and generates a control signal for performing the search process in the state 1 (step S3).

As shown in FIG. 16, in the state 1,
Succession, reproduction, and crossover processing by the replication / crossover processing unit 46, mutation processing by the mutation processing unit 47, inversion processing by the inversion processing unit 49, and search processing by the hill climbing processing unit 51 are successively performed. (Step S
4).

After that, the GA operation transition control processing unit 55 repeats the search processing in the same state until the transition condition to the next state is satisfied (step S5, NO), and when the transition condition to the next state is satisfied. (Step S5, YE
S), it is determined whether or not the end condition is satisfied (step S6).

The transition condition to the next state is (3) when the state 1 transits to the state 2 and the state 2 transits to the state 3.
It is expressed by an equation, and the case of state 3 to state 1 corresponds to condition 1. In addition, the termination condition is that the maximum number of executions of the search process is reached, for example. If the end condition is not satisfied (step S6, NO), the GA operation transition control processing unit 55 updates the transition flag s according to the next state (step S7), and in the state selected by the value of the transition flag s. A control signal for performing the search process of is generated (step S3). In step S7, the transition flag s is updated in the order of 1, 2, 3.

When s = 2, the state transits to the state 2, and the copy / crossover processing unit 46 takes over, reproduces and crosses over, and the mutation processing unit 47 performs mutation processing.
Inversion processing by the inversion processing unit 49 and neighborhood search processing unit 48
The neighborhood search processing by and the search processing by the hill-climbing processing unit 51 are continuously performed (step S4). Further, when s = 3, the state transits to the state 3, and the copy / crossover processing unit 46 continues the takeover process and the recruitment processing unit 50 accepts the new individual (step S4).

When the end condition is satisfied (step S6, Y
ES), the GA operation transition control processing unit 55 generates a control signal instructing the end of the search process, and ends the process. At this time, the one with the highest fitness value among the individuals of the last generation is the output unit 4 as a solution.
It is output from 4.

Next, referring to FIGS. 17 to 22, the processing by the problem solving arithmetic unit of FIG. 14 will be described in more detail. FIG. 17 is a flowchart of the crossover process by the duplication / crossover processing unit 46, and FIG. 18 shows a state in which the child chromosomes c _i and c _j are generated from the parent chromosomes p _i and p _j by the crossover process. In FIG. 18, taking a chromosome composed of 10 genes as an example, numbers 1 to 10 represent each gene.

When the processing is started in FIG. 17, first, two intersection points of the parent chromosomes p _i and p _j are determined (step S1).
1) Determine the part gc to be copied from the parent p _{j to the} child c _i (step S12). At this time, the left and right ends of each chromosome are considered to be connected. For example, in FIG. 18, the parent p
The three genes 8, 5, 7 of _j will be copied to the offspring c _i .

Next, a copy of the parent p _i as a parent p _i ', the parent p
The value of the gene contained in the portion (gc portion) corresponding to gc of _i 'performs reordering of the gene to be the same as those contained in gc portion of the parent p _j (step S13). Then, the order of genes other than the gc portion of the parent p _i ′ is set to be the same as the order of corresponding genes of the parent p _i (step S14).

Next, the gene of the gc portion of the parent p _j is copied to the gc portion of the child c _i (step S15), and the g of the parent p _i ′ is copied.
The gene of the part other than c is copied to the part other than gc of the child c _i (step S16). Thus, copied to gc portion of the gene 8,5,7 child c _i of the parent p _j, genes of the parent p _i 'l, 2,6, and, 9,4,3,10 child c _i
Are copied to parts other than gc.

Next, the positions of the parent p _i and the parent p _j are completely exchanged and the same processing is performed to generate the child c _j via the parent p _j ′ (not shown). Thus, in the crossover process, a part of two chromosomes is copied and combined to generate another two chromosomes. The sequence order of the genes in the chromosomes before the crossover treatment is consistently preserved in the chromosomes after the crossover treatment.

FIG. 19 shows the process of accepting a new individual by the recruitment processing unit 50. In the process of accepting new individuals, new chromosomes generated by randomly generating each gene are introduced into the population. This will generate a next-generation population with a higher variety of solutions. The excellent individual of the previous generation (previous generation) having a large fitness value is succeeded to the next generation (next generation) by the replication / crossover processing unit 46.

FIG. 20 is a flowchart of the search processing by the hill-climbing processing section 51, and FIG. 21 is a diagram showing replacement of adjacent genes in this processing. When the process is started in FIG. 20, first, replacement is performed for all adjacent genes i and i + 1, and the increase (gain) of the fitness value is examined (step S21). When there is no positive gain in this (step S22, NO), the input chromosome is output as it is, and the process ends.

When there is one or more positive gains (step S22, YES), the replacement that maximizes the gain is performed (step S23), and the gain is not affected by the replacement performed. It is checked whether other positive gain replacements remain (step S24). If the replacement of the positive gain remains (step S24, YE
S), the next positive gain replacement that is close in position is performed (step S25), and the processes of steps S24 and S25 are repeated until the positive gain replacement is eliminated by going around the chromosome.

Then, when there is no replacement of the positive gain to the extent that the replacement is not affected (step S2
4, NO), returning to step S21, the fitness value gains of all the adjacent replacements are checked again. After that, the process of FIG. 20 is repeated until the positive gain disappears in step S22. By adopting such a mountain climbing method, a more excellent individual can be obtained in a short time.

FIG. 22 is a diagram showing an example of the inversion processing by the inversion processing section 49. In FIG. 22, the order of some of the genes 6, 2, 8, 5 of the chromosome is reversed to 5, 8,
It becomes 2, 6 and another chromosome is generated. This inversion process is included in the set of mutation operations in FIG.

23 to 25 are simulation results of the traveling salesman problem of FIG. 4 by the problem solving arithmetic unit of the present invention. In these figures, Optimum indicates an ideal fitness value (fitness value of the optimal solution), With State indicates a result when the arithmetic device of the present invention, that is, the concept of state transition is introduced, and No State indicates The result when the state transition is not performed (state 0) is shown. 24 is an enlarged view of the results of generation 0 to 35000 in FIG. 23, and FIG.
2 is an enlarged view of a portion of fitness 18000 to 20000 in FIG.

In this simulation, the number of individuals in each population is 16, the length of the chromosome of each individual is 100, the crossover probability is 1.0, the mutation probability is 0.01, and the number of individuals inherited from the previous generation is 6. , And the inversion probability was 0.1. The crossover probability of 1.0 means that when two child chromosomes are generated from two parent chromosomes, the crossover points are calculated and determined with a probability of 1.0. If the crossover probability is 0.8, one of the parent chromosomes is simply used as a child chromosome without determining the crossover point by calculation with the remaining probability of 0.2. Also, 0.1
The inversion probability of 1 means that when one chromosome is given, the inversion process of a gene in a randomly determined part of the chromosome is performed with a probability of 0.1.

By using the concept of state transition, the ideal fitness value is reached in 1/3 to 1/2 the time compared with the case where the concept is not used, and the concept of state transition is not used. In some cases, it can be seen that the ideal value, that is, the optimum value of the fitness value may never be reached.

By introducing the concept of state transition in this way, the fitness value is quickly converged to the optimum value, but the neighborhood search in state 2 and the acceptance of a new individual in state 3 accelerate this convergence. Especially effective for.

In the genetic algorithm, when the diversity of individuals in the population is reduced, the fitness value cannot be improved even if crossover is performed. Therefore, when the diversity of individuals decreases, it is necessary to recover the diversity by some method. Acceptance of new individuals is an effective means of restoring this diversity.

In normal mutation processing, the points in the n-dimensional space representing each individual move only once per generation, but in hill climbing processing and neighborhood search, it is 1
There are many movements per generation. Furthermore, in normal mutation, the change in fitness value as a result of the movement of points can be positive or negative in probability, whereas in hill climbing processing and neighborhood search, it is always controlled to be positive or zero. It Therefore, the use of these search methods facilitates local search in the search space, and the probability of moving to a point having a large fitness value in a short time, that is, in a small number of generations as compared with the usual mutation processing, is increased. growing. Appropriate combination of these search methods and genetic algorithm will eventually promote global search in the search space.

Accepting a new individual in the state 3 is a process prepared only for the purpose of recovering diversity, and in this process, a part of the uniformized solution candidate group is replaced with a new solution candidate. It is possible to reach a solution with a higher fitness value while always maintaining the diversity of the group.

In the above description, it is assumed that a plurality of search methods are combined in each state to search for an optimum solution.
Naturally, it is also possible to search for the optimum solution using only one, for example, only the neighborhood search.

[0085]

As described in detail above, according to the present invention, in general, by searching for an optimal solution while repeating the state transition between a plurality of states in which a plurality of optimization methods are respectively combined, Compared with the method, it is possible to obtain a high-quality solution in a short time, and it greatly contributes to speeding up of problem solving operations for mathematical programming problems such as traveling salesman problems.

Further, according to the present invention, the sequence order of the genes in the chromosome before the crossover treatment is conserved in the chromosome after the crossover treatment.

[Brief description of drawings]

FIG. 1 is a block diagram showing a principle configuration of the present invention.

FIG. 2 is a block diagram showing a basic configuration of a problem solving calculation device of the present invention.

FIG. 3 is an explanatory diagram of state transition of an optimum solution search state.

FIG. 4 is a diagram showing an example of arrangement of cities in the traveling salesman problem.

5 is a diagram showing the position (coordinates) of each city in FIG.

FIG. 6 is a diagram illustrating an example of a coding result of solution candidates.

FIG. 7 is an explanatory diagram of state transitions in the example.

FIG. 8 is a diagram showing an example of a combination of operations in each state.

FIG. 9 is a diagram showing the concept of neighborhood search.

FIG. 10 is a diagram showing a concept of acceptance (recruitment) of a new individual.

FIG. 11 is an explanatory diagram of the sum of standard deviations under the first condition.

FIG. 12 is an explanatory diagram of a rate of change in fitness value under a third condition.

FIG. 13 is a block diagram showing the configuration of a problem solving calculation device using a genetic algorithm.

FIG. 14 is a block diagram showing a configuration of a problem solving arithmetic unit that performs parallel processing.

FIG. 15 is a flowchart (part 1) of the optimum solution search process.
Is.

FIG. 16 is a flowchart (part 2) of the optimum solution search process.
Is.

FIG. 17 is a flowchart of a crossover process.

FIG. 18 is a diagram illustrating an example of crossover processing.

FIG. 19 is a diagram showing a process of receiving a new individual.

FIG. 20 is a flowchart of mountain climbing processing.

FIG. 21 is a diagram showing adjacent replacement.

FIG. 22 is a diagram showing an inversion process.

FIG. 23 is a (first) diagram showing a simulation result by the GA algorithm.

FIG. 24 is a diagram showing a simulation result by the GA algorithm (No. 2).

FIG. 25 is a diagram showing simulation results by the GA algorithm (No. 3).

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Optimal solution search means 2 Search process observation and state transition means 11 Search module 12 Control module 13 Search part 14 Observation part 15 Transition control parts 16-1, 16-2, 16-3, 16-M Search state 30, 41- 1, 41-2, 41-N Cell 31, 42 Input section 32, 44 Output section 33, 43 Memory 34, 45 Fitness value calculation processing section 35, 46 Duplication / crossover processing section 36, 47 Mutation processing section 37, 48 Neighborhood search processing unit 38 Evaluation observation processing unit 39, 55 GA operation transition control processing unit 49 Inversion processing unit 50 Recruitment processing unit 51 Mountain climbing processing unit 52 Condition 1 processing unit 53 Condition 2 processing unit 54 Condition 3 processing unit 56 Migration value distribution Processor 57 Parallel processing controller

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Toshihiro Nishimura             1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture             Within Fujitsu Limited (72) Inventor Hiroyuki Okada             1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture             Within Fujitsu Limited (72) Inventor, Adachi             1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture             Within Fujitsu Limited (72) Inventor Hajime Oi             1-6-1, Marunouchi, Chiyoda-ku, Tokyo Stock             Ceremony company Fujitsu System Research Institute

Claims (4)

[Claims] 1. A problem solving operation device for searching a search space of a solution for a problem to obtain an optimum solution, the memory storing a group of chromosomes which are solution candidates for the problem, and first and second parents. In the chromosome, the portion between the two crossover points is the copy portion, the copy of the first parent chromosome is the third parent chromosome, and the copy portion of the third parent chromosome is the copy of the second parent chromosome. Genes of the third parent chromosome are rearranged so that they are composed of genes having the same value as the gene contained in the copy portion, and the order of genes other than the copy portion of the third parent chromosome is the first parent chromosome. In the same order as the corresponding genes of the second parent chromosome, copy the gene of the copy part of the second parent chromosome to the copy part of the offspring chromosome, and copy the gene of the part other than the copy part of the third parent chromosome. The gene of the child chromosome A crossover processing means for generating the child chromosome on the memory by copying the child chromosome to a portion other than the portion, and an optimal solution searching means for searching the optimal solution by using the child chromosome as a solution candidate. Characteristic problem solving computing device. 2. A problem solving arithmetic unit for searching a search space of a solution for a problem to find an optimum solution, the memory storing a group of chromosomes which are solution candidates for the problem, and first and second parents. In the chromosome, the portion between the two crossover points is the copy portion, the copy of the first parent chromosome is the third parent chromosome, and the copy portion of the third parent chromosome is the copy of the second parent chromosome. Genes of the third parent chromosome are rearranged so that they are composed of genes having the same value as the gene contained in the copy portion, and the order of genes other than the copy portion of the third parent chromosome is the first parent chromosome. In the same order as the corresponding genes of the second parent chromosome, and copy the gene of the copy portion of the second parent chromosome to the copy portion of the first offspring chromosome, except for the copy portion of the third parent chromosome. The part of the gene is the first child The first child chromosome is generated on the memory by copying to a part other than the copy part of the chromophore, and a copy of the second parent chromosome is used as a fourth parent chromosome, and the fourth parent chromosome is used. Rearranging the genes of the fourth parent chromosome such that the copy portion of the chromosome is composed of genes of the same value as the genes contained in the copy portion of the first parent chromosome, The order of the genes other than the copy part is the same as the order of the corresponding genes of the second parent chromosome, and the gene of the copy part of the first parent chromosome is transferred to the copy part of the second offspring chromosome. Generating the second offspring chromosome on the memory by copying and copying a gene of a part other than the copy part of the fourth parent chromosome to a part other than the copy part of the second offspring chromosome Crossover processing means for performing the above-mentioned first and second Problem solving arithmetic apparatus characterized by comprising an optimal solution search means for searching the optimal solution using a child chromosome as the solution candidates. 3. A problem solving calculation method for finding an optimum solution by searching a search space for a solution to a problem by a problem solving calculation device, wherein the crossover processing means is a solution candidate for the problem stored in a memory. In the first and second parent chromosomes, the portion between the two crossover points is the copy portion, the copy of the first parent chromosome is the third parent chromosome, and the copy portion of the third parent chromosome is the copy portion. The third gene so as to be composed of a gene having the same value as the gene contained in the copy part of the second parent chromosome.
Rearranging the genes of the parent chromosome of the third parent chromosome so that the order of the genes other than the copy portion of the third parent chromosome is the same as the order of the corresponding genes of the first parent chromosome, The gene of the copy part is copied to the copy part of the offspring chromosome, and the gene of the part other than the copy part of the third parent chromosome is copied to a part other than the copy part of the offspring chromosome to obtain the memory. A problem solving calculation method, wherein the child chromosome is generated above, and the optimum solution searching means searches for the optimum solution by using the child chromosome as a solution candidate. 4. A problem solving calculation method for finding an optimum solution by searching a search space of a solution for a problem by a problem solving calculation device, wherein the crossover processing means is a solution candidate for the problem stored in a memory. In the first and second parent chromosomes, the portion between the two crossover points is the copy portion, the copy of the first parent chromosome is the third parent chromosome, and the copy portion of the third parent chromosome is the copy portion. The third gene so as to be composed of a gene having the same value as the gene contained in the copy part of the second parent chromosome.
Rearranging the genes of the parent chromosome of the third parent chromosome so that the order of the genes other than the copy portion of the third parent chromosome is the same as the order of the corresponding genes of the first parent chromosome, Copy the gene of the copy part to the copy part of the first child chromosome, and copy the gene of the part other than the copy part of the third parent chromosome to a part other than the copy part of the first child chromosome. Thereby generating the first offspring chromosome on the memory, using the copy of the second parent chromosome as the fourth parent chromosome, and the copy portion of the fourth parent chromosome is the first parent chromosome. Genes of the fourth parent chromosome are rearranged so that they are composed of genes having the same value as the gene contained in the copy portion of the chromosome, and the order of genes other than the copy portion of the fourth parent chromosome is the second gene. In the same order as the corresponding genes on the parent chromosome of A gene of the copy part of the first parent chromosome is copied to the copy part of the second offspring chromosome, and a gene of a part other than the copy part of the fourth parent chromosome is transferred to the second offspring. The second child chromosome is generated on the memory by copying to a portion other than the copy portion of the chromosome, and the optimal solution search means uses the first and second child chromosomes as solution candidates to A problem solving operation method characterized by searching for an optimum solution.