JP2003016421A - Optimization problem processor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the efficiency of genetic algorithm. SOLUTION: A gene statistical arithmetic part 24 generates a probability model according to information of a chromosome group stored in a chromosome group storage part 22 and stores the model in a probability model storage part 25. A chromosome generation part 26 generates a new chromosome according to the probability model and a chromosome selection part 27 selects a chromosome from the chromosome group according to the probability model. A GA arithmetic part 23 performs operations for the calculation of an evaluation function of a chromosome, the selection of a chromosome, crossover, mutation, etc. A probability control part 29 controls operations regarding the probability model.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a genetic algorithm (Ge algorithm based on a stochastic model) for solving an optimization problem.
The present invention relates to a processing device for operating netic Algorithm (GA).

[0002]

2. Description of the Related Art Conventionally, various systems using computers have been developed to solve optimization problems such as scheduling and parameter fitting.
In particular, as computer performance has improved in recent years, stochastic optimization methods such as simulated annealing have attracted attention as a method for solving problems that were difficult to solve with conventional expert systems and the like. Research has been conducted as a practical method. Among various probabilistic optimization methods, GA has received special attention.

In recent years, how to effectively use the abundant CPU (Central Processing Unit) power that accompanies the cost reduction of computers for solving problems has been
It has become a challenge. GA is also a promising way to overcome difficult problems with computer power.

[0004]

However, the above-mentioned conventional GA has the following problems. Conventional GA
In the above, only the evaluation function (fitness) is used as an index for optimization, but such a framework can be a great advantage of GA and at the same time a drawback.

It is said that GA is hard to be caught by a local solution, but GA does not have a mechanism to get out of the local solution. Therefore, when trying to solve a practical problem, since the number of GA individuals is smaller than that in the solution space, there is a tendency to be actually bound by a local solution. Further, as a property of GA, when a solution falls into a local optimal solution, the evaluation function has to be calculated many times for the same gene, which is a very inefficient framework.

There are two types of GAs, a simple GA in which one chromosome group is an operation target, and a parallel GA in which a plurality of chromosome groups are operation targets. Among them, in the simple GA, individual chromosomes (sequences) are identified / used by using the fitness of the solution.
You have selected. At this time, information such as difference between individuals is not particularly considered, and the fitness of the solution is not appropriate as an index of similarity between individuals. Therefore, it is difficult to get out of the local optimum solution.

In parallel GA, the information of the best chromosome is used as the information representing a certain group, and the fitness and the Hamming distance between the best chromosomes of the groups are compared. However, information about the entire population is not used. Although the best Hamming distance between chromosomes is an indicator of the distance between individual sequences, nothing is known about the population as a whole.

An object of the present invention is to provide an optimization problem processor using a more efficient GA.

[0009]

FIG. 1 is a principle diagram of an optimization problem processor according to the present invention. The optimization problem processing device of FIG. 1 includes a group storage unit 11, a model storage unit 12, a generation unit 13, a selection unit 14, an operation unit 15, and an output unit 16, and obtains a solution of the optimization problem using GA. Perform processing.

In the first aspect of the present invention, the group storage means 11 stores information on an individual group, and the model storage means 1
2 stores information on a probabilistic model that represents the occurrence probability of alleles of an individual population. The generation unit 13 refers to the probabilistic model to generate a new individual, and stores the generated individual in the group storage unit 11 as a next-generation individual. Operating means 15
Performs GA operation on the individual population in the population storage means 11, and the output means 16 outputs the operation result.

The group storage means 11 stores the sequence data of each individual (chromosome) of the individual population, and the model storage means 12
Stores the probability that each allele appears at each locus within the population as the data of the probabilistic model. The generation unit 13 generates a new individual based on the probabilistic model, thereby generating a next-generation individual population including the new individual. The operation means 15 performs operations such as selection, crossover, and mutation on the thus-generated individual population. When the predetermined termination condition is satisfied, the operation result up to that point is output from the output means 16 as the processing result.

According to such a processing apparatus, it is possible to generate a new individual by using the allele that appears with a high probability in the individual population and incorporate it into the next generation. Since such individuals are highly likely to have good evaluation values and reflect the characteristics of the probabilistic model, it is possible to escape from the local optimum solution and perform efficient search.

Further, in the second aspect of the present invention, the population storage means 11 stores the information of the individual population, and the model storage means 12 stores the information of the probabilistic model representing the appearance probability of the allele of the individual population. To do. The selecting means 14 selects an individual from the individual population with reference to the probabilistic model, and stores the selected individual in the group storing means 11 as a next-generation individual. The operation unit 15 performs GA operation on the individual population in the population storage unit 11, and the output unit 16 outputs the operation result.

In this case, the selecting means 14 selects an individual based on the probabilistic model, so that a next-generation individual population including the selected individual is generated. The operation means 15 performs operations such as selection, crossover, and mutation on the thus-generated individual population. Then, when the predetermined termination condition is satisfied, the operation result up to that point is used as the processing result, and the output unit 1
It is output from 6.

According to such a processing apparatus, it is possible to preferentially select an individual containing a large number of alleles that appear in the individual population with a high probability, and incorporate it into the next generation. Therefore, similarly to the processing apparatus in the first aspect, it is possible to escape from the local optimum solution and perform an efficient search.

Further, in the third aspect of the present invention, the group storing means 11, the model storing means 12, and the operating means 1
A plurality of 5 are provided respectively. The plurality of population storage means 11 each store information of a plurality of individual populations, and each of the plurality of model storage means 12 stores information of a probabilistic model that represents the occurrence probability of the allele of each individual population. The selection means 14 refers to the probabilistic model, compares two populations of a plurality of individual populations, selects an individual from at least one of them, and selects the selected individual as a next-generation individual, and a corresponding population. It is stored in the storage means 11. The plurality of operation means 15 perform GA operation on the individual groups in the plurality of group storage means 11, and the output means 16 outputs the operation result.

Each model storage means 12 stores the data of the probabilistic model related to the individual population in the corresponding population storage means 11, and each operation means 15 stores the corresponding population storage means 11.
The GA operation is performed on the individual population within. The selection unit 14 compares two populations based on the probability model of each individual population and selects an individual from one of the populations, whereby a next-generation individual population including the selected individual is generated. The corresponding operation means 15 performs operations such as selection, crossover, and mutation on the thus-generated individual population. When the predetermined termination condition is satisfied, the operation result up to that point is output from the output means 16 as the processing result.

According to such a processing apparatus, by using the probabilistic model reflecting the information of the entire population, the similarity between the two individual populations in the parallel GA can be accurately determined. Also, when two populations are similar,
By selecting individuals so that they deviate from each other, these groups can be distributed to different search areas. This makes it possible to improve the efficiency of the parallel GA.

The group storage means 11 of FIG. 1 corresponds to, for example, a chromosome group storage unit 22 of FIG. 2 described later and a GA unit 32 of FIG. 9 described later. Also, the model storage means 1 of FIG.
2 is, for example, the stochastic model storage unit 25 of FIG.
Corresponds to the stochastic model storage unit 33. Further, the generating means 13 in FIG. 1 corresponds to, for example, the chromosome generating section 26 in FIG. 2, and the selecting means 14 in FIG. 1 is, for example, in the chromosome selecting section 27 in FIG. 2 and the inter-probability model control section 34 in FIG. Corresponding to. Further, both the operation means 15 and the output means 16 in FIG. 1 are, for example, the GA calculation unit 23 in FIG. 2 and the G operation in FIG.
It corresponds to the A section 32.

[0020]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings. Figure 2 is a simple GA
It is a block diagram of the optimization problem processing apparatus using (SingleGA, SGA). The processing device of FIG.
1, chromosome population storage unit 22, GA calculation unit 23, gene statistical calculation unit 24, stochastic model storage unit 25, chromosome generation unit 2
6, a chromosome selection unit 27, an end determination unit 28, and a stochastic model control unit 29. Solid arrows represent exchanges of processing data, and broken arrows represent exchanges of control data.

The initial chromosome generation unit 21 initializes the GA chromosome group to generate initial values for each chromosome. The chromosome group storage unit 22 stores information on the chromosome group, and G
It also includes a storage area used by the A calculation unit 23. GA calculation unit 2
3 is the calculation of the evaluation function of the chromosome, the selection of the chromosome, the crossover,
GA operation such as mutation is performed.

The gene statistical calculation unit 24 performs statistical calculation based on the information of the chromosome population stored in the chromosome population storage unit 22 to generate a probabilistic model, and the stochastic model storage unit 2
5 stores the generated probabilistic model. The chromosome generation unit 26 generates a new chromosome based on the stochastic model,
The chromosome selection unit 27 selects a chromosome from the chromosome population based on the stochastic model.

The end determination unit 28 determines whether the search by the GA calculation unit 23 is to be ended or continued, and the stochastic model control unit 29 determines that the chromosome group storage unit 22, the GA calculation unit 23, the gene statistical calculation unit 24, The probabilistic model storage unit 25, the chromosome generation unit 26, and the chromosome selection unit 27 control operations related to the probabilistic model.

FIG. 3 is a flow chart of GA processing by the processing apparatus of FIG. First, the early chromosome generation part 21
Generates an initial chromosome population, and the chromosome population storage unit 22
(Step S1). Next, the GA calculation unit 23
Calculates the value of the evaluation function for each chromosome in the chromosome population storage unit 22 (step S2), and the stochastic model control unit 29
Determines whether the conditions for generating the probabilistic model are satisfied (step S3). As this condition, for example,
It is used that the predetermined generation of GA is reached. The predetermined generation is set using a predetermined generation interval or the like.

If the condition is not satisfied, then the end determination unit 28 determines whether or not a preset end condition is satisfied (step S4). As the termination condition, the number of generations of GA has reached a certain value, the evaluation function value (evaluation value) of the best chromosome has reached a certain value, and the interruption of the termination instruction by the user has occurred. To be

If the end condition is not satisfied, then the GA calculation unit 23 performs a normal GA optimization calculation. Here, a selection operation is performed on the chromosome population of the chromosome population storage unit 22 (step S9), and a crossover operation is performed (step S1).
0), a mutation operation is performed (step S11), and the processing from step S2 is repeated.

In this way, the GA calculation is repeated, and if the condition for generating the probabilistic model is satisfied in step S3, the probabilistic model control unit 29 interrupts. Then, under the control of the stochastic model control unit 29, the gene statistical calculation unit 24
Generates a probabilistic model of the chromosome population and stores it in the probabilistic model storage unit 25 (step S5). As a result, the probabilistic model is updated at predetermined generation intervals.

Next, the probabilistic model control unit 29 determines whether to generate or select a chromosome (step S).
6). Which is to be performed may be determined based on an instruction from the user or may be determined based on preset control information.

In the case of chromosome generation, the chromosome generating section 26 is
A new chromosome is generated using the probabilistic model of the probabilistic model storage unit 25 and incorporated into the chromosome group of the chromosome group storage unit 22 (step S7). As the new chromosome, a consensus sequence of the probabilistic model (the sequence with the highest probability), a suboptimal consensus sequence, or the like is used.

In the case of chromosome selection, the chromosome selection unit 2
7 evaluates each chromosome based on the probabilistic model, selects a chromosome having a relatively good evaluation, and passes it to the GA calculation unit 23 (step S8). After that, the GA calculation unit 23 performs the processing from step S9 onward, and if the termination condition is satisfied in step S4, outputs the chromosome having a good evaluation value at that time as the processing result, and terminates the processing.

Next, referring to FIGS. 4 to 8,
A specific example of SGA will be described. As an optimization problem, consider a problem that minimizes the evaluation function f (x _i ) (i = 1, 2, 3, 4) represented by the following equation.

[0032]

[Equation 1]

Where x_iThe range of possible values of is 0 ≦ x
_iIt is an integer of ≦ 3. This evaluation function f (x_i ) Is for each i
For x_i The minimum value becomes 0 when = 1. Solve this problem
For x_i Is a gene, and alleles are 0
Let it be an integer of 3. At this time, the sequence of each chromosome is [0,
1, 2, 3] ∈ x₁ , X₂ , X ₃ , X_Four Of four integers
Set (x₁, X₂ , X₃ , X_Four ). Number of individuals is 5
The randomization of the set of chromosomes set in
As a result,
Assume that the value of the evaluation function is as shown in FIG. this
A stochastic model as shown in Fig. 5 is generated from the chromosome population.
To be done.

The probability model of FIG. 5 represents the appearance probability of each allele at each locus. For example, for x ₁ , only the chromosome 2 among the chromosomes 1 to 5 in FIG. 4 has the allele “0”. Therefore, the appearance probability of the allele “0” in x ₁ is 1/5 = 0.2.
In addition, x ₁ = 1 is 2 of chromosome 1 and chromosome 4.
Is one. Therefore, the allele "1" at x ₁
The appearance probability of is 2/5 = 0.4.

[0035] Similarly, the probability of occurrence of allele "2" and "3" in the x _1, respectively 0.4 and 0.0, and the sum of the probabilities of occurrence of all alleles in x ₁ is 1 . The same applies to the appearance probabilities at other loci.

The chromosome generation unit 26 refers to this stochastic model to generate a new chromosome (consensus sequence) in which alleles having a high occurrence probability are combined.
Here, the highest occurrence probability (0.4
Alternatively, the consensus sequence shown in FIG. 6 is generated by selecting the allele of (0.6).

In FIG. 6, the appearance probability of each chromosome corresponds to the result obtained by multiplying the appearance probability of the allele shown in FIG. 5 for all loci. Also, log-od
ds is called a logarithmic odds ratio and is defined by the following equation.

[0038]

[Equation 2]

In general, the base of the logarithm of the log odds ratio is arbitrary, but 2 is used as the base in the calculation of FIG. Further, P _{i on} the right side of the equation (2) represents the appearance probability of the allele in x _i , and the summation is performed for i = 1 to 4.

This logarithmic odds ratio is a score representing the goodness of fit of each individual in the target probability model compared with the background probability model. By referring to this score, the probability of each individual targeting It can be determined whether or not the model fits. Here, since there are four alleles and a stochastic model of a background of equal probability is assumed, log on the right side of equation (2)
(1/4) appears.

The chromosome generating unit 26 restores the chromosome having a good evaluation value to the original chromosome population among these consensus sequences. In this case, since the number of consensus sequences is larger than the number of individuals in the population, the sequence of the best (minimum) evaluation value "111"
In this example, eight consensus sequences with the same probability are generated, but the number of consensus sequences with the maximum probability is usually smaller than the number of individuals in the population.

For the chromosome population and the best consensus sequence in FIG. 4, the appearance probability and log odds ratio are calculated based on the probability model in FIG. Chromosome 1
Of the 5, the worst evaluation value is 3 of chromosomes 2, 3, and 5.
Therefore, by exchanging any of these with the consensus sequence “1110”, a new chromosome group in which a probabilistic model is added is generated.

As described above, it is possible to create a new chromosome having a high evaluation value by using the probabilistic model created from the chromosome population. The chromosomes created by the probabilistic model retain the building blocks of the original population,
The new chromosome generated from this is considered to give an even better solution.

Further, an effective evaluation function fe in which a logarithmic odds ratio is added to the evaluation function f (x _i ) of the equation (1)
(X _i ) is defined by the following equation, for example. fe (x _i ) = {1 / (f (x _i ) +0.01)} * log-odds (3) As a result, the minimization problem of f (x _i ) becomes the maximization problem of fe (x _i ). The probability based on the probabilistic model is added by being replaced and multiplying the value of log-odds.

The chromosome selecting unit 27 selects a predetermined number of chromosomes having a high effective evaluation function value from the chromosome population, and
It is passed to the calculation unit 23. At this time, the chromosomes in the population are sorted in descending order of effective evaluation function value, and a predetermined number of chromosomes are selected from the top.

When the effective evaluation function value of the equation (3) is calculated for each chromosome shown in FIG. 7, it becomes as shown in FIG. For example, comparing chromosome 2 and chromosome 3, the original evaluation function values are the same, but the effective evaluation function values are different. In this case, by performing selection according to the effective evaluation function value, the individual having a higher appearance probability is preferentially selected.

As described above, by using the effective evaluation function in which the evaluation of the log odds ratio based on the probabilistic model and the evaluation function of GA are combined, a probabilistic model can be added to GA, and better chromosome evaluation is possible. Becomes

Next, FIG. 9 shows a parallel GA (ParallelGA,
It is a block diagram of the optimization problem processing apparatus using PGA).
The processing device of FIG. 9 includes an inter-GA control unit 31, a GA unit 32, a probabilistic model storage unit 33, a probabilistic model control unit 34, and a distance calculation unit 35. Here, three GA units 32 and three stochastic model storage units 33 are shown, but in actuality, the number (arbitrary) of the number of chromosome groups to be processed in parallel is provided.

Each GA unit 32 corresponds to the initial chromosome generation unit 21, the chromosome group storage unit 22, the GA operation unit 23, and the end determination unit 28 in FIG. 2, and performs optimization using GA.
The inter-GA control unit 31 controls the GA units 32 (initialization, generational progress, end determination, etc.), as in a normal parallel GA.

Each stochastic model storage unit 33 has a corresponding GA.
It also stores a probabilistic model of the chromosome population of the unit 32, and also includes a storage area used for generation and calculation of the probabilistic model. The inter-probabilistic-model control unit 34 performs generation of a probabilistic model and arithmetic / control between probabilistic models, and the distance calculation unit 35 performs distance calculation (similarity calculation) between probabilistic models. The inter-GA control unit 31 and the inter-probability model control unit 34 perform control in cooperation with each other.

FIG. 10 is a flow chart of GA processing by the processing apparatus of FIG. First, the GA unit 32 generates an initial chromosome group (step S11) and performs one generation of optimization calculation in parallel (step S12). Next, the inter-probabilistic-model control unit 34 determines whether or not the condition for generating the probabilistic model is satisfied (step S3). This condition is the same as in the case of the processing apparatus of FIG.

If the condition is not satisfied, then each GA unit 3
2 determines whether or not a preset ending condition is satisfied (step S14). This termination condition is also the same as in the case of the processing device of FIG.

If the termination condition is not satisfied, the GA unit 32
Repeats the processing from step S12,
If the condition for generating the probabilistic model is satisfied in 13, the inter-probabilistic model control unit 34 interrupts. And each G
Gene statistical calculation is performed on the chromosome population of the A section 32 to generate a probabilistic model of each chromosome population, which is stored in the probabilistic model storage section 33 (step S15).

Next, the distance calculation unit 35 calculates the correlation or the like (distance) between the probabilistic models according to the instruction from the probabilistic model control unit 34 (step S16). Then, the inter-probabilistic-model control unit 34 sets an effective evaluation function (effective fitness) of each chromosome group based on the result of the distance calculation, and evaluates each chromosome using the effective evaluation function. Then, a chromosome with a relatively good evaluation is selected from each chromosome group, and each GA unit 32
(Step S17).

Thereafter, the GA unit 32 carries out the processing from step S12 onward, and if the termination condition is met in step S14, the processing is terminated. Then, the inter-GA control unit 31
Indicates that each GA part 3 has a chromosome with a good evaluation value at that time.
It collects from 2 and outputs it as a processing result.

As a specific example of PGA, consider the problem of minimizing the evaluation function f (xi) (i = 1, 2, 3, 4) expressed by the following equation.

[0057]

[Equation 3]

[0058] range of possible values of x _i is an integer of 0 ≦ x _i ≦ 3. This evaluation function f (x _i ) has a minimum value 0 at x _i = 0, x _i = 1 or x _i = 2 for each i. At this time, the parallel GA operates as follows, for example.

Each GA unit 32 performs optimization calculation in parallel, and the inter-GA control unit 31 appropriately initializes each chromosome group, interrupts at a set generation interval, and compares fitness. . In addition, the inter-probabilistic-model control unit 34 interrupts at a set generation interval to generate a probabilistic model of each chromosome group.

For example, PGA using three chromosome populations
, Three stochastic models P1 and P as shown in FIG.
It is assumed that 2 and P3 are generated. At this time, the distance calculation unit 35 calculates the following relative entropy (Kullback-Leibler divergence) as the distance between the probabilistic models according to the instruction of the inter-probability model control unit 34.

[0061]

[Equation 4]

Here, P and Q represent two probabilistic models to be compared, and H (P | Q) represents the relative entropy of P and Q. The sum of the right side of the equation (5) is i = 1 to 4
And x _i = 0-3. For example, in FIG.
The relative entropy of the stochastic models P1 and P2 of is calculated as follows. H (P1 | P2) = 0.2log (0.2 / 0.4) + 0.4log (0.4 / 0.4) + 0.4log (0.4 / 0.2) + 0.4log (0.4 /0.4) +0.2 log (0.2 / 0.4) +0.4 log (0.4 / 0.2) +0.4 log (0.4 / 0.2) +0.4 log (0.4 / 0) .4) +0.2 log (0.2 / 0.2) +0.4 log (0.4 / 0.2) +0.2 log (0.2 / 0.4) +0.2 log (0.2 / 0.2) ) + 0.2log (0.2 / 0.2) = 0.2log (1/2) + 0.4log (2) + 0.2log (1/2) + 0.4log (2) + 0.4log (2) +0. 4log (2) + 0.2log (1/2) = log (2) (6) This relative entropy is 0 if the two probabilistic models are equal. The larger the difference, the larger the value. Since the similarity between the two probabilistic models reflects the similarity between corresponding chromosome populations, the similarity between populations can be determined using relative entropy.

For example, if the relative entropy is smaller than a predetermined threshold value, the inter-probabilistic model control unit 34 determines that the two groups are similar, and if it is equal to or larger than the predetermined threshold value, then The two groups are judged not to be similar.

When the two groups are similar to each other, the evaluation function of the one group is changed by using the logarithmic odds ratio based on the other group as a penalty, so that the former group has no similarity. Can be guided to.

Here, an example of a method of calculating a penalty will be described using a chromosome group as shown in FIG. 12
Indicates the calculation result of the chromosome population and the evaluation function f (x _i ) of the equation (4). The probabilistic model of this chromosome population is in agreement with the probabilistic model P1 of FIG. Stochastic model P1
And P2 are similar, for each chromosome (2)
The logarithmic odds ratio of the equation is calculated based on the probabilistic model P2 as follows. Chromosome 1 (1130) log-odds = log (0.4) + log (0.4) + log (0.2) + log (0.2) -4log (1/4) = 0.712287 Chromosome 2 (0312) log -Odds = log (0.4) + log (0.2) + log (0.4) + log (0.2) -4log (1/4) = 0.712287 Chromosome 3 (2103) log-odds = log (0 .2) + log (0.4) + log (0.2) + log (0.2) -4log (1/4) =-0.287713 chromosome 4 (1210) log-odds = log (0.4) + log ( 0.4) + log (0.4) + log (0.2) -4log (1/4) = 1.712287 Chromosome 5 (2301) log-odds = log (0.2) + log (0. ) + Log (0.2) + log (0.4) -4log (1/4) =-0.287713 These logarithmic odds ratios represent the goodness of fit of each individual to the probability model P2, and their values are large. It means that the probability model P2 is more fitted. Therefore, in order to lower the evaluation of an individual log odds ratio is large, the evaluation function f (x _i), the effective evaluation function f as follows
Define e (x _i ). fe (x _i ) = f (x _i ) + α * log−odds (7) where α is a constant. The inter-stochastic model control unit 34
Each chromosome is evaluated using this fe (x _i ), and a predetermined number of chromosomes having a good evaluation value are selected and passed to the corresponding GA unit 32. In this case, fe (x _i ) of the individual fitted to the probabilistic model P2 becomes larger than f (x _i ) and the evaluation value becomes worse. Therefore, as a result, the corresponding GA unit 32 searches for more other search points deviated from the stochastic model P2.

When α = 10.0 is calculated and the effective evaluation function value of the equation (7) is calculated for each chromosome of FIG.
It becomes like 3. Further, from the distribution of the probabilistic model P2 in FIG. 11, it can be seen that the population of this probabilistic model exists near the point that minimizes Out 1.

[0067]

[Outer 1]

Can be picked up. In FIG. 13, the chromosome 4 having the best evaluation function value is an individual in this vicinity, and its log odds ratio is the largest. Therefore, the evaluation based on the effective evaluation function value is significantly deteriorated.

On the other hand, since the logarithmic odds ratio of the chromosome 3 and the chromosome 5 in the region deviated from the stochastic model P2 is small, the evaluation by the effective evaluation function value is good. Thus, by using the effective evaluation function of Expression (7), there is an effect of excluding the neighborhood of another group from the search range of a certain group.

As described above, in a PGA having a plurality of chromosome populations, the populations are made different from each other by comparing the populations using a probability model and adjusting the competition of the search region based on the comparison result. It can be assigned to the search area. Therefore, the search efficiency as a whole is improved.

Next, with reference to FIGS. 14 to 17, a description will be given of the processing in the case where the processing device of FIGS. 2 and 9 performs scheduling of an airline schedule. FIG. 14 shows a configuration for the GA calculation unit 23 and the GA unit 32 in this case to calculate an evaluation function (fitness). The flight object 41 and the flight schedule management unit 42 of FIG.
It is programmed by object-oriented programming as shown in 7).

The flight schedule management unit 42 decodes the given chromosome data to obtain scheduling parameters, and sends a message instructing the simulation based on the obtained parameters to the flight object 41.

The flight object 21 holds data of airports and spots, performs flight simulation based on the passed parameters, and obtains the obtained simulation result in the flight schedule management unit 42.
Return to.

The flight schedule management unit 42 calculates the fitness from a returned simulation result by a predetermined algorithm and outputs it. When the end condition is satisfied, the chromosome having the highest fitness at that time is decoded and the flight schedule described by the obtained parameters is output as the schedule result.

Flight data for each flight included in the airline schedule is as follows:
For example, as shown in FIG. 15, flight number (Flight-ID), desired departure time (Depart-time), time width (Time-Window)
), And the information of the assignable model (Available-Ship-Type). Here, the flight number is # 3,
The desired departure time is 10:00, and the time width is -20 minutes and +10 minutes. This is the departure time of Flight # 3 is 9:
It is meant to be limited between 40 and 10:10. Also, the assignable model (Ship-Type) is B-747,
Limited to B-777 and B-767.

In this case, the purpose of scheduling is to determine the departure times and aircraft types of all flights so as not to generate unallocatable flights while keeping these restrictions. Now, the flight numbers of the flights included in the airline schedule are # 1, # 2.
# 3 ,. ． ． , #Last, the chromosome data for dealing with this problem is coded as shown in FIG. 16, for example.

In the chromosome of FIG. 16, each stool data has two loci, Time and Ship-Type, and their alleles are 0 to 255. Here, the value of the Time gene is set to t, and Ship
When the value of the -Type gene is s, the departure time and the type of flight # 3 are given by the following equation. Time corresponding to departure time = (t% 7) (8) Machine corresponding to model = (s% 3) (9) "%" represents the remainder calculation, for example, t% 7 is t divided by 7. Corresponds to the remainder (0,1,2,3,4,5,6). The same applies to s% 3. The correspondence between the obtained remainder value and time / model is as shown in FIG. In FIG. 17, the departure time candidate is 9:40.
Seven times obtained by dividing 10:10 at 5 minute intervals are used, and one value of the remainder is associated with each time. Further, one surplus value is associated with each of the three assignable models B-747, B-777, and B-767.

If such correspondences are defined for all flights # 1 to #last, the chromosome data can be decoded by the remainder calculation similar to the equations (8) and (9). The flight schedule management unit 42 passes the parameters such as the departure times and the assigned aircraft types of all the flights thus obtained to the flight object 41, and the flight object 41 simulates the flight schedule described by these parameters. The fitness is dynamically calculated according to the obtained simulation result.

The present invention can be applied to various optimization problems such as a delivery planning problem, a staffing problem, a shop scheduling in a factory, etc., in addition to the scheduling of airline schedules.

By the way, the processing apparatus shown in FIGS.
For example, it can be configured using an information processing device (computer) as shown in FIG. The information processing apparatus of FIG. 18 includes a CPU (central processing unit) 51, a memory 52, an input device 53, an output device 54, an external storage device 55, a medium drive device 56, and a network connection device 57.
They are connected to each other by a bus 58.

The memory 52 is, for example, a ROM (read onl).
y memory), RAM (random access memory), etc., and stores programs and data used for processing.
The CPU 51 performs the necessary processing by executing the program using the memory 52.

For example, the early chromosome generating part 21, G in FIG.
A calculation unit 23, gene statistical calculation unit 24, chromosome generation unit 2
6, chromosome selection unit 27, end determination unit 28, probabilistic model control unit 29, GA inter-GA control unit 31, GA unit 3 of FIG.
2, inter-probability model control unit 34, and distance calculation unit 35
Is stored in a particular program code segment of memory 52 as a software component described by the program.

Further, the chromosome group storage unit 22 and the probability model storage unit 25 in FIG. 2 and the probability model storage unit 33 in FIG.
Corresponds to a specific storage area of the memory 52. In the case of the parallel GA shown in FIG. 9, the plurality of GA units 32 perform optimization calculation in parallel by multitask processing.

The input device 53 is, for example, a keyboard, a pointing device, a touch panel, etc., and is used for inputting instructions and information from the user. Output device 54
Is, for example, a display, a printer, a speaker, etc., and is used for inquiring to the user and outputting the processing result.

The external storage device 55 is, for example, a magnetic disk device, an optical disk device, a magneto-optical disk device, a tape device or the like. The information processing device is the external storage device 55.
In addition, the programs and data described above are stored, and if necessary, they are loaded into the memory 52 for use.

The medium driving device 56 drives the portable recording medium 59 and accesses the recorded contents. Portable recording medium 5
Reference numeral 9 denotes a memory card, a floppy (registered trademark) disk, a CD-ROM (compact disk read only memor)
y), an optical disk, a magneto-optical disk, or any other computer-readable recording medium is used. The user
The above-mentioned program and data are stored in the portable recording medium 59, and they are loaded into the memory 52 for use as needed.

The network connection device 57 is a LAN (lo
It is connected to any communication network such as a cal area network) and performs data conversion accompanying communication. Further, the information processing device receives the above-mentioned program and data from another device via the network connection device 57, and if necessary,
They are loaded into the memory 52 and used.

FIG. 19 shows a computer-readable recording medium capable of supplying a program and data to the information processing apparatus of FIG. The programs and data stored in the portable recording medium 59 or the database 61 of the server 60 are loaded into the memory 52. At this time, the server 60 generates a carrier signal for carrying the program and data, and transmits the carrier signal to the information processing device via an arbitrary transmission medium on the network. Then, the CPU 51 executes the program using the data and performs the necessary processing.

Further, the optimization problem processing device of FIG.
It can be realized by a parallel computer equipped with a plurality of processing elements (PEs) other than the information processing device such as 8. In this case, parallel processing is performed by each PE executing the program of each GA unit 32.

(Supplementary Note 1) An optimization problem processing device using a genetic algorithm, which includes a group storage unit for storing information on an individual population and information on a probabilistic model representing the occurrence probability of alleles of the individual population. Model storing means for storing, generating means for generating a new individual by referring to the probabilistic model, and storing the generated individual in the group storing means as a next-generation individual, and an individual group in the group storing means On the other hand, an optimization problem processing device comprising an operating means for performing an operation of a genetic algorithm and an output means for outputting an operation result. (Supplementary Note 2) The optimization according to Supplementary Note 1, wherein the generating unit generates the new individual by combining alleles having high occurrence probabilities with respect to a plurality of loci of one individual. Problem processor. (Supplementary Note 3) An optimization problem processing device using a genetic algorithm, which is a model for storing population storage means for storing information on an individual population, and information for a probabilistic model representing the occurrence probability of alleles of the individual population. Storage means, selecting means for selecting an individual from the population of individuals with reference to the probabilistic model, and storing the selected individual as the next-generation individual in the population storage means; and for the population of individuals in the population storage means An optimization problem processing device, comprising: an operation unit for performing an operation of a genetic algorithm and an output unit for outputting an operation result. (Supplementary note 4) The optimum according to supplementary note 3, characterized in that the selecting means evaluates the individuals of the individual population using an effective evaluation function based on the probability model, and selects a predetermined number of individuals in descending order of evaluation. Problem solver. (Supplementary note 5) An optimization problem processing device using a genetic algorithm, comprising: a plurality of group storage means for respectively storing information of a plurality of individual populations; and a probabilistic model representing probability of occurrence of alleles in each individual population. A plurality of model storing means for storing information and the probabilistic model are referred to, two groups of the plurality of individual groups are compared, an individual is selected from at least one of the two groups, and the selected individual is selected. Is output as a next-generation individual, a plurality of operating means for performing a genetic algorithm operation on the individual populations in the plurality of population storing means, and an operation result are output. An optimization problem processing device, comprising: (Supplementary Note 6) The selection means uses an effective evaluation function based on a probability model of one of the two populations,
6. The optimization problem processing device according to appendix 5, wherein individuals of the other group of the two groups are evaluated, and a predetermined number of individuals are selected from the other group in order of good evaluation. (Supplementary Note 7) A program for a computer that processes an optimization problem using a genetic algorithm, wherein information on an individual population is stored in a population storage unit of the computer, and the occurrence probability of alleles of the individual population is stored. Is stored in the model storage unit of the computer, a new individual is generated by referring to the probabilistic model, the generated individual is stored in the group storage unit as a next-generation individual, A program for causing the computer to execute a process of performing a genetic algorithm operation on an individual population in a population storage unit and outputting an operation result. (Supplementary note 8) A program for a computer that processes an optimization problem using a genetic algorithm, wherein information on an individual population is stored in a population storage unit of the computer, and the occurrence probability of alleles of the individual population is stored. Is stored in a model storage unit of the computer, an individual is selected from the individual population by referring to the probabilistic model, and the selected individual is stored in the population storage unit as a next-generation individual. A program for causing a computer to perform a process of performing a genetic algorithm operation on an individual population in the population storage unit and outputting an operation result. (Supplementary Note 9) A program for a computer that processes an optimization problem using a genetic algorithm, wherein information on a plurality of individual populations is stored in a plurality of population storage units of the computer, and Information on a probabilistic model representing the occurrence probability of an allele is stored in a plurality of model storage means of the computer, and the probabilistic model is referenced to compare the probabilistic models of two populations of the plurality of individual populations. , An individual is selected from at least one of the two populations, the selected individual is stored as a next-generation individual in a corresponding population storage unit, and a genetic algorithm is applied to each of the populations in the plurality of population storage units. A program for causing the computer to perform a process of performing the operation of, and outputting the operation result. (Supplementary Note 10) A recording medium recording a program for a computer that processes an optimization problem using a genetic algorithm, the program storing information on an individual population in a population storage unit of the computer, Information of a probabilistic model representing the occurrence probability of alleles of the individual population is stored in a model storage unit of the computer, a new individual is generated by referring to the probabilistic model, and the generated individual is used as a next-generation individual. A computer-readable recording medium that stores in the group storage unit, performs a genetic algorithm operation on an individual population in the group storage unit, and causes the computer to perform a process of outputting an operation result. (Supplementary Note 11) A recording medium recording a program for a computer that processes an optimization problem using a genetic algorithm, the program storing information on an individual population in a population storage unit of the computer, Information of a probabilistic model representing the occurrence probability of alleles of the individual population is stored in the model storage unit of the computer, an individual is selected from the individual population by referring to the probabilistic model, and the selected individual A computer-readable record characterized by storing as an individual in the group storage unit, performing a genetic algorithm operation on an individual population in the group storage unit, and causing the computer to execute a process of outputting an operation result. Medium. (Supplementary Note 12) A recording medium recording a program for a computer that processes an optimization problem using a genetic algorithm, the program storing information on a plurality of individual populations in a plurality of population storage units of the computer. Stored in a plurality of model storage means of the computer, the information of the probabilistic model representing the appearance probability of alleles of each individual population, among the plurality of individual populations by referring to the probabilistic model. Compare the two population probabilistic models,
An individual is selected from at least one of the two populations, the selected individual is stored as a next-generation individual in the corresponding population storage unit, and the individual populations in the plurality of population storage units are
A computer-readable recording medium, characterized in that the computer is caused to perform a process of outputting a genetic algorithm operation and outputting an operation result.

[0091]

EFFECTS OF THE INVENTION According to the present invention, it becomes possible to incorporate into the next generation a chromosome that makes GA operation efficient by using a probabilistic model generated from a GA chromosome population. Therefore, the search efficiency of the solution is improved as compared with the case where the probabilistic model is not used.

Further, by evaluating the difference between populations using the probabilistic model of each chromosome population of parallel GA, it becomes possible to disperse these populations in different regions. Therefore, the search efficiency of the parallel GA is improved.

[Brief description of drawings]

FIG. 1 is a principle diagram of an optimization problem processing device of the present invention.

FIG. 2 is a configuration diagram of a first processing device.

FIG. 3 is a flowchart of first GA processing.

FIG. 4 is a diagram showing a first chromosome population and evaluation function values.

FIG. 5 is a diagram showing a probabilistic model of a simple GA.

FIG. 6 is a diagram showing a consensus sequence.

FIG. 7 is a diagram showing a comparison between a chromosome population and a consensus sequence.

FIG. 8 is a diagram showing a first effective evaluation function value.

FIG. 9 is a configuration diagram of a second processing device.

FIG. 10 is a flowchart of second GA processing.

FIG. 11 is a diagram showing a stochastic model of a parallel GA.

FIG. 12 is a diagram showing a second chromosome population and evaluation function values.

FIG. 13 is a diagram showing a second effective evaluation function value.

FIG. 14 is a diagram illustrating an example of a GA calculation unit and a GA unit.

FIG. 15 is a diagram showing an example of specifying flight data.

FIG. 16 is a diagram showing chromosome data.

FIG. 17 is a diagram showing a correspondence relationship for decoding.

FIG. 18 is a configuration diagram of an information processing device.

FIG. 19 is a diagram showing a recording medium.

[Explanation of symbols]

11 Group storage means 12 Model storage means 13 means of generation 14 Selection means 15 Operation means 16 Output means 21 Early Chromosomal Development 22 Chromosome population storage 23 GA calculation unit 24 Gene statistical operation part 25, 33 Probabilistic model storage unit 26 Chromosome origin 27 Chromosome selection part 28 End determination unit 29 Probabilistic model control unit Control unit between 31 GA 32 GA part 34 Stochastic model control unit 35 Distance calculator 41 flight objects 42 Flight Schedule Management Department 51 CPU 52 memory 53 Input device 54 Output device 55 External storage device 56 medium drive 57 Network connection device 58 bus 59 Portable recording medium 60 servers 61 Database

Claims (5)

[Claims] 1. An optimization problem processing device using a genetic algorithm, comprising: a group storage unit for storing information on an individual population; and information on a probabilistic model representing the occurrence probability of alleles of the individual population. Model storing means, generating means for generating a new individual by referring to the probabilistic model, and storing the generated individual in the group storing means as a next-generation individual; An optimization problem processing device, comprising: an operating means for operating a genetic algorithm and an output means for outputting an operation result. 2. An optimization problem processing device using a genetic algorithm, comprising: a population storage means for storing information on an individual population; and information on a probabilistic model representing the occurrence probability of alleles of the individual population. Model storing means, selecting means for selecting an individual from the individual population with reference to the probabilistic model, and storing the selected individual in the group storing means as a next-generation individual; On the other hand, an optimization problem processing device comprising an operating means for performing an operation of a genetic algorithm and an output means for outputting an operation result. 3. An optimization problem processor using a genetic algorithm, comprising a plurality of population storage means for respectively storing information of a plurality of populations, and a probabilistic model representing the probability of occurrence of alleles in each population. Of a plurality of model storing means for storing the information of the above and the probabilistic model, two groups of the plurality of individual groups are compared, and an individual is selected from at least one of the two groups and selected. A selection unit that stores the individual as a next-generation individual in the corresponding group storage unit, and a plurality of operation units that perform the operation of the genetic algorithm for the individual populations in the plurality of population storage units and operation results. An optimization problem processing device comprising: an output unit for outputting. 4. A program for a computer that processes an optimization problem using a genetic algorithm, wherein information on an individual population is stored in a population storage unit of the computer, and alleles of the individual population appear. Information of a probabilistic model representing a probability is stored in a model storage unit of the computer, a new individual is generated by referring to the probabilistic model, and the generated individual is stored in the group storage unit as a next-generation individual, A program for causing a computer to perform a process of performing a genetic algorithm operation on an individual population in the population storage unit and outputting an operation result. 5. A program for a computer that processes an optimization problem using a genetic algorithm, wherein information on an individual population is stored in a population storage unit of the computer, and alleles of the individual population appear. Information on a probabilistic model representing a probability is stored in a model storage unit of the computer, an individual is selected from the population of individuals by referring to the probabilistic model, and the selected individual is stored in the population storage unit as a next-generation individual. A program for causing a computer to perform a process of performing a genetic algorithm operation on an individual population in the population storage unit and outputting an operation result.