JPH1185720A - Method and device for searching optimum solution - Google Patents

Abstract

PROBLEM TO BE SOLVED: To efficiently search an optimum solution with less searches by evaluating the propriety of each solution concerning an applied solution group, performing the search of the optimum solution for generating a new solution group, and repeatedly performing the evaluation and search until it is judged that the required optimum solution can be found. SOLUTION: This device is provided with a search part 100 and a recursive learning part 200. An initial solution generating part 110 forms an initial chromosome group for performing the search. A searched result evaluating part 130 evaluates the respective generated chromosomes through suitability calculation using an evaluation function. A solution generating part 120 performs the search on each generation while using genetic control such as selection, crossing-over and mutation. A case extracting part 210 judges whether or not a case for generating judgement rules from the evaluated chromosomes is to be stored. A case storage part 220 holds and stores the cases judged to be stored as a case group. A search knowledge generating part 230 generates the judgement rules for limiting the direction of the optimum solution search from the stored case group.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optimum solution search method and an optimum solution search apparatus, and more particularly, to a method of inductive learning using examples to limit the direction of the optimum solution search so that the optimum solution can be searched with a smaller number of searches. The present invention relates to a technique for efficiently searching at high speed.

[0002]

2. Description of the Related Art In general, various industrial processes such as scheduling for determining a production order of products, adjustment of control parameters inherent in a control model, and design for arranging parts having various shapes in a two-dimensional area. There is a need in the art for optimization problem techniques and, in fact, applications.

[0003] Here, the optimization problem is defined as a problem in which a solution that maximizes or minimizes a value of a given evaluation function as much as possible under a predetermined constraint condition is determined from a solution set. Is done.

[0004] In such an optimization problem, generally, when the solution space becomes large, it takes a very long time to search. Therefore, various approaches have been attempted to improve the efficiency of the solution search. Among these, as a technique for efficiently searching for an optimal solution, a technique that has recently attracted attention is a genetic algorithm (Genetic Algorithm,
Hereinafter, it is referred to as “GA”. ). GA is an algorithm that models the state of chromosome evolution based on the principle of biological evolution (selection, crossover, mutation) in the natural world. GA considers this chromosome as a solution corresponding to each problem, assigns a value representing a part of the solution to each locus in the chromosome, and applies genetic manipulation through evaluation based on the evaluation function for each problem. By going on, it is applied to various optimization problems ("Genetic Algorithm", Takeshi Aiin, Tomoharu Nagao, Shokodo, 1993).

A general processing procedure by the GA will be described with reference to a flowchart shown in FIG.

When solving a certain optimization problem, first, the size of the population, an evaluation function for determining the goodness of the solution, the probability of performing a genetic operation, the number of searches, the various thresholds, and other necessary values for the operation of the GA. The parameters are set, and the length, coding method, etc., of the general expression method of the solution to the problem are determined as the gene expression on the chromosome (S10).
0). First, a plurality of chromosome patterns, which are solutions to the problem, are randomly generated, and an initial chromosome group is created (S101).

Thereafter, the following processing loop is performed until the convergence condition of the chromosome population is satisfied (S112). That is, for each individual (chromosome) in the chromosome population, the evaluation of fitness, which is a criterion of chromosome quality, is performed using the evaluation function (S104), and it is determined that all chromosomes of the generation have been evaluated. (S102, S10
3), the selection (S
114), crossover (S115) and mutation (S116) are performed to generate a next-generation chromosome population.

[0008] Here, the selection is a process of stochastically selecting chromosomes to be left in the next generation and selecting the remaining chromosomes according to the degree of fitness. In addition, crossing is the process of generating a new individual by rearranging the chromosome between two individuals, and mutation is replacing the value of a certain locus on the chromosome with another allele, This is the process of generating a new individual in the vicinity.

The GA is a method that can efficiently search an optimal solution from a solution space because it can eliminate the redundancy due to the combination by using the concept of gene manipulation such as the above-mentioned crossover and mutation. have. However, on the other hand, it is necessary to quickly approach the vicinity of the optimal solution because there are still random search elements in the determination of loci to be mutated during genetic manipulation and the determination of gene breaks in crossover. However, there is a case where the person once approaches the vicinity and then moves away. That is, there is a disadvantage that convergence near the optimal solution is not good. For this reason, a large number of searches are required to find the optimal solution, and particularly when the solution space to be searched is large, it is necessary to check the fitness of a large number of chromosomes. It was difficult to find the optimal solution.

[0010] In order to solve such a drawback of the GA, a method called a hybrid GA, which combines a search by the GA and another method such as a local search, has been developed. Conventionally known "optimization problem solving processing method and apparatus"
Japanese Patent Application Laid-Open No. 7-219920 is also one of those which follow the flow of such a method, in which an AI processing unit, a GA processing unit using a deterministic method such as a method based on artificial intelligence, and each of these processing units are used. It comprises a planning engine unit having a corresponding correction unit.

The details of the processing will be described below. First, as the first step, the AI processing unit searches for the optimal solution in the solution space using the basic rules for search, and among the set of variables constituting the solution, the value that is the optimal solution is For what is found, the solution space is limited by fixing the found value as part of the solution. Then, as a second process, the GA processing unit performs a search using GA, targeting only the range of the solution space limited by the first process, thereby speeding up the search for the optimal solution. .

[0012]

However, the above-described search method and apparatus have the following problems. That is, first, whether or not the limitation of the solution space in the AI processing unit is appropriate and effective depends on how appropriately the basic rules used for the AI search can be prepared. However, the determination and accumulation of the essential basic rules need to have been previously performed by another means such as a human system. For this reason, the time required to accumulate the basic rules and the validity thereof largely depend on experience. Second, since the planning engine is configured to correct the solution in a human system, the longer the number of searches, the longer it takes.

For this reason, especially when the solution space is large, the above-described preparation of the basic rules and the correction of the solution become a bottleneck, and the problem of speeding up the total optimal solution search can be sufficiently solved. This is difficult to achieve, and furthermore, there is a limit that the accuracy of the obtained solution may be impaired depending on the contents of the basic rules and the evaluation method used by the AI processing unit.

As described above, the present invention requires a large number of searches to find an optimal solution because the convergence in the vicinity of the optimal solution in the prior art is poor. This was done to solve the problem that the optimal solution could not be found within a short time.
Then, the purpose is to limit the direction of the optimal solution search by inductive learning using cases, and to provide an optimal solution search method and apparatus capable of efficiently searching for the optimal solution with a smaller number of searches. Is to provide.

Another object of the present invention is to further refine the set of cases used for inductive learning, thereby further improving the accuracy of limiting the direction of searching for an optimal solution.

In addition, another object of the present invention is to realize an optimum solution search more easily by holding a solution evaluation result as positive or negative in a case and performing a search based on this value. .

In addition, another object is to realize an optimum solution search more easily by internally generating a threshold value used for determination of case extraction.

[0018]

In short, the method of the present invention (claim 1) evaluates the goodness of each solution with respect to a given solution group, and evaluates the solution group obtained as a result of the evaluation. Solution search method for searching for an optimum solution for generating a new solution group by performing the above-described evaluation and the search repeatedly until it is determined that the required optimum solution has been obtained. Selecting at least a solution based on the evaluated solution and a value based on the evaluation result as a case according to the evaluation result, and using the set of the selected cases, restricting a search direction of the optimum solution. This is characterized in that a determination rule for performing the determination is generated recursively. According to this method, a decision rule for restricting the direction of the optimal solution search is automatically generated by inductive learning from a set of cases accumulated based on the result of the solution evaluation. In addition, a solution can be searched for in a direction in which a solution having a high evaluation value is expected to exist. That is, it is possible to efficiently search for the optimal solution with a smaller number of searches.

In the invention of claim 2, the optimum solution search method further comprises: storing the selected case in a case holding means;
Based on the value of the evaluation result, one or more cases that are not most suitable for storage are determined, and the case set that has been determined is deleted from the case set to refine the case set. The set of cases can be refined using the value of the goodness of fit that is the result of. In other words, as more cases are accumulated, it becomes possible to improve the accuracy of the restriction on the direction of the optimal solution search.

According to a third aspect of the present invention, there is provided a method for searching for an optimal solution using a genetic algorithm, wherein the step of searching for an initial solution and the calculation of the degree of goodness indicating the goodness of the searched solution are performed. Performing, and determining, based on the fitness, whether or not to store the solution for which the fitness is obtained, as a case for performing inductive learning. Selectively storing in the case holding means as
A step of inductively generating a decision rule used for the optimal solution search from the set of stored cases, and a step of restricting the direction of the optimal solution search by using the decision rule to search for a new solution; Wherein the cases each have at least a class attribute determined based on the attribute value of the solution and the fitness of the solution, and the fitness is obtained for all the solutions in the solution population of the generation. In such a case, a decision rule is generated based on the value indicated in the classification class, and when performing an optimal solution search, a part of the solution is excluded from the search based on a pattern indicated by the decision rule to determine a solution. It is characterized in that the direction of search is restricted.
According to such a method, a decision rule for restricting the direction of the optimal solution search by GA is automatically generated by inductive learning from a set of cases accumulated based on the classification class derived from the degree of suitability of the solution, Using this determination rule, a solution can be searched for in a direction in which a solution having a high degree of matching is expected to exist. That is, it is possible to efficiently search for the optimal solution with a smaller number of searches.

Further, in the invention according to claim 4, the classification class is either a positive value indicating that the degree of fitness is equal to or more than a predetermined value or a negative value indicating a degree of fitness equal to or less than a predetermined value. , Based on the positive and / or negative values,
By refinement of the case set and generation of the decision rule, it is possible to hold the evaluation result of the solution as positive or negative in the case and perform a search based on the binary.
That is, it is possible to more easily perform the optimal solution search.

Further, in the invention according to claim 5, the upper limit threshold value used for the determination of storage of the case is a predetermined value obtained from a higher-order group of the goodness-of-fit in the initial solution group, By setting the lower threshold value to a predetermined value obtained from the sub-group of the goodness of fit in the initial solution group, it is possible to internally generate a threshold value used for determination of case extraction. Become. That is, it is possible to more easily perform the optimal solution search. Note that the predetermined value here is determined by the processing speed, computer resource status, and the like.
This is a value obtained according to an appropriate value of the number of stored cases.

Further, the apparatus of the present invention (claim 6) includes an initial solution generating section for searching for an initial solution, a search result evaluating section for evaluating the solution quality of the searched solution, and a new solution group from the searched solution group. A search unit having a solution generation unit that searches for a solution, and a case extraction unit that determines whether to store the evaluated solution as a case for performing inductive learning,
At least a case storage unit that selectively stores the cases determined to be stored, and an inductive learning unit that has a search knowledge generation unit that generates a determination rule used for optimal solution search from the set of stored cases. The inductive learning unit selects at least a solution based on the evaluated solution and the value based on the evaluation result as a case according to the evaluation result, and uses the set of the selected cases to perform an optimal solution search. It is characterized in that a decision rule for restricting a direction is recursively generated, and the solution generating unit restricts the direction of the optimal solution search by performing a search using the decision rule. According to such an apparatus, a decision rule for restricting the direction of the optimal solution search is automatically generated by inductive learning from a set of cases accumulated based on the result of the solution evaluation, thereby using the decision rule. In addition, a solution can be searched for in a direction in which a solution having a high evaluation value is expected to exist. That is, it is possible to efficiently search for the optimal solution with a smaller number of searches.

In the invention according to claim 7, the case storage unit further determines one or a plurality of cases which are not most suitable for storage from the case set based on the value of the evaluation result. By refining the case set by deleting the determined case from the case set, the case set can be refined by using the value of the degree of conformity as a result of the evaluation. In other words, as more cases are accumulated, it becomes possible to improve the accuracy of the restriction on the direction of the optimal solution search.

According to a further aspect of the present invention, there is provided an apparatus for searching for an optimal solution using a genetic algorithm, wherein an initial solution generating section for searching for an initial solution, and a fitness degree indicating goodness of the solution with respect to the searched solution. A search unit having a search result evaluation unit for performing calculation, a solution generation unit for searching for a new solution from a solution group that has been searched, and a solution for which the degree of goodness is obtained are stored as examples for performing inductive learning. A case extraction unit for determining whether or not to perform storage based on the degree of suitability, a case storage unit for selectively storing at least a solution determined to be stored as a case in a case holding unit, and an induction from the set of stored cases An inductive learning unit having a search knowledge generation unit for generating a decision rule in a dynamic manner, wherein the cases are classified into a classification class determined based on an attribute value of the solution and the fitness of the solution, respectively. Has at least, the search knowledge generating unit, when the degree of goodness is obtained for all the solutions of the solution group of the generation, generates a determination rule based on the value indicated in the classification class, The solution generation unit limits the direction of the solution search by removing a part of the solution from the search based on the pattern indicated by the determination rule. According to such a method, from a set of cases accumulated based on a classification class derived from the goodness of fit of a solution,
By automatically generating a decision rule for restricting the direction of the optimal solution search by GA by inductive learning, a solution is searched for in a direction in which a solution with a high degree of fitness is expected to exist using this decision rule. be able to. That is, it is possible to efficiently search for the optimal solution with a smaller number of searches.

In the ninth aspect of the present invention, the classification class is either a positive value indicating that the degree of fitness is equal to or more than a predetermined value or a negative value indicating a degree of fitness equal to or less than a predetermined value. , Based on the positive and / or negative values,
By refinement of the case set and generation of the decision rule, it is possible to hold the evaluation result of the solution as positive or negative in the case and perform a search based on the binary.
That is, it is possible to more easily perform the optimal solution search.

Further, in the invention according to claim 10, the upper limit threshold value used for the determination of the storage of the case is a predetermined value obtained from the higher-order group of the fitness in the initial solution group, By setting the lower threshold value to a predetermined value obtained from the sub-group of the goodness of fit in the initial solution group, it is possible to internally generate a threshold value used for determination of case extraction. Become. That is, it is possible to more easily perform the optimal solution search.

A program for realizing the above-described optimum solution search function can be stored in a recording medium, and the recording medium is read by a computer system, and the program is executed while controlling the computer. Thereby, the above-described optimal solution search can be realized. Here, the recording medium includes general devices capable of recording a program in a machine-readable state, such as a memory device, a magnetic disk device, and an optical disk device.

[0029]

Embodiments of the present invention will be described below in detail with reference to the drawings. The purpose of this embodiment is to obtain an optimal solution for a control parameter adjustment problem existing in a control system using a GA.

As shown in FIG. 2, the optimal solution search device according to the present embodiment includes a search unit 100 and an induction learning unit 200. In FIG. 2, the solid line represents the transition of the control,
A broken line indicates data input / output (IO).

The search unit 100 further includes an initial solution generation unit 110 for forming an initial chromosome group for performing a search, and a search result evaluation unit for evaluating each of the generated chromosomes by calculating a fitness using an evaluation function. 130 and a solution generation unit 120 that performs a search in each generation using genetic operations such as selection, crossover, and mutation. Further, a configuration may be adopted in which the solution of the search result is held using the search result file 11. The search result does not necessarily need to be stored in a file format, but can be stored in a memory according to the computer resource status and the like.

The inductive learning unit 200 is a component for realizing the new function of the present embodiment, and determines whether or not to store it as an example for generating a determination rule from the evaluated chromosomes. Case extraction unit 210, a case storage unit 220 for storing and storing cases determined to be stored as a case set, and search knowledge for generating a determination rule for limiting the direction of optimal solution search from the stored case set. And a generation unit 230. The means for holding the case set may be a structure using the case base 12, or may be a structure for holding the case set in a memory particularly in the case of a problem requiring high-speed processing. Furthermore, if the judgment rules generated from the case set are also stored in the knowledge base 13, instead of using all cases to generate judgment rules, only newly added and deleted cases are used. By partially correcting the judgment regulation in a batch, it is possible to accelerate the search and apply the judgment rule to other problems. In addition, the control database 10 stores various control parameters such as initial parameters for GA search and is appropriately referred to from each component. This is also considered in consideration of a demand for high-speed processing and versatility. A configuration in which the data is held in a memory as appropriate can be adopted.

This embodiment is configured as described above, and the flow of the processing will be described below with reference to the flowchart shown in FIG.

Here, four parameters (p1 to p
4) is to be optimized, and each parameter is represented using three bits. That is, if one solution in this question is expressed as a chromosome, it becomes a sequence of genes consisting of 12 bits. Here, for example, p1 =
The solution of 0.0, p2 = 1.4, p3 = 1.2, and p4 = 1.2 is expressed as the chromosome shown in FIG. 4 from the bit expression shown in FIG.

In searching for an optimum solution, first, as initial processing, various parameters necessary for operating the present embodiment of the optimum solution search method are set. Specifically, values g1 to g4 used for GA search by the search unit and T1 to T4 used for case storage and the like by the induction learning unit are set (S000).

Next, first, the value of each locus on the chromosome to be subjected to genetic manipulation, here, the value of 0 or 1, is determined using random numbers. By generating g1 chromosomes thus created, an initial chromosome population (chromosome population of the 0th generation) is created (S001). Further, in this step, the number g1 of generated chromosomes is set as the number of searches for the 0th generation. For example, if the value of g1 is 1
When set to 0, as shown in FIG.
Up to 10 chromosomes are generated, and the number of searches is also set to 10. Note that the initial value at each locus does not necessarily need to use a random number, but may be given as an initial value in S000 according to the pattern in question or the degree of experience.

Next, from the chromosome population, chromosomes that have not been evaluated yet, that is, whose fitness has not been calculated by the evaluation function, are extracted one by one (S002).

In this case, the chromosome to be extracted is
It is determined whether it is present in the chromosome population (S00
3) If the extracted chromosome exists, that is, if the evaluation (calculation of the degree of fitness) has not been performed in the current generation, the process proceeds to the evaluation step of S004. on the other hand,
If the extracted chromosome does not exist, that is, if all the chromosomes have been evaluated, the process proceeds to the step of determining convergence in S012. For example, assuming that the fitness of the chromosomes c1 to c4 among the ten chromosomes in FIG. 5 has been calculated, the chromosome c5 is extracted, and the process proceeds to S004. On the other hand, if the calculation of the fitness of all the chromosomes in FIG. 5 has been performed, there is no chromosome to be extracted in S002, and the process proceeds to S012.

Assuming that the chromosome c5 has been extracted as described above, the evaluation of the chromosome of c5, that is, the calculation of the fitness is performed using an evaluation function corresponding to each problem (S004). Assuming that the fitness of each chromosome is calculated by a predetermined evaluation function as shown in FIG. 6, the fitness of chromosome c5 is given as 16.

Next, it is determined whether or not the evaluated chromosome is to be stored as a case used for generating a determination rule based on the value of the degree of fitness calculated in S004 (S005). That is, when the value of the fitness of the extracted chromosome is larger than the upper threshold T1, it is determined that the chromosome is stored as a positive case, and when it is smaller than the lower threshold T2, it is stored as a negative case. judge. Further, when neither of the above cases is satisfied, that is, T2 or more T
It is determined that chromosomes of 1 or less are not stored as cases.
That is, the stored chromosomes (cases) and the non-stored chromosomes (cases) have the relationship shown in FIG. For example, if T1 and T2 are given as 11 and 9, respectively, it is determined that the chromosomes c1, c5, c7, c8, and c10 are stored as positive cases. It is determined that the chromosomes c2, c4, c6, and c9 are stored as negative cases. Further, it is determined that storage is not performed for chromosome c3. In the storage determination process of the case in S050, the determination is performed using threshold values T1 and T2 given from outside. However, the threshold values T1 and T2 may be set not to be given externally, for example, by setting the fitness of the upper half of the initial chromosome population and the fitness of the lower half of the initial chromosome population.

As described above, the chromosome determined to be a correct case in S005 is stored in the case base 12 as a correct case (S006).

When the correct cases are stored, it is further determined whether or not the number of correct cases stored in the case base is larger than the correct upper limit T3 (S00).
7). At this time, if it is T3 or less, it is determined that the upper limit of the number of stored normal cases has not been reached, and the process proceeds to S002. On the other hand, T
If it is larger than 3, it is determined that the upper limit of the number of stored normal cases has been reached, and the process proceeds to S008. For example, assume that the value of T3 is 2. At this time, if the cases stored in the case storage unit are given as shown in FIG. 8, since there is only one positive case, it is determined that the upper limit of the positive case storage has not been reached, and S002 Proceed to. On the other hand, if the cases stored in the case storage unit are given as shown in FIG. 12, the number of positive cases is three, so it is determined that the upper limit of the positive case storage has been reached, and the process proceeds to S008. move on.

If it is determined in S007 that the upper limit of the positive cases has been exceeded, a chromosome with the lowest matching degree is searched for from the positive cases stored in the case storage unit, and the chromosome is retrieved from the case storage unit. It is deleted (S008). For example,
If an example is given as in FIG. 12, according to FIG.
Of the three positive cases, the one with the smallest fitness is
Since (c5, correct) is selected, the case of c5 is deleted from the case storage unit. Therefore, the case set stored in the case storage unit after the processing of S008 has the contents shown in FIG.

On the other hand, the chromosome determined to be a negative case in S005 is stored in the case base 12 as a negative case (S009).

When a negative case is stored, it is further determined whether or not the number of negative cases stored in the case base 12 is larger than the negative case storage upper limit T4 (S01).
0). At this time, if it is T4 or less, it is determined that the upper limit of the number of stored negative cases has not been reached, and the process proceeds to S002. On the other hand, T
If it is larger than 4, it is determined that the upper limit of the number of stored negative cases has been reached, and the process proceeds to S011. For example, assume that the value of T4 is 2. At this time, if the cases stored in the case storage unit are given as shown in FIG. 9, since there is only one negative case, it is determined that the upper limit of the negative case storage has not been reached, and S002 Proceed to. On the other hand, if the cases stored in the case storage unit are given as shown in FIG. 10, the number of negative cases is three, so it is determined that the upper limit of negative case storage has been reached, and the process proceeds to S011. move on.

If it is determined in step S010 that the upper limit of the negative cases has been exceeded, the chromosome with the highest matching degree is searched from the negative cases stored in the case storage unit, and the chromosome is searched from the case storage unit. It is deleted (S011). For example,
If an example is given as in FIG. 10, according to FIG.
Of the three negative cases, the best fit is (c
Since (2, negative) is selected, the case of c2 is deleted from the case storage unit. Therefore, the case set stored in the case storage unit after the processing of S011 has the contents shown in FIG.

By performing the above-described case storage processing of S005 to S011 for the initial generation (0th generation) of FIG. 5, the cases having the contents shown in FIG. 14 are stored in the case base 12. .

On the other hand, if it is determined in S003 that the fitness of all the chromosomes in the chromosome population has been calculated, first, it is determined whether or not the chromosome population of the relevant generation has sufficiently converged. That is, a termination condition is determined (S012). Specifically, depending on whether the number of searches so far is greater than g2, if the number of searches is less than or equal to g2, it is determined that the chromosome population has not converged,
Proceeding to S013, on the other hand, if the number of searches is greater than g2, the chromosome population has converged, that is, the optimal solution for the given problem has been found, and the optimal solution search process ends.

For example, assume that the value of g2 is set to 100. At this time, at the stage of calculating the fitness of the initial generation (0th generation), the number of searches is given as 10, so that it is determined that the chromosome population has not converged, and the process proceeds to S013. On the other hand, at the stage of calculating the fitness of the 10th generation,
Since the number of searches is given as 110, it is determined that the chromosome population has converged, and the processing of the optimal solution search device ends.
Note that the convergence determination (determination of the end of the solution search) here does not necessarily need to be a method using the upper limit of the number of searches. For example, for a type of problem in which processing time is required to pursue the accuracy of the solution even if it takes some time. It is also possible to make a determination based on the value of the degree of fit to the best solution or the degree of convergence for the best solution. However, by appropriately setting the number of searches so that the search is completed within a predetermined time, it becomes easy to deal with a problem in which an optimal solution is to be obtained within a practical time. That is, by appropriately changing the conditions for convergence determination according to the problem, it is possible to cope with various optimization problems of different requirements.

If it is determined in S012 that the chromosome population has not yet converged, first, a determination rule for restricting the direction of searching for an optimal solution is generated, and the following genetic operation is performed using the rule. (S014-S016).

That is, in the judgment rule generation processing performed first, for each case stored in the case base 12, each bit of the chromosome is attributed, the positive case is classified into the classification class “positive”, and the negative case is classified into the classification class Interpret as "negative". Also,
According to this interpretation, the IDF algorithm (references "Shigeaki Sakurai, Dai Araki, Generation of Fuzzy Decision Tree by Inductive Learning, Transactions of the Institute of Electrical Engineers of Japan, vol. 113-C, no. 7,
488-494 (1993) ") is applied to the case set to generate a decision rule in the form of a decision tree (S013). This determination rule is the knowledge for controlling the search direction. For example, FIG.
Are interpreted as cases having attribute values and classification classes shown in FIG. For this set of cases, I
By applying the DF, knowledge of the tree structure shown in FIG. 16 is generated. Here, in this case, the tree structure (search direction control knowledge) of FIG. 16 further includes “if A2 = 0 and A3 = 0 and A5 = 0, negative”, “A2 = 0 and A3 = 0 and A5 = 1”. If A2 = 0 and A3 = 1, it is positive "and" If A2 = 1, it is negative ". Note that the possible values of the classification class of each case are not necessarily limited to positive and negative. This can be reflected in the decision rules. Further, the subdivided value can be held as information different from the classification class. Further, the method used for generating the determination rule is not limited to IDF. Instead of using IDF to learn such search direction control knowledge, for example, refer to the reference document “Translated by Setsuo Osuka, Artificial Intelligence Dictionary, Maruzen, pp.177-1
Page 78 (1991) ".

Next, first, a chromosome to be subjected to genetic manipulation is selected. That is, according to the probability of selection for each chromosome calculated by equation (1), g
One chromosome is extracted, and a chromosome group that is the basis of the next-generation (first-generation) chromosome group is generated (S014). Here, in equation (1), fi represents the degree of fitness for chromosome i.

[0053]

(Equation 1) The calculation formula (1) used for this selection is a formula prepared according to the type of the optimization problem. Further, in the present embodiment, when making a selection, processing is not particularly performed in consideration of the contents of the case. However, it is also possible to make a selection using a selection pressure that reflects the content of the case,
In such a case, the efficiency of the search is further improved.

Next, the search total number is updated by adding the number of chromosomes included in the chromosome group to the search total number. For example, in the case of the chromosome population of FIG. 5, the probability of each chromosome is calculated as shown in FIG. In the case of this example, the number g1 of chromosomes to be selected is given as 10, and therefore, on average, one chromosome is selected for every probability of 0.1. However, in the actual selection, since such selection is performed using random numbers, a chromosome having a probability of less than 0.1 may be selected. Here, it is assumed that the chromosome group of FIG. 18 has been selected. In addition, the number of searches is updated to 20 by generating the chromosome population.

Next, the selected chromosome group shown in FIG. 18 is crossed using search direction control knowledge (S015). That is, first, for two chromosomes extracted using random numbers from the chromosome group selected in S150, a breakpoint is first determined, and chromosomes separated at the breakpoint are exchanged. Next, the intersection processing is performed using the search direction control knowledge. That is, first, it is determined whether or not there is a bit pattern in the extracted two chromosomes that matches the bit pattern whose classification class is “positive”. Here, the bit pattern whose classification class is “positive” is determined in step S01.
In the judgment rule generated in step 3, the conclusion is “positive”
Corresponding to the condition part of the decision rule. For example, in the case of the determination rule of FIG. 16, the second bit 0 (A2 = 0), the third bit 1 (A3 = 1), and the second bit 0 (A2 =
0), third bit 0 (A3 = 0), fifth bit (A5 =
There are two “positive” bit patterns 1). If this bit pattern does not exist, it is determined that the intersection with respect to the extracted chromosome is completed. on the other hand,
If this bit pattern is present, the gene (between the other cut chromosome and the other chromosome (so that the bit pattern appears on the chromosome storing many genes of the original chromosome where the bit pattern exists) Bit) is exchanged. The intersection using this search direction control knowledge is performed until the intersection rate calculated by the equation (2) becomes equal to or more than the threshold value of g3.

[0056]

(Equation 2) For example, it is assumed that chromosome c7 and chromosome c3 have been extracted from FIG. 18, and that chromosomes c11 and c12 have been generated by the intersection as shown in FIG. Here, as shown in FIG. 19, the chromosome c7 includes a bit pattern having a “positive” classification class of the second bit 0, the third bit 0, and the fifth bit 1; The second and third bits of the chromosomes c11 and c12 are exchanged so that the same bit pattern as in the case expected to be high appears. As a result, chromosome c13,
c14 is generated. Here, the value of the threshold value g3 is set to 0.
In the case of 8, four crossings are performed, and eight chromosomes are recreated. FIG. 21 shows the chromosome population after the re-creation.

After the processing of the intersection, as shown in FIG.
Mutation using the search direction control knowledge is performed on the chromosome population after the crossover (S016). That is, for each bit of the chromosome of the chromosome group, the bit is inverted using the search direction control knowledge. . Specifically, in the case of a bit included in the bit pattern corresponding to the bit pattern of the classification class “positive”, it is determined that the bit pattern is not mutated. On the other hand, the other bits are inverted with a probability of g4. For example, chromosome c1 included in the chromosome population of FIG.
In the case of 4, bits other than the second, third, and fifth bits that match the “positive” bit pattern are targeted for mutation.
In the case of the chromosome c14, if a mutation occurs only in the seventh bit, a chromosome c21 is generated from the chromosome c14 as shown in FIG. Here, if the mutation rate g4 is given as 0.1, the total chromosome population is 1
As shown in FIG. 21, there are 20 bits, and as shown in FIG. 21, there are 14 bits constituting a bit pattern in which the classification class is “positive”. Is 10.6 bits inverted. At this time, FIG. 23 shows an example of the result of mutation performed on the chromosomes included in the chromosome population of FIG.
In FIG. 23, ten bits are inverted.

In this embodiment, crossover and mutation are performed by directly using only the judgment rules for which the classification class is “positive” (S015, S01).
6). However, at the beginning of a search with a small number of cases, the correct decision rule is not always generated, so the decision rule with a classification class of “positive” is ranked according to the number of cases that make up the decision rule. Is performed, and as the search progresses, the number of determination rules used for storing the bit pattern is increased.

Furthermore, crossover and mutation are performed not only using the judgment rule for the classification class being “positive”, but also in combination with or using the judgment rule for the classification class being “negative”. Is also good. That is, for the intersection,
For a bit pattern with a negative classification class, the genes of two more chromosomes may be exchanged so that this bit pattern does not appear. Alternatively, a part of the bit pattern may be always inverted so that the bit pattern is broken. In addition, other than the method described in the present embodiment, various modifications can be made without departing from the spirit of the present invention.

The above is the processing of the optimal solution search performed for one generation. By repeating these processes recursively for the next-generation chromosome population until it is determined that the chromosome population has converged (S012),
Search for the optimal solution.

As described above, according to the present embodiment, the following effects can be obtained. In other words, by using cases selected according to the degree of fitness for genetic manipulation, bit patterns with a higher degree of fitness can be easily left in the next generation of chromosomes. It is now possible to reach a solution.

[0062]

As described above, according to the present invention,
The following effects are obtained. That is, from the generated solutions, the solutions and classification classes extracted according to the value of the degree of goodness are accumulated as cases, and a decision rule for limiting the direction of the optimal solution search from such a set of cases is obtained by inductive learning. Since it has a function of automatically generating, it is possible to limit the direction of searching for an optimal solution to a direction in which a solution having a high degree of fitness (better solution) is expected to exist using the generated determination rule. Therefore, the effect is obtained that randomness in the search is reduced, the degree of convergence of the solution near the optimal solution is improved, and the optimal solution can be obtained with a smaller number of searches. By making the search more efficient, both the solution evaluation time and the solution search time in the optimization problem processing can be reduced. For this reason, as a result, it is possible to obtain an optimum solution at a higher speed. Similarly, in an optimization problem of a practical level, that is, a problem of obtaining a so-called suboptimal solution, it is possible to find an optimal solution within a realistic time.

In addition, the present invention has a function of automatically accumulating cases used for generating decision rules, that is, acquiring knowledge itself without preparing in advance, so that the load of acquiring decision rules can be reduced. As a result, it is possible to obtain an effect that the speed of the total search processing can be increased.

Further, since a case set as a basis for generating a decision rule has a function of refining using a range of the degree of conformity, a function is provided.
As the number of generations increases and the number of cases accumulated increases, the direction of searching for an optimal solution can be more limited to the direction in which a better solution is expected to exist. As a result, the degree of convergence of the optimal solution can be further improved, and the optimal solution search can be performed more efficiently.

Further, a case which is a basis for generating a decision rule is as follows.
Since it has the function of retaining the evaluation results by positive and negative classification classes, by generating judgment rules using the values of the classification classes, it is possible to simplify the processing without the need for a large-scale AI, case-based inference system, etc. This makes it possible to perform the optimal solution search in a short time.

Further, since a threshold value used for determination of case extraction is internally generated, there is no need to input a threshold value from the outside in advance for determination of case storage. can get. This allows
It is possible to more easily search for an optimal solution without depending on human experience.

As described above, when the present invention is used, practical effects in various industrial fields such as reduction of production cost and distribution cost and improvement of product accuracy are exhibited according to the field to which the optimization problem is applied. This is an invention that is extremely effective in industry.

[Brief description of the drawings]

FIG. 1 is a flowchart showing an algorithm of an optimal solution search method according to the present invention.

FIG. 2 is a functional block diagram showing a functional configuration of an optimal solution search device according to the present invention.

FIG. 3 is a diagram describing a correspondence between a value of a parameter to be adjusted and a bit expression according to the embodiment of the present invention.

FIG. 4 is a diagram showing a chromosome describing one solution of the problem described in the embodiment.

FIG. 5 is a diagram showing an initial chromosome population generated by random numbers.

FIG. 6 is a diagram describing a relationship between chromosomes stored in an initial chromosome population and their fitness.

FIG. 7 is a diagram for explaining a relationship between cases stored in a case base and cases not stored.

FIG. 8 is a diagram illustrating a state immediately after chromosome c1 is stored in the case base.

FIG. 9 is a diagram illustrating a state immediately after chromosome c2 is stored in the case base.

FIG. 10 is a diagram illustrating a state immediately after chromosome c6 is stored in the case base.

FIG. 11 is a diagram illustrating a state immediately after chromosome c2 is deleted from the case base.

FIG. 12 is a diagram illustrating a state immediately after chromosome c7 is stored in the case base.

FIG. 13 is a diagram illustrating a state immediately after chromosome c5 is deleted from the case base.

FIG. 14 is a diagram showing chromosomes finally stored in a case storage unit from chromosomes of an initial chromosome population on a case basis.

FIG. 15 is a diagram in which chromosomes finally stored in the case storage unit from chromosomes of the initial chromosome population are re-expressed as cases.

FIG. 16 is a diagram showing a decision rule learned by applying IDF to the case set of FIG. 15;

FIG. 17 is a diagram showing a probability of selecting a chromosome to be stored in the next generation for a chromosome stored in an initial chromosome population.

FIG. 18 is a diagram showing a chromosome population generated by selection from an initial chromosome population.

FIG. 19 is a diagram showing the intersection of two chromosomes c7 and c3.

FIG. 20 is a diagram illustrating a manner in which crossed chromosomes are modified in order to save a bit pattern whose classification class is “positive” for chromosomes c13 and c14.

FIG. 21 is a diagram showing a chromosome population obtained by performing crossover on the chromosome population of FIG. 18.

FIG. 22 is a diagram showing a state in which a mutation is performed.

FIG. 23 is a diagram showing a chromosome population obtained by performing mutation on the chromosome population of FIG. 21.

FIG. 24 is a flowchart showing an algorithm for searching for an optimal solution using a conventional GA.

[Explanation of symbols]

p1 to p4 Parameters to be adjusted c1 to c29 Number of chromosome g1 to g4 Parameters for starting GA T1 to T4 Parameters used in case storage processing

Claims (10)

[Claims] The present invention evaluates the quality of each solution with respect to a given solution group, and searches for an optimum solution for generating a new solution group with respect to the solution group obtained as a result of the evaluation. An optimal solution search method for outputting an optimal solution by repeatedly performing the evaluation and the search until it is determined that the required optimal solution has been obtained, wherein at least the evaluated solution and the evaluation result A value based on the evaluation result, and
An optimal solution search method characterized by recursively generating a decision rule for restricting a direction of searching for the optimal solution using the selected set of cases. 2. The method for searching for an optimal solution further stores the selected case in a case holding unit, and stores the selected case in a storage based on a value of the evaluation result from a set of the stored cases. The method according to claim 1, wherein one or more unsuitable cases are determined, and the case set is refined by deleting the determined case from the case set. 3. A method for searching for an optimal solution using a genetic algorithm, wherein a step of searching for an initial solution, a step of calculating a goodness of fit for the searched solution, and a step of calculating goodness of fit. Determining whether or not to store the solution obtained as a case for performing inductive learning based on the fitness, at least selecting the solution determined to be stored in the case holding means as a case as a case And a step of inductively generating a decision rule used for searching for an optimal solution from the set of stored cases, and limiting the direction of searching for an optimal solution by using the decision rule to generate a new solution. Wherein the case has at least a classification class determined based on an attribute value of the solution and a degree of goodness of fit of the solution, respectively. When the degree of goodness is obtained for all the solutions in the solution group of the generation, a judgment rule is generated based on the value indicated in the classification class, and when the optimum solution search is performed, the judgment rule indicates An optimal solution search method characterized by restricting the direction of solution search by removing a part of the solution from the search based on the pattern. 4. The classification class is either a positive value indicating that the degree of fitness is equal to or greater than a predetermined value or a negative value indicating a degree of fitness equal to or less than a predetermined value. The method according to claim 3, wherein the case set is refined and the decision rule is generated based on the value. 5. An upper limit threshold value used for determination of storage of the case is a predetermined value obtained from an upper group having the goodness of fit in an initial solution group, and the lower limit threshold value is The optimal solution search method according to any one of claims 2 to 4, wherein the predetermined value is a predetermined value obtained from a sub-group of the fitness levels in the initial solution group. 6. An initial solution generating section for searching for an initial solution, a search result evaluating section for evaluating the solution quality of the searched solution, and a solution generating section for searching for a new solution from the searched solution group. A search unit having, a case extraction unit that determines whether or not to store the evaluated solution as a case for performing inductive learning; a case storage unit that selectively stores at least the cases determined to be stored; And an inductive learning unit having a search knowledge generating unit that generates a decision rule used for an optimal solution search from the stored set of cases, and wherein the inductive learning unit includes at least the evaluated solution and The value based on the evaluation result, according to the evaluation result,
Selected as a case, and using the selected set of cases,
An optimization method for inductively generating a determination rule for limiting a direction of an optimal solution search, wherein the solution generation unit limits a direction of the optimal solution search by performing a search using the determination rule. Solution search device. 7. The case storage unit further determines, from the case set, one or more cases that are not most suitable for storage based on the value of the evaluation result, and stores the determined case. 7. The optimal solution search device according to claim 6, wherein the case set is refined by deleting the case set. 8. An apparatus for searching for an optimal solution using a genetic algorithm, comprising: an initial solution generating section for searching for an initial solution; and a search result evaluating section for calculating a degree of goodness of the searched solution to indicate a good solution. A search unit having a solution generation unit for searching for a new solution from the searched solution group; and determining whether or not to store the solution with the goodness of fit as a case for performing inductive learning. A case extraction unit that determines based on the degree, a case storage unit that selectively stores at least a solution determined to be stored as a case in a case holding unit, and a recursive determination rule generated from a set of the stored cases. An inductive learning unit having a search knowledge generating unit; and the case has at least a classification class determined based on an attribute value of the solution and a fitness of the solution. The search knowledge generating unit generates a determination rule based on the value indicated in the classification class when the fitness is obtained for all the solutions in the solution group of the generation. An optimal solution search apparatus characterized in that a direction of a solution search is limited by removing a part of the solution from the search based on a pattern indicated by the determination rule. 9. The classification class is either a positive value indicating that the degree of fitness is equal to or more than a predetermined value or a negative value indicating a degree of fitness equal to or less than a predetermined value; 9. The optimal solution searching device according to claim 8, wherein the case set is refined and the decision rule is generated based on the value. 10. The upper limit threshold value used for the determination of storage of the case is a predetermined value obtained from an upper group having the goodness of fit in the initial solution group, and the lower limit threshold value is:
The optimal solution search device according to any one of claims 6 to 9, wherein the initial solution group is a predetermined value obtained from a sub-group of the fitness levels.