JP3280487B2 - Planning method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a means for providing an optimal plan in various plans in various fields, and more particularly, to a plan planning problem or the like in which the number of permutations and combinations becomes enormous with a simple configuration. It relates to means to solve the problem at high speed.

[0002]

2. Description of the Related Art Conventionally, in a variety of fields (for example, a printed pattern design of an electronic substrate, a manufacturing process, a sewer piping design, a distribution system, etc.), it is the largest or the largest in a problem of planning. Various methods have been proposed for determining an item to be minimized and finding an optimal solution that is a plan for maximizing or minimizing the item within a practically acceptable time.

[0003] For example, the document "" Travel salesman problem ""
Breakthrough method-Amazing high performance using chaos, Science Asahi,
1993-Feb. Or JP-A-2-3045.
As described in Japanese Patent Publication No. 87 “Shortest distance, shortest time or minimum transportation cost calculation device”, optimization of planning problems in various fields can be realized by applying an interconnected neural network, chaos, etc. It is intended to realize a means to perform within an acceptable time.

[0004] Also, the document "HANDBOK OFG"
ENETIC ALGORITHM (Van Nost
rand Reinhold Computer Li
As described in “Barry)”, a so-called “genetic algorithm” that simulates the evolution of living organisms and finds a suboptimal solution globally has also attracted attention as a promising means.

[0005]

The so-called "enumeration method" for examining all conceivable combinations of plans for a given planning problem is described in the above. The common idea of recent optimization means, including application examples, is to first create a plan and change the contents of the plan little by little and efficiently (that is, to make a random plan). Instead of trying to find the optimal solution with a small number of planning), and finally, in the planning problem, evaluate the value of the objective function, which is the function representing the item that you want to maximize or minimize, A good plan (eg, a plan that reduces the value of the objective function) is adopted as a plan for the next candidate, and finally, in order to obtain an optimal solution in a short time, that is, a plan that maximizes or minimizes the objective function. Also It is.

However, according to the conventional method using a neural network, chaos, or the like, first, every time a new plan is created, a parameter which is a parameter at the time of planning for optimizing the objective function is used. The number n of components of the target plan is at least 2-3 times (ie, n ²
To n ³ (times)), it is necessary to perform a predetermined process for planning, and secondly, there is no theoretical proof that the optimal solution can be reached, and the optimality is evaluated empirically. Therefore, there is a problem that it takes a long processing time to reach an optimal solution or a sub-optimal solution, and the probability of reaching the optimal solution is extremely low.

[0007] For example, in the system described in the above-mentioned document, a so-called “Traveling Salesman Problem (TS)” which determines the shortest route among routes that visit 30 locations only once each time.
P) "solution to recent computers (for example, 10-
Even if a workstation having a capacity of 100 (MIPS) is used, it takes a long time of 20 seconds. In addition, the optimal solution is erroneously obtained with a probability of 3 (%).

[0008] On the other hand, the aforementioned "genetic algorithm"
Is to search for an optimal solution globally by associating the elements of the plan with "chromosomes", which are the main elements of genes in biological evolution, and providing a plurality of these chromosomes.

[0009] As a result, although the performance for surely finding the optimal solution is inferior to the means using a neural network, chaos, etc., the processability, especially the convergence to the optimal solution at the initial stage of the search start, is greatly improved. Likely to be. However, in order to simulate genetic and evolution, enormous processing such as complicated mating, mutation, evaluation, selection, and reevaluation must be repeatedly performed, and effective application to actual industrial fields is extremely difficult. It was difficult.

Therefore, the present invention solves the problems related to processing using a “genetic algorithm”,
An object of the present invention is to provide a means for obtaining a plan that maximizes or minimizes an objective function from a planning problem having a large number of permutations in an extremely short time.

[0011]

The following means are conceivable to solve the above-mentioned problems.

That is, setting means for accepting at least a given problem to be planned and values of variables necessary for solving the problem, and an item to be minimized or maximized in the problem to be planned. Optimizing means for creating a plan to create an objective function to be represented, minimizing or maximizing the value of the created objective function, and storage means for storing at least variables necessary for the planning, Means for generating an initial plan for generating a predetermined number (population number) of parent plans of the first generation, calculating means for calculating a value of an objective function corresponding to the plan, and a plurality of plans. and planning rearrangement means for arranging the descending order or the ascending order of the objective function value, in a case where a plurality of plan is given, by selecting the number of each plan is assigned according to the objective function value <br/> When you are Parent plan selection means for selecting a predetermined number (population number) of parent plans by using a number designated by the predetermined number (population number) which is predetermined for each return, and using the number indicated by the constant as the selection number; A child plan generating means for generating a child plan by replacing any two elements with respect to the selected parent plan;
Control means for activating the calculating means and the plan rearranging means, generation replacing means for selecting a plan corresponding to the number of populations as a new parent plan according to the rearranged order among the rearranged plans, and A plan including an optimal plan selecting means for repeatedly activating the parent plan selecting means, the child plan generating means, the control means, and the generation changing means up to a predetermined number of generations, and selecting a plan for maximizing or minimizing the objective function value. It is a planning device.

The child plan generation means generates two random numbers uniformly distributed within the range of the number of parent plan elements for the selected parent plan, and arranges them in the order specified by the random numbers. A means for exchanging two elements and generating a child plan is preferred.

When calculating the objective function value for the given plan, the arithmetic means calculates only the change of the objective function due to the change of the plan element, and adds the change to the objective function value before the change. It is preferably a means for adding minutes. Further, it is preferable that the display device further includes a display unit, and the display unit displays the plan selected by the optimal plan selection unit.

It is to be noted that the storage means stores in advance a predetermined number (number of population) constants predetermined for each repetition of the generation and random numbers used when generating the child plan. Is also conceivable.

The following planning method is also conceivable.

That is, the contents of a given plurality of plan candidates are changed, an objective function value for each plan candidate is calculated for each predetermined number of changes, and the number of plan candidates is reduced to a predetermined value based on the calculated value. Restriction, a planning method for planning the value of the objective function to minimize or maximize, if the plan is a permutation problem, change a part of the permutation element list,
When the plan is a combination problem, at least one of the elements to be selected is changed and selected, and a change value of the objective function value caused by the change is calculated. By adding to the objective function values of the candidates, an objective function value for the changed plan candidate is obtained, and for each of the predetermined number of changes, the order of the objective function values of each plan candidate is indicated by a previously given selection constant. This is a planning method in which a plurality of planned candidates are selected, and one plan is selected from the selected plan candidates.

Further, the plurality of given plan candidates are respectively made to correspond to one chromosome, and the value of the objective function representing the item to be minimized or maximized in the plan is made to correspond to the adaptation value. Based on this, a predetermined number of parent plans are selected, and mating, mutation,
And performing a process of performing at least one type of genetic operation among the inversions and planning a plan to minimize or maximize the objective function value, wherein the selection of the parent plan is based on the adaptive value A genetic planning method determined by the descending order or the ascending order is also conceivable.

[0019]

The present invention is a planning means which does not include redundant processing such as selection, population restriction and crossing in the conventional genetic algorithm, and which does not lower the optimality of the solution which is extremely clear and required.

That is, according to the present invention, in planning,
When using a high-level computer language such as C language, it is possible to use only one line for the repetition processing for the number of people in one generation, and it is possible to obtain a plan with the same optimumness as the conventional method. Becomes

Means for realizing the above functions can be achieved by discovering the following important laws in the evolution of living things and applying them.

Since the genetic algorithm is described in detail in the above-mentioned document, only the outline thereof will be described here.

First, the maximum population of individuals for each generation is determined in advance, and a plan is associated with each individual. Each individual prepares in advance an objective function defined for expressing an evaluation item, and is evaluated based on the value of the objective function.

Next, the ratio of the evaluation value to the sum of the evaluation values of the entire population is calculated.

In a certain generation, two or more parent components are exchanged for one or more “parents” selected according to the ratio (dominantly inherited). "Mating operation" to generate "child" and "mutation operation" to change one parent element according to a predetermined mutation rate, "Inversion operation to reverse the arrangement of one parent element" , Etc., a predetermined number of “child individuals” are generated.

Next, for a parent individual and a child individual, a predetermined number of individuals are made to survive according to a predetermined procedure, and the process of shifting to the next-generation process is repeated a predetermined number of times.

In the above-described processing, in the conventional method, a selection criterion corresponding to the evaluation value is generated for every individual for each generation, so that many processing steps such as a ratio calculation for the whole are required. . Dominant parent selection also requires many processing steps.

Further, the gene operator processing and the objective function value evaluation processing also require at least the power of two or more processing steps of the number of planned elements.

However, when the definition of the adaptation function is constant in the evolution of organisms, it can be statistically detected that the criteria for selecting a parent in dominant inheritance hardly change for each generation. That is, the variation in the objective function value in the initial generation is such that the exponent in the exponential function constituting the objective function is large, that is, decreases as the generation progresses. There is almost no difference in the objective function value between individuals. This process is the same for any problem.

That is, by obtaining such transitions experimentally or empirically in advance for each problem, no detailed and complicated dominant genetic processing is required at the time of actual planning.

Next, it becomes possible to make use of important natural rules regarding the processability of the gene operator.

Since the mating operator propagates from two different individuals, the evaluation of the generated offspring individuals (processing for calculating the objective function value) must be performed strictly.
On the other hand, the mutation operator and the inversion operator are operations in which a part of one individual is changed to obtain a new offspring individual. Therefore, the evaluation is based on the evaluation value of the parent and the evaluation of the changed part. Just add the value. That is, the evaluation step can be performed without depending on the number of elements to be planned.

In order to obtain a result equivalent to that of the conventional genetic algorithm by applying the above-mentioned important natural laws, only the following processing (this processing is an example) is required. is there.

(Step 1) An evaluation value of the initial population is calculated.

(Step 2) Individuals are rearranged in descending order (or in ascending order) of evaluation values.

(Step 3) The following processing is repeated for a predetermined number of generations.

(Step 4) The following step 5 is repeated a predetermined number of times.

(Step 5) A mutation operation is performed on a predetermined parent individual based on the rank of the evaluation value, a child individual is generated, the evaluation value of the changed part is calculated, and the parent individual is evaluated. The evaluation value of the child individual is obtained in addition to the evaluation value.

(Step 6) Individuals are rearranged in descending order of the evaluation value.

(Step 7) The individual having the maximum evaluation value is output.

Here, assuming that C1, C2, C3, C4, and C5 are constants and the number of elements of the optimal target problem is n, steps 1 and 2 may be C1 × n (times).

The number of repetitions in step 3 is C2 ×
n (times) is sufficient.

Step 4 is the mutation rate,
Since it is smaller than n, processing of C3 × n (times) is sufficient. Step 5 is a predetermined number of times C4 (times) that does not depend on n since the calculation is only for the changed portion. Step 6
Is C5 × n by using a bucket sort or the like.
(Times).

As a result, according to the present invention, it is possible to make a plan with at most n ² (times) processing times.

For example, in the conventional method, n ³ (number of) steps are included in the preparation of one plan, and when this is repeated n ³ (times), a total of n ⁶ (times) processing steps are performed. Cost.

For example, in the literature, an objective function E representing an item to be optimized, that is, minimized or maximized, is described.
(I) is the total distance, and E is used to minimize the total distance.
(I) is defined as follows.

E (i) = ΣΣΣda · Vbc (i) · (V
bc-1 (i) + Vbc + 1 (i)) (The first Σ is the sum of a = 1 to n, the second Σ is
The sum of b = 1 to n, the third Σ represents the sum of c = 1 to n. Here, dij represents the distance between the points i and j, and Vij represents the probability of visiting the point i at the jth time.

In order to execute the arithmetic processing of this equation, at least n ³ (times) calculations are required.

Strictly speaking, in the example described in the above-mentioned document, the term n ⁴ exists, so that a huge amount of calculation is required as n ⁷ (times), and the invention is applied to a planning problem when n is 30 or more. Is not realistic.

The fastest of the conventional genetic algorithms is the one that makes a plan in the order of n ³ (times). Let's compare with this.

Using a computer capable of executing 10 ⁷ instructions per second (ie, having a capability of 10 (MIPS)), trying to solve an n = 10,000 optimization problem, Assuming that the number of processing steps of one individual in each means is 1,000, the processing time Told in the conventional fastest genetic algorithm is at least Told = (1000 × n ⁴ ) / (10 (MIPS)) = ( 10 ³ × 10 ¹⁶ ) / (10 ⁷ ) = (10 ¹⁹ ) / (10 ⁷ ) = 10 ¹² ≒ 3 (10,000 years) On the other hand, the processing time Tnew in the present invention is: Tnew = (1000 × n ² ) / (100 (MIP
S)) = (10 ³ × 10 ⁸ ) / (10 ⁷ ) = (10 ¹¹ ) / (10 ⁷ ) = 10 ⁴ (seconds) ≒ 3 (time) Since the processing time is reduced to 1/10 ⁸ This means that the processing speed has been increased. That is, a speedup of 100 million times is realized.

This indicates that the problem that can be solved within the same time is dramatically increased if the allowable processing time is determined at the same time as the achievement of the high speed.

[0053] For example, Nold the number of target solution can be optimized in the conventional method, when the allowable time is 10,000 ^{(s), nold = 4 √ (10000} × 10 7/10 3) = 4 √ ( 10 ⁸⁾ = 100 ⁽⁴ √ it is while a representative of the fourth root), subject number N of solutions can be optimized in the present invention
new is, Nnew = √ (10000 × 10 7/10 3) = √ (10 8) = 10000. That is, it is possible to solve an optimization problem having 10,000 elements in about 3 hours.

[0054]

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

FIG. 1 shows a configuration example of a genetic planning device 1 (hereinafter, often referred to as an “optimizing device”) according to the present invention.

As in the example shown in FIG. 1, the present apparatus comprises an optimizing means 2, a setting means 3, a display means 4, and a storage means 5.
And is configured.

The setting means 3 is a means having at least a function of receiving a given problem to be planned, a function of receiving constants indicating parameters required for planning, and the like, and can be realized by, for example, a keyboard, a mouse, or the like.

The optimizing means 2 is a means for drafting an optimal plan. The optimizing means 2 creates an objective function representing an item to be minimized or maximized in a given problem to be planned, and calculates the value of the objective function by: It is a means for performing at least the processing of the following steps in order to maximize or minimize it.
It can be realized by an electronic device such as a PU, a ROM (in which a program for performing a predetermined process is stored in advance), and a RAM.

Here, the processing performed by the optimizing means will be outlined in steps.

First, in step 1, an objective function value for a "chromosome", which is a plan drafted for a predetermined number (hereinafter, often referred to as "population"), is calculated. , The “evaluation value” of the plan. Such an evaluation value may be referred to as “fitness”.

Next, as step 2, the chromosome is
A process of rearranging the evaluation values obtained by the calculation in descending order is performed. In the present embodiment, the plan that maximizes the objective function is obtained.However, in the case of the minimum value, it can be dealt with by a small change such as making the reciprocal of the objective function value of the chromosome an evaluation value. . Of course, it is also possible to arrange chromosomes in ascending order instead of descending evaluation values.

In step 3, the processing from step 4 to step 6 described below is performed for a predetermined number of generations (ie,
(Repeated number of times).

In step 4, control is performed so that step 5 described below is repeatedly performed a predetermined number of times.

Step 5 is predetermined for each generation, and is performed for an individual (hereinafter referred to as a “parent individual”) selected according to the ratio of the evaluation value of each individual to the sum of the evaluation values of all individuals. Plural integer random numbers uniformly distributed within the length range of the individual (from "1" to "1" if the length of the individual is "10")
It is an integer random number taking a value up to "0"), rearranging the elements of the selected parent individual or a part of the element list of the parent individual to generate "child individuals", and the objective function value of the changed part Is calculated and added to the objective function value of the parent individual to determine the evaluation value of the child individual.

Step 6 is a process performed after the repetition of Step 4 is completed, that is, for each generation transition. The parent individual group (which is a set of parent individuals) and the child individual group (which is a set of child individuals) ), The individuals are rearranged by the number of “populations” in descending order of the evaluation value of each individual.

Step 7 is an individual having the largest evaluation value in the process up to step 6, ie,
Output a plan that satisfies the purpose in the plan.

The storage means 5 is means for storing at least the problem given via the setting means 3, constants used for optimization, and the like, and is realized by, for example, a RAM or the like.

The display means 4 is a means for displaying information stored in the storage means 5 via the setting means 3, necessary constants, processing results by the optimizing means (planning results, etc.), and a liquid crystal display. It can be realized by a display device, an EL display, a CRT or the like.

Next, the processing procedure of the optimizing means 2 will be described with reference to FIG.

This means comprises: a step A for evaluating all individuals corresponding to the step 1; a step B for sorting all the individuals in descending order of the evaluation value corresponding to the step 2; 3 is selected, a new individual is generated by an operation such as a change in a part of the individual, or a change in the arrangement, and the degree of change of the objective function value for the changed part is calculated. Then, this is added to the previously obtained evaluation value of the parent individual to determine the evaluation value of the child individual.
And the parent and child populations are rearranged in descending order of the evaluation value of each individual, and selected for the number of “populations”. Steps D and C corresponding to step 6 are defined as C2 ×
n (times) (for example, C2 = population number, n is the number of elements to be planned) A function of repeatedly updating the pointer “PP” so as to repeat the process, and the process of step C is performed by C1 × n (times) Repeat Step D to C1
(Times) (for example, C1 = 20)
It has a function of repeatedly updating the pointer "gn".

First, the operation of the present invention will be described in detail with reference to FIG.

FIG. 3 shows a so-called "Travel Salesman Problem (TSP)" as an example of a planning problem, and shows a state in which a problem given via the setting means 3 has been set. Such a state may be displayed on the display means, for example).

Now, the problem is that, starting from the point “0: ●”, visiting the points “1” to “10” only once,
This is a problem of determining, for example, a route having the longest distance (of course, a problem of determining the shortest route) among routes returning to the re-point "●".

Here, the objective function is the sum of distances, and the purpose of optimization is to maximize the distance. However, even if the objective function is the sum of the time required to visit all places, It goes without saying that any means may be used, such as the sum of the energy consumed by the means used to visit a car or the like.

When finding the shortest distance, it goes without saying that the problem can be solved by using the reciprocal of the longest distance.

FIG. 4 shows data stored in the storage means 5, in which the distance D (f, t) from the point f to t is defined in a matrix. For example, from point 1 to point 2
Is obtained by one search that D (1,2) = 17.

Hereinafter, each step processing shown in FIG. 2 will be described in accordance with this problem.

As shown in the left side of FIG. 6, for example, the initial parent chromosome in which the numbers of 10 cities are randomly arranged, that is, 10 plans are stored in the storage means 5 in advance. ing.

In step A, the objective function, that is, the sum total F (P
(I)) is calculated as follows.

F (P (i)) = ΣDm → m + 1 (Σ is m
= 1 to 10) where i = 1, P (1) = (1, 2, 3, 4, 5, 6 , 7, 8, 9, 1
Since 0), the objective function F (P (1)) = D 1 → 2 + D 2 → 3 + D 3 → 4 + D 4 → 5 + D 5 → 6 + D 6 → 7 + D 7 → 8 + D 8 → 9 + D ₉ → the _{10 + D 10 → 11 = 17} + 23 + 27 + 41 + 34 + 45 + 43 + 12 + 22 + 24 = 288. However, in this description, for convenience of calculation, the point “●” is set to “11”. Similarly, values of the objective function from P (2) to P (10), that is, the “evaluation value” of the individual are obtained. In FIG. 2, for convenience of explanation, P
(1) = 24, P (2) = 18,..., P (10) = 13
It is assumed that the value of.

[0081] Next, in step B, sort each individual in descending order of evaluation value of the parent individual to be included in the parent set PS ₁ generation = 1. As a result, as shown in FIG. 2, a of the work area array a (j) (j = 1 to 20) in the storage means
P (9), P (3), P
(7), P (8), P (1), P (2), P (10),
Parent individuals are arranged in the order of P (4), P (5), and P (6).

The above steps A and B are steps for performing preprocessing of the optimization procedure.

Next, only two steps C and D
With the types of processing, the conventional optimization processing that requires a complicated and huge procedure can be achieved in an extremely short time as follows.

FIG. 11 shows a processing procedure of a conventional standard genetic algorithm.

Here, step A and step B correspond to step AG and step BG, respectively.
According to the conventional method, a parent individual selection operation for simulating dominant genetic evolution is required in step CG or step FG, and this operation is indispensable for characterizing a genetic algorithm. It has been assumed that.

However, this operation requires many processing steps, which has been a major factor in preventing the practical use of the genetic algorithm.

Therefore, in the present invention, an important property was discovered by examining the theory of biological evolution and performing enormous information processing simulations. As a result, while obtaining the same result as the parent individual selection operation, the number of processing steps is zero, that is, unnecessary.

FIG. 7 is an explanatory diagram of important properties in selection and dominant inheritance in the above evolution.

A descending order array a of the evaluation value of the above-mentioned generation = 1
The sum of the evaluation values in (1) to (10) is as follows: Σa (i) (i = 1 to 10) = 303 with reference to FIG. Using this, the result of calculating the ratio of each evaluation value to the above sum is shown in percentage (%).

The lower right part of FIG. 8 is a trend graph in which the horizontal axis is a (i) and the vertical axis is ap (i) (%) of the evaluation value. This approximates an exponential function having an index P (gn) determined by “generation = gn”, and ap (i) = a (i) ∧P (gn) + C (gn)
(“∧” indicates a power). Here, C (gn) is a constant determined by the generation gn.

The lower left part of FIG. 8 shows the ratio (%) of each evaluation value.
Is a pie chart that determines the “degree of dominance” of each individual, and is called a “roulette wheel”.

The dominant genetic mechanism is that “the higher the adaptability to the environment to which the individual belongs, the higher the survival rate and the preservation rate of offspring”. Therefore, the higher the evaluation value ratio (%), the higher the evaluation value ratio (%). What is necessary is just to raise the probability of becoming a “parent” of descendant generation.

For example, as shown in the lower left diagram of FIG.
Define a roulette wheel with (%) as the minimum scale,
What is necessary is just to generate a uniform random number corresponding to “1 to 1000”, and set the individual corresponding to the location as a parent.

In the example shown in the drawing, for example, it is assumed that the integer random number generated first time is i1 = 88, and indicates the “range from 1 to 277”, that is, the range of 27.7 (%). Therefore, a (1) is selected as the “parent individual”. If the integer random number generated the second time is i2 = 925, the evaluation value ratio (%) from a (1) to a (7) is 9
Since 1.7 and a (8) are 3.3 (%), the scale falls within the range of 917 to 950, so that a
(8) is selected as the “parent individual”.

In this manner, uniform integer random numbers for the number of parent individuals required for the genetic operation are generated, the roulette wheel is searched, and the parent individuals are determined.

Note that even if such a roulette wheel is not specially prepared, for example, the plans are arranged in the order of large (or small) objective function values, selection numbers are assigned, and several populations are set in advance. Of course, it is also possible to select a plan indicated by a constant (a random number generated in advance) which is determined only as a selection number and select it as a parent plan.

FIG. 7 shows that the above processing is performed from generation 1 to generation 20.
2 shows the transition of the evaluation value of a surviving individual when a certain genetic operation is performed. According to the lower left figure, the evaluation value has a large variation in the initial generation, but as the generation progresses, the variation decreases.
It can be seen that at generation = 20, the value converges near the optimum value.

The lower right part of FIG. 7 is a plot of the same data in the evaluation value ratio (%).

The above equation: ap (i) = a (i) ∧P (gn) + C (gn)
(“∧” indicates a power).

By the way, in the traveling salesman problem to be optimized in this embodiment, the position and number of cities were changed, and statistical processing and analysis were performed. As a result, P (gn)
And C (gn) are affected by the initial parent individual and the genetic operation, but are found to be "the same when the parameters and genetic operation procedure of the initial individual are fixed".

In other words, it indicates that "if the optimization target and the genetic operation are determined, the parent which is dominantly selected for each generation is determined by the evaluation value rank." That is, it is not necessary to perform the roulette wheel creation processing and the generation of uniform random numbers each time during the planning process, and these values can be determined in advance. That is, these values may be determined in advance and stored in the storage unit.

Now, the selected individual constant P (gn, p
p) (P (gn, pp) indicates a generation gn and a selected individual constant at the time of processing pp. gn is generation = 1 to 2
0, pp are the processing number pointers = 1 to 10) are secured in the storage means 5. As shown in FIG. 8, in this example, ten uniform random numbers are created in advance in the roulette wheel created by the selection ratio of the roulette wheel for each generation in FIG. Is stored in P. That is, for each generation, a parent plan from which a child plan is generated is selected in accordance with a predetermined constant.

These values need not be changed as long as the target plan, the objective function, and the like are the same.

Next, the processing in step C of FIG. 2 will be described. The process of step C is performed for each generation gn, that is, pp (times), which is the population number. In this embodiment, since the population is 10, the processing is performed 10 times.

There are various types of genetic operations (operators), and they are mainly described as “crossing”, “mutation”, and “mutation”.
It can be classified as "inversion".

“Mating” is performed for at least two or more parent individuals, and generates a child individual having the characteristics of each parent individual.

The present method has a feature that an individual having a certain good evaluation value is generated by a genetic operation on a very small number of individuals in order to effectively inherit the properties of a dominant parent individual. Since the element for improving the value is limited to the property of the limited parent and individual in the same environment, there is also a disadvantage that the evaluation value is not improved after reaching a certain evaluation value. Further, since the mating operation is complicated and its evaluation must be performed for every element, many processing steps are indispensable for one mating operation and evaluation.

Therefore, when a plan having a moderate degree of optimality is prepared in a relatively short time, there is room for practical use, but in practice, it is combined with other genetic operations or other optimization means. Is often used only for the initial state generation process.

On the other hand, “mutation” and “inversion” are operations for changing a part of one parent individual or an arrangement of genes (corresponding to elements to be planned) in the parent individual. Unlike mating, all possible solutions can be searched for, but there is a disadvantage that the convergence speed to the optimal solution varies due to the variation in the evaluation value of the initial individual.

Since the object of the present invention is to solve an actual problem at a high speed, the following means are used. The following genetic operation is considered to be a kind of mutation, but the genetic operation can be performed in exactly the same way in the inversion operation.

FIG. 5 illustrates a case where the process of step C in FIG. 2 is adapted to the traveling salesman problem.

The parent individual P selected by the method described above
(1) is P (1) = (1,2,3,4,5,6,7,8,9,1)
0), and the evaluation value at this time is F (P
(1)) = 288.

Next, two kinds of integer random numbers J and K uniformly distributed in the range of 1 to 10 are generated.

At this time, J ≠ K.

Next, the J-th element and the K-th element in the element array of P (1) are exchanged, and a new child individual C (1) is generated. Now, assuming that J = 3 and K = 8, C (1) = (1, 2, 8, 4, 5, 6, 7, 3, 9, 1)
0) Evaluation of the C (1) _{is, C (1) = D 1} → 2 + D 2 → 8 + D 8 → 4 + D 4 → 5 + D 5 → 6 + D 6 → 7 + D 7 → 3 + D 3 → 9 + D ₉ → the _{10 + D 10 → 11 = 17} + 45 + 24 + 41 + 34 + 45 + 32 + 27 + 22 + 24 = 311. Here, the evaluation of the child individual will be described by a method of accumulating the distances of all the routes between the traveling cities.

A second device in the present invention lies in that the steps required for this evaluation process are determined without depending on the number n of planning target elements.

In the above description, the integration processing is performed at least for n
Because the number of points is 10,000 points,
Each time a child individual is generated, 10,000 or more calculations are required.

However, as can be seen from FIG. 5, there are two mutated points due to the mutation operation.
In order to obtain the evaluation value of C (1), it is not necessary to add up all the routes, and only the route that has changed from P (1) needs to be recalculated. Understand. That is, F (C (1)) = F (P (1)) − Σ (distance of the deleted path) + Σ (distance of the added path) = F (P (1)) − (D ₂ → ₃ a _{+ D 3 → 4 + D 7} → 8 + D 8 → 9) + (D 2 → 8 + D 8 → 4 + D 7 → 3 + D 3 → 9) = 288- (23 + 27 + 43 + 12) + (45 + 24 + 32 + 27) = 288-105 + 128 = 311 . That is, extra calculations to be canceled are not performed.

The above processing is performed by setting the mutation constant J (gn, p) preset in the actual storage means 5 shown in FIG.
This will be described using p) and K (gn, pp). J (gn,
pp) and K (gn, pp) are the generations gn (gn
Is the ppth (pp is the generation pointer)
The number of mutation operations (mutation rate) is a mutation constant.

In the above method, the parent individual P (gn, pp) has been selected and its evaluation value F (P (gn, pp))
Has been obtained. Here, if j = J (gn, pp) and k = K (gn, pp), a child C generated from P (gn, pp)
The evaluation value of (gn, pp) is F (C (gn, pp)) = F
(P (gn, pp))-(Dj-1 → j + Dj → j + 1 + Dk-1 → k +
Dk → k + 1) + (Dj−1 → k + Dk → j + 1 + Dk−1 → j + Dj → k +
1) It can be seen that the value of the objective function is calculated only by performing the addition and subtraction processes eight times without depending on the optimization target number n.

In the case of "inversion", only one change is made, and if the same idea as described above is applied, four additions,
It is only necessary to perform the subtraction.

FIG. 6 shows the chromosomes (child chromosomes) of the offspring which were multiplied when the above genetic manipulation was performed using J and K.

As described above, the evaluation of each individual is performed at a very high speed in a certain processing step, that is, in a certain processing time regardless of the number of chromosome elements.

Next, Step D is performed for each transition of the generation gn. Individuals are rearranged in the descending order of the evaluation values of the parent individual group and the child individual group, and individuals are selected by the number of populations. . This is nothing but generation of a parent individual set of the generation “gn + 1”.

The number of steps for such processing can be at most C × n by using bucket sorting or the like.
(Times) It goes without saying that it can be performed in the following.

Thus, in this embodiment, generation = 2
When the processing up to 0 is completed, the individual having the largest evaluation value among the generated parent individual sets, that is, the plan is output as the optimal solution. By outputting to a display means such as a CRT, the processing result can be observed at any time.

FIG. 9 shows the results of a processing performance experiment when the number of elements to be planned is "100".

For the problem that the optimum value is known to be “100.0” in advance, the processing capacity is 100 (MIP
S) (Computation that can be performed 10 ⁸ times per second) is performed by using a computer. The horizontal axis represents the processing time, and the vertical axis represents the average value of all the individual evaluation values. The state of the evaluation value transition with respect to the time transition is plotted.

As means for optimizing, in addition to the present invention, a conventional standard genetic algorithm and a plan close to the optimum value by changing the plan randomly are left as optimization candidates. And the enumeration method (random search method).

Since the number of objects to be optimized is n = 100, the processing for n in the present invention required to obtain a solution having a desired optimality, for example, an evaluation value of 99.0 (%) or more of the optimal solution. As described above, when the processing order is O (n), the number of times is O (n) = C1 × n ² . Here, C1 is the number of processing steps of the computer required for one mutation or repetition processing, and is set to C1 = 10 ⁴ in this embodiment.

On the other hand, the conventional standard genetic algorithm whose processing procedure is shown in FIG. 11 has n ² within a loop of a square repetition processing of repetition of generation and repetition of population.
Since the processing includes mating, evaluation, and the like, which require up to n ³ (times) processing steps, the number of processing times for n is O (n) = C2 × n ⁴ . Here, it is assumed that C2 = C1 = 10 ⁴ .

In the case of the enumeration method (random search method), although it depends on the search method, the realistic number of finite processes and the processing time required to obtain an optimal solution or a solution having a predetermined optimality are as follows. , There is no guarantee how much.

Under the above assumptions, when planning is performed by each method, as shown in FIG. 9, in the present invention, a solution can be obtained in only about 1 second. So, to get the same solution, 10,000
(Seconds) processing time is required. Under these conditions, it can be seen that it is extremely difficult to find a solution having the desired optimality within a practical finite time by the processing based on the enumeration method (random search method).

On the other hand, FIG. 10 is a graph in which the time until a sub-optimal solution is obtained is plotted with the number n of planned objects plotted on the horizontal axis.

In the conventional genetic algorithm, n (the number of components of the plan to be planned) is 100 and 10,000
It takes a processing time of 0 (second), and it can be seen that it is difficult to obtain an effective solution for a large problem with n more than that.

On the other hand, according to the present invention, 100 (M
IPS), it is possible to use 1
A solution will be obtained within a processing time of 0000 (seconds) / 3 (time) or less.

Further, 10 (TMIPS) (TeraMips = means to perform 10 ¹⁰ operations per second)
When using a high-speed computer having the following calculation speed, (processing time (seconds)) = (number of processing steps required for optimization) / (processing steps executable in one second) = (C1 × ^{n 2) / (10 (TMIPS} )) = (10 3 × (10000) 2) / (10 10) is a = 10 ^11/10 can planning at 10 = 10 (seconds).

Conversely, if a time of 10,000 (seconds) is given, the above equation is transformed to the
Calculating the, the n = √ ((processing time (sec)) × (10 (TMIPS) ) / C1) = √ (10 4 × 10 10/10 4) = √ (10 10) = 10 5.

That is, in three hours, it is possible to actually make a plan having 100,000 plan elements. This indicates that the method according to the present invention has the capability to cope with extremely difficult planning problems such as, for example, pattern design on an electronic substrate.

FIG. 12 shows an example in which the present invention is applied to a problem of optimizing a production plan in the manufacturing industry, which is in great need.

The present embodiment is an example of a problem in which a plan for efficiently performing six types of operations 1 to 6 in the manufacturing facility A is prepared. Since there is only one facility, a setup time shown in the drawing is required for changing the jig, cleaning, setting of NC processing parameters, and the like at the time of work transfer.

When this plan is examined in association with the "traveling salesman problem", the work is made to correspond to the traveling points, the setup time is made to correspond to the distance between the traveling points, and the total work time is taken as the objective function. It is the same as minimizing (or maximizing).

In the above-described embodiment, the maximum of the objective function value is determined. However, when the objective function value is minimum, the ratio of the roulette wheel table value is set to the reciprocal, and the sorting direction is changed from descending order to ascending order. Needless to say, it can be easily handled.

As a result, the "traveling salesman problem" described above corresponds one-to-one. This further
This is equivalent to minimizing the total setup time, and the initial setup time of the parent individual P (1) having the best evaluation value among the initial parent individuals is “77 (minutes)”. "39 (minutes)" by the device according to (5) and 50 (%)
However, the total working time is reduced.

The number of facilities actually arranged in a large-scale factory is hundreds, and the number of operations ranges from thousands to tens of thousands per month.
FIG. 10 shows that a realistic optimal solution can be obtained in a very short time, and it is considered that the present invention exerts its effect as the scale of the manufacturing industry increases.

The same problems as those in this embodiment include the following problems. (1) Delivery plan (for example, the time required for delivery when a product is delivered through all predetermined delivery points using a delivery vehicle). Problem of minimizing delivery time), (2) vehicle allocation plan (for example, when allocating vehicles having a plurality of vehicles at a certain point, minimize the time until all vehicles have been allocated to a predetermined point) Problem), (3) Rolling plan in iron making (for example, problem of minimizing setup time in each process in consideration of a plurality of rolling processes), (4) Storage and retrieval plan of automatic warehouse (for example, stacker crane, etc.) The problem of minimizing the sum of the moving distances of the crane when loading and unloading luggage, etc.), (5) Material removal plan (for example, when taking a predetermined pattern from a given material, Minimize remaining Programming problem like (material, the pattern shape of the plane, a three-dimensional, etc.)), etc., applicable to various planning are considered.

FIG. 13 shows an embodiment of the hardware configuration according to the present invention.

In this embodiment, a control processor 11 for controlling the flow of a series of processes for solving a planning problem, an arithmetic processor 12 for performing operations such as addition, subtraction, multiplication and division, and a maximum number of populations are prepared. A parallel processing mechanism 13 for simultaneously evaluating a plurality of parent individuals;
And the like, and have a storage register 14 for storing constants and the like, and these components are connected by a bus line 15.

Control processor 11, arithmetic processor 1
2. The parallel processing mechanism 13 includes, for example, a CPU, ROM, RA
M, various types of CMOS, TTL, a program built in ROM, and the like. The storage register 7 is realized by, for example, a RAM.

Therefore, the apparatus according to the present invention is incorporated in a conventional serial processing type processor as a sub CPU (processing apparatus), and the number of combinations or the number of permutations giving the optimum value out of the number of permutations is determined. When it is necessary to solve a planning problem for obtaining a pattern, the sub CPU is activated to perform a problem solving process.

Thus, the processing performance in solving the planning problem is further improved.

[0152]

According to the present invention, with a simple structure,
This has the effect of providing a means for quickly creating an optimal plan for a given problem.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an optimization device.

FIG. 2 is an explanatory diagram of a processing procedure of an optimization unit.

FIG. 3 is an explanatory diagram illustrating a setting example of planning target information;

FIG. 4 is an explanatory diagram showing an example of setting distance information between cities in the traveling salesman problem.

FIG. 5 is an explanatory diagram of a mutation operation and a high-speed evaluation method.

FIG. 6 is an explanatory diagram of haploid growth by a mutation operation.

FIG. 7 is an explanatory diagram of rules in selection and dominant inheritance.

FIG. 8 is an explanatory diagram of ultra-high-speed processing by quantification of the law of nature.

FIG. 9 is an explanatory diagram showing an evaluation value and a processing time.

FIG. 10 is an explanatory diagram showing a processing time and the number of planning target elements.

FIG. 11 is an explanatory diagram of a processing procedure of a conventional genetic algorithm.

FIG. 12 is an explanatory diagram of an application example to a production planning system.

FIG. 13 is a configuration diagram of hardware according to the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Genetic planning device, 2 ... Optimization means, 3 ... Setting means, 4 ... Display means, 5 ... Storage means, 11 ... Control processor, 12 ... Operation processor, 13 ... Parallel processing mechanism, 14
… Storage register

──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Hitoshi Onizawa 3-2-1, Sachimachi, Hitachi City, Ibaraki Prefecture Within Hitachi Engineering Co., Ltd. (56) References JP-A-6-223050 (JP, A) JP-A Sho 63-58569 (JP, A) Hirozo Kamichika, Scheduling system that has taken the lead in the low-growth era, Nikkei Computer, Nikkei BP, July 26, 1993, 315, pp. 73-82 Naota Sawabe, 3 other members, drafting a software development plan using genetic algorithm, IEICE technical report KBS E93-1-4, IEICE, May 19, 1993 , Vol. 93, No. 30, pp. 25-32 (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 19/00 G06F 17/60 G06N 3/00 JICST file (JOIS)

Claims (7)

(57) [Claims] 1. A setting means for receiving a given problem to be planned and values of variables required for solving the problem.
In the problem to be planned, create an objective function representing an item to be minimized or maximized, and optimizer for planning a plan for minimizing or maximizing the value of the created objective function, and Storage means for storing necessary variables, wherein the optimizing means comprises: an initial plan generating means for generating a predetermined number (population number) of first generation parent plans; and an objective function corresponding to the plan. Calculation means for calculating the value of, a plan rearrangement means for arranging a plurality of plans in descending or ascending order of the objective function value,
When a plurality of plans are given and a selection number of each plan is assigned in accordance with the objective function value, a predetermined number (population number) of constants predetermined for each repetition of generations A parent plan selecting means for selecting a predetermined number (population number) of parent plan plans using the number indicated by the constant as the selection number, and replacing any two elements with the selected parent plan. A child plan generating means for generating a child plan, a control means for activating the arithmetic means and the plan rearranging means for the parent plan and the generated child plan, and a rearranging order among the rearranged plans. Generation change means for selecting a plan only for the number of populations as a new parent plan in accordance with the above, and the parent plan selection means, child plan generation means, control means and generation replacement means from the second generation to a predetermined number of generations. Recurring Is allowed, planning apparatus, characterized in that it comprises an objective function value, and the optimal plan selection means of selecting the plan to the maximum or minimum, the. 2. The planning apparatus according to claim 1, wherein, when a plurality of plans are given, the parent plan selecting means sums up objective function values for each plan and objective function values for each plan. When it is assumed that the selection number of each plan is assigned according to the order of the ratios, a predetermined number (population number) of constants predetermined for each generation repetition, and the number indicated by the constant is selected. A planning apparatus wherein a predetermined number (population number) of parent plans are selected as numbers. 3. The planning device according to claim 1, wherein the child plan generating means generates two random numbers uniformly distributed within the range of the number of parent plan elements for the selected parent plan. A two-element arrangement arranged in the order specified by a random number is exchanged to generate a child plan. 4. The planning device according to claim 1, wherein the calculating means calculates only a change in the objective function due to a change in the planning element when calculating the objective function value for the given plan. A planning device, wherein the change is added to an objective function value before change. 5. The planning device according to claim 1, further comprising display means, wherein said display means displays the plan selected by said optimum plan selection means. 6. The planning device according to claim 1, wherein the storage means stores a predetermined number (population number) of constants (P (gn, pp)) predetermined for each repetition of the generation, and The random numbers used when generating the plan are J (gn, pp), K (g
n, pp) (where gn is the generation, pp represents the number of processings for each generation, X (gn, pp) represents the number at the time of the pp-th processing in the generation gn, and X = P,
J, K), 1 ≤ P (gn, pp) ≤ pmax (pmax is the population number), and P (gn, pp) uniformly distributed in the range of: J (gn, pp) ≠ K (gn , Pp) and 1 ≦ J
(Gn, pp) ≦ n, 1 ≦ K (gn, pp) ≦ n (n
Is the number of elements that make up the plan)
A planning device, wherein (gn, pp) and K (gn, pp) are stored in advance. 7. The contents of a given plurality of plan candidates are changed, an objective function value for each plan candidate is calculated at a predetermined change count, and the number of plan candidates is reduced to a predetermined value based on the calculated value. A planning method for causing a processing device to make a plan for limiting and maximizing a value of an objective function, wherein the processing device, when the plan is a permutation problem, includes a list of elements in the permutation. If the plan is a combination problem, at least one of the elements to be selected is changed and selected, and a change in the objective function value caused by the change is calculated. By adding to the objective function value of the plan candidate before change,
Obtain an objective function value for the changed plan candidate, and select, for each of the predetermined number of changes, the number of plan candidates planned by the number indicated by the predetermined selection constant with respect to the order of the objective function values of each plan candidate. And selecting one plan from the selected plan candidates.