JPH08129586A - Schedule generating method - Google Patents

Abstract

PURPOSE: To provide a method which speedily divides an order unless an optimum solution can be found in a process of finding the optimum solution by the application of GA. CONSTITUTION: This method consists of a step S1 wherein a problem to be scheduled is molded with a chromosome having an order number as its length and plural kinds of gene, a step S2 wherein an individual as a solution for the modeled problem is generated, a step S10 wherein respective generated individuals are evaluated, a step S11 wherein individuals are selected on the basis of the evaluation results, a step S12 wherein the selected individuals are crossed over, and a step S20 wherein the generation rate of dead genes as a result of the crossing-over is calculated and compared with a predetermined reference generation rate, and a step S8 wherein the order is divided is included unless an executable individual can be generated in the individual generating step or according to the comparison result of the generation rate.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a genetic algorithm (hereinafter GA; G) for production scheduling in consideration of order division.
enetic Algorithms)).

[0002]

2. Description of the Related Art Generally, in a manufacturing process of a product, when a required production capacity is considerably large, a plurality of manufacturing facilities are used to cope with it.

[0003] By the way, since the equipment is usually additionally introduced with the introduction time being shifted with the increase of the production scale, the production capacity varies depending on the individual equipment. In such a production site environment, in order to realize production in time for delivery, measures have conventionally been taken such as dividing orders and assigning the same product to different production facilities.

For the combination optimization problem such as production scheduling, there have been proposed some methods for obtaining an optimum solution by GA, which is attracting attention for its effectiveness.

For example, Japanese Laid-Open Patent Publication No. 4-281550 discloses a device for obtaining a suboptimal solution of a combinatorial optimization problem by a genetic method, and in order to execute GA at high speed, a plurality of individual processing devices are provided and processed individually. A plurality of individuals to be held are grouped and held, and evaluation, selection, crossover, and mutation processing of each grouped individual is performed in parallel, the processing content is copied to the shared memory, and the shared memory is used by the data aggregation device. The total sum of evaluation values of each individual and the ratio to the whole are calculated, and each individual processing device re-acquires the next generation of individual from the shared memory in the process of selection processing and parallelizes crossing, mutation, evaluation, etc. A technique is disclosed in which, after processing and repeating the series of these processes, the data aggregating device outputs the highest evaluated individual.

Further, Japanese Patent Application Laid-Open No. 4-233069 discloses that
Regarding the scheduling method at the time of process change that re-schedules when the process of the work order changes, in addition to the master process information for each product type, there is process information for each work order, and this process information can be changed during reproduction processing, division, and merge In order to perform rescheduling and automatically create a work schedule, the master process information for each product type is first copied to the process information for each work order, and the work order is rescheduled according to the changed process information to create a new work. A technique for automatically creating scheduling is disclosed.

[0007]

[Patent Document 1] Japanese Unexamined Patent Application Publication No.
In the -281550 publication, there is a problem in that it takes a long time to create a schedule that satisfies the constraint condition and that a planning expert needs to perform work such as order division for obtaining a possible solution.

Further, in Japanese Patent Laid-Open No. 4-233069, there is a problem that it takes a long time because the rescheduling is made and the verification is repeated. The present invention has been made in view of the above problems of the prior art, and provides a method for quickly dividing an order when a solution cannot be obtained in the process of obtaining an optimal solution by applying GA. The purpose is.

[0009]

According to the present invention, a step of modeling a problem to be scheduled by a chromosome having an order number length and a plurality of kinds of genes, and an individual serving as a solution to the modeled problem. , The step of evaluating each created individual, the step of selecting an individual based on the evaluation result, the step of intersecting between the selected individuals, and the occurrence rate of the lethal gene depending on the result of the crossing. And a step of comparing with a predetermined reference incidence rate, and when the number of executable constant individuals cannot be created at the time of creating the individual, or a step of dividing the order according to the result of the comparison of the incidence rates. And consists of.

[0010]

[Operation] The problem of the production schedule is modeled to create an individual. At this time, if the executable individual cannot obtain various constants, the individual is re-created by dividing the order from the order with the smallest delivery deadline at the time of modeling. When an appropriate first generation individual is obtained, GA is executed to perform individual processing such as individual evaluation, selection, and intersection. When the desired value cannot be obtained due to the lethal gene incidence after crossing, the order is returned to the initial modeling, the order is divided, and the processing is executed again. When the lethal gene occurrence rate becomes appropriate, a second generation individual is prepared and similarly executed, and thereafter this series of operations is repeated.

[0011]

[Example] (Outline of problem) An outline of the problem of production schedule will be explained.
You. This is the delivery date L_jn types of orders with (j = 1,2, ..., n)
O_j(j = 1,2, ..., n) of m units with the same function but different production capacity
Machine M _iDelivery delay when processing in parallel with (i = 1,2, ..., m)
Scheduling that minimizes total production time C without generating
The problem is However, order O_j Is any
Machine m_i At time P_ijShall be processed in
Order splitting is not feasible unless constants are obtained.
Do not do it. (Applying GA) Applying GA to the above problems
And the total production time
To the evaluation value and the delivery date to the constraint condition.

First, an arbitrary number of individuals satisfying the constraint, which are expressed by a one-dimensional array in which the genes represented by machine numbers (1 to m) are arranged in the order of n, are created to form an initial population. After that, the individuals selected according to the evaluation value repeat crossing and mutation to advance the generation and raise the overall evaluation value.

As a result of repeating the above-described processing until the evaluation value of the individual group converges or until the process is terminated, the individual having the best evaluation value obtained is used as the identified schedule.

However, in the process of this identification, depending on the individual, there is a possibility that a lethal gene that causes a delayed delivery may appear. If only individuals that do not meet such constraint conditions can be expected, it is determined that scheduling is not possible, the order is divided, and then rescheduling is performed.

However, in this case, it is assumed that the order is evenly divided into several due to management problems in the field, and by applying the GA to scheduling considering order division by increasing the number of loci by the number of divisions. To be realized. (Calculation example) Fig. 1 shows the result of one calculation example to which the above GA is applied.
Shown in Note that the order number is 16 and the machine number is 5, and FIG. 1 shows the maximum value, the minimum value, and the average value of the evaluation values in the population of each generation.

It can be seen from the figure that the average value and the maximum value of the evaluation values decrease as the generation progresses, and the whole population is composed of relatively good individuals, so that the above method can lead to good results. .

Further, as a result of attempting rescheduling after order division for a gene in which only a lethal gene occurs and which cannot be scheduled, a feasible solution could be obtained.

As described above, it has been shown that the problem of delivery delay in the normal scheduling can be solved by dividing the order. (Specific Example) An embodiment of the schedule creating method of the present invention will be described in detail below with reference to the drawings.

First, FIG. 2 is a concrete flowchart of the schedule creating method. In the figure, in step S1, the target problem as described in the outline of the problem is modeled, and in step S2, the individual is created. In this case, as shown in FIG. 3, a chromosome A having a length of the order number is created and a machine number B is used as a gene.

Next, in step S3, it is determined whether or not the constraint condition is satisfied. For example, in FIG. 4, order G
Is not completed at that delivery date, which means that delivery time is broken. Fig. 5 shows an example in which none of the orders has a delivery deadline.

When an individual that does not satisfy the constraint condition is generated in step S3, the individual is recreated, and it is checked whether the number of times of creation has reached a preset number of times of creation. Check at S4. Here, if the number of times of re-creation does not reach the specified value, the number of times of re-creation is counted in step S5 to re-create the individual.

In step S6, the number of times individuals are created (the number of times individuals have been successfully created plus the number of failures) has been counted, and a preset group size (how many individuals to evolve as one group In this case, it is checked whether or not the individual creation processing for the number of individuals) has been performed.

The check in step S6 functions only when an individual satisfying the constraint conditions is created within the prescribed number of times of recreating. If the predetermined number of times the individual has been created has not been reached in step S6, the process returns to step S2 to newly create the individual.

At least two individuals are required for evolution. In step S7, it is checked whether or not the number of individuals finally created through step S6 is two or more. If the number is one or less, the order is divided in step S8, the process returns to step S1, and the process from the modeling of the target problem is performed again.

An initial population (first generation) is constructed in step S9 by a plurality of OK individuals checked in step S7. Next, in step S10, the fitness of the created first generation initial population for each problem environment is obtained and evaluated.

For example, as shown in FIG. 6, when the fitness of each individual constituting the group is obtained as 82, 57, ..., 64, the individuals with high fitness ( For example, 82 and 64 individuals) are selected (see FIG. 7), and these individuals are crossed in the next step S12 (see FIG. 8).

By intersecting the individuals thus selected, individuals having a new pattern (gene sequence) are created.
S13 is a step of checking whether or not there is a delivery deadline in the new pattern of individuals created in step S12, and if the constraint condition is satisfied, it is determined whether a prescribed number of individuals have been created. Check in S14.

When the number of individuals has not reached the specified number in step S14, the process returns to step S11 and the process is repeated from the selection. If the individual crossed in step S13 does not satisfy the constraint condition, it is checked in step S15 whether or not the specified number of recrossings has been reached. If not, the number of recrossings is incremented by 1 and counted. (Step S16), the number of times of re-crossing with the same individual pair is accumulated, and the process returns to step S12. If it has reached, the number of times of unsuccessful intersection is increased by 1 and counted (step S17),
After a specified number of recrossings, the logarithm of individuals for which no feasible solution was obtained is accumulated.

Then, in step S18, the individual to be cross-processed is copied as it is as a next-generation individual, and then copied in step S18.
Proceed to 14. If the specified number of individuals has been created in step S14, the next generation is composed of the same number of individuals as the initial population created in step S19.

The next generation individual created is step S20.
Checks whether the incidence of lethal genes is high or low. To compare this incidence,

[0031]

[Equation 1]

If the value on the left side is considerably larger than the value on the right side, the process returns to step S8, the order is divided, and the modeling of the target problem in step S1 is performed again. Here, for example, by assigning one order to one machine, constraints may not be satisfied or the evaluation result may not be good, so divide the order into several and assign it to another machine. Such order division will be performed.

9 and 10 are views showing an example of such order division. FIG. 9 shows before order division (same as FIG. 4) and after FIG. Here, order G did not meet the delivery date before order division, but machines 2 and 3
The delivery date will be met after the division.

If the lethal gene occurrence rate is suppressed to a low level in step S20 by performing division or the like, it is checked in step S21 whether the fitness is improved and the final generation is reached.

When the fitness of the next generation created here is checked and no improvement is found, or when the process is not repeated until the preset generation, the evaluation of each individual in step S10 The subsequent processing is executed again.

[0036]

Since the present invention is configured as described above, it becomes possible to judge the necessity of order division in a short time, and to create a good schedule even for a person other than a planning expert. .

This effect can be further shortened by carrying out twice before the evaluation of the created individual and after the creation of the next generation individual.

[Brief description of drawings]

FIG. 1 is a graph showing the result of scheduling using the present invention.

FIG. 2 is a flow chart illustrating the method of the present invention.

FIG. 3 is a conceptual diagram when creating an individual.

[Fig. 4] Conceptual diagram when checking constraint conditions (due to deadline)
Is.

[Figure 5] Conceptual diagram when checking constraint conditions (no deadline for delivery)
Is.

FIG. 6 is a conceptual diagram when an individual is evaluated.

FIG. 7 is a conceptual diagram when selecting an individual pair.

FIG. 8 is a conceptual diagram of intersection of selected individual pairs.

FIG. 9 is a conceptual diagram at the time of order division (before division).

FIG. 10 is a conceptual diagram at the time of order division (after division).

Claims (3)

[Claims] 1. A method of modeling a problem to be scheduled by a chromosome having an order number of length and a plurality of kinds of genes, and a step of creating an individual serving as a solution to the modeled problem. The step of evaluating each individual, the step of selecting an individual based on the evaluation result, the step of crossing between the selected individuals, the incidence of the lethal gene resulting from the crossing is calculated, and a predetermined criterion is set. A schedule creating method comprising: a step of comparing with an occurrence rate; and a step of dividing an order according to a comparison result of the occurrence rate. 2. In the step of creating the individual,
The schedule creating method according to claim 1, wherein when the executable individual cannot create various constants, the order is divided. 3. The schedule creating method according to claim 2, wherein the order is divided in order from the order with the smallest delivery deadline among the orders.