JPH05225203A - System for resolving job shop scheduling problem - Google Patents

Abstract

PURPOSE:To obtain the satisfactory resolution of a large-scale problem at high speed by applying an genetic algorithm to a job shop scheduling problem. CONSTITUTION:Probelm data and the parameter of the genetic algorithm are inputted from an input part 1. The resolution of the problem is expressed by an individual used for the genetic algorithm, and the evaluation of each individual is expressed by the maximum value (total work time) of a component for each individual. First of all, a random schedule constituting an initial individual group is generated by an initial individual group generation part 2. The individual groups are selected by a selection processing part 5, when an end condition is not satisfied, the individual groups are paired by two by two and impressed to a schedule calculation part 3 by a cross processing part 4, and any new individual and the evaluation value are obtained from the schedule calculation part 3. This processing is repeated to all the pairs of individuals in the individual group and returned to the processing of the selection processing part 5. The operations of respective parts are controlled by a control part 7.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a job shop scheduling problem solving method capable of improving the efficiency of all work in factory automation such as a factory by reducing the time until the end of work as much as possible. is there.

[0002]

2. Description of the Related Art There is a method called a genetic algorithm as a method for obtaining a suboptimal solution of a problem. Regarding this genetic algorithm, for example, the document “Genetic Algorithms in
Search, Optimization and Machine Learning "(D
avid E. Goldberg, Addison Wesley), an overview of which is provided below.

In the genetic algorithm, a set P of L-dimensional vectors V = (V ₁ , V ₂ , _VL ) is given as an input value. Each element of P represents a solution to a given problem.
Let p be the original number of P. Each element is called an individual, and P is called an individual group. The genetic algorithm is an iterative process with the following procedure as one cycle. (1) Construct P as a set of randomly generated individuals. This is called the initial population. (2) The goodness of each original solution of P is evaluated according to a given evaluation scale, and the result is expressed as an evaluation value. (3) In accordance with the evaluation value obtained in (2), the number of individuals with low evaluation is reduced, and the number of individuals with good evaluation is increased, and as a result, the proportion of individuals with better evaluation is higher in the population P. This operation is called "selection". <Method of selection (one example)> The evaluation value of each individual P is calculated. 2. The individual evaluation items of P are arranged in a line in the order of poor evaluation value. Then, the score E _n is assigned to the individual with the worst evaluation value ( _denoted as V _n ).
= (N-1) is given. 3. A group of individuals is created so that the ratio of the number of individuals V _n to the next generation is E _n . (4) Pair two elements of P, and generate two new individuals based on the paired two individuals. This operation is "crossover"
Call. The above-mentioned document describes in detail a crossover method (provisionally named as simple crossover method) for obtaining a new individual by exchanging a part of vectors of paired individuals. The simple crossover method cannot be applied to problems with complicated constraints such as the job shop scheduling problem handled in the present invention.

(5) Select some individuals of P with low probability,
Change the individual a little. This operation is called "mutation". For mutation, for example, a method is known in which two components are randomly selected from the components of the vector of each individual and the components are exchanged with each other (tentatively named simple mutation method). The simple mutation method cannot be applied to problems with complex constraints such as the job shop scheduling problem handled in the present invention. By repeating the above processing, each individual of the individual group P reaches the suboptimal solution of the given problem.

The job shop scheduling problem is a problem in which N jobs are processed by M machines.
At this time, 1. Order of machines that process each work (technical order) 1. Two of the processing times on each machine for each job are given in advance. Also, 1. Machine does not break down 2. 2. Each machine cannot handle more than one job at the same time. Add conditions such as no interruption of work. Under this condition, a solution that minimizes the total time required to finish processing all jobs is obtained. This is to find the optimal solution for the job shop scheduling problem.

As a conventional method for solving the job shop scheduling problem, a method called Giffler &Thompson's active schedule generation method (hereinafter abbreviated as GT method) is known. For example, the document "Scheduling Problem" (written by Ichiro Nabeshima) , Morikita Publishing Co., Ltd.). The outline will be described below.

It is assumed that jobs and machines are numbered 1, ..., N and 1, ... M, respectively. A set of work and machine is called work. The work (i, j) refers to a process on the machine that processes the work whose number is i at the j-th position. GT
Law is a series of processes as follows. (1) Of unscheduled work, the technical sequence defines the first work as a whole (Cut) as follows. Cut = {(1,1), (2,1), ..., (N, 1)} (2) Obtain the earliest completion time (EC) for each element of Cut. The initial value of EC is given by the processing time of EC (i, j) = (i, j) (εCut). (3) Among the elements of Cut, the work (i ₀ , j ₀ ) having the earliest completion time is obtained. EC (i ₀ , j ₀ ) = min {EC (i, j) | (i, j)
(ΕCut)} (4) Of the elements of Cut, the whole G _c that is processed on the same machine as the work (i ₀ , j ₀ ) and has overlapping processing time is obtained.
This G _c will be called a conflict set. (5) Select one work from G _c , and set it as work (i _c , j _c ). (6) processing operations (i _c, j _c) the time EC (i _c, j _c) to. A schedule partially scheduled in this way is called a partial schedule. (7) Working from Cut the original (i _c, j _c) removing the work is technically sequence instead (i _c, j _c) following a is task (i _c, j _c +1) of was added and the Cut Update. However, (i
_{If c} , j _c ) is the last work in the technical sequence, add nothing. (8) to Cut the original work (i _c, j _c) work to be processed by the same machine on the (i, j) earliest completion time for (E
C ') is defined as follows.

EC '= max {EC (i, j), EC ( _ic , j
_c ) + ((i _c , j _c ) processing time)} (9) For work (i _c , j _c +1), EC ′ is defined as follows. However, it is assumed that the machine that processes MLC = (i _c , j _c +1) finishes the last scheduled work. EC '(work (i _c , j _c +1)) = max {MLC, EC (work (i _c , j _c )) + (machining time of work (i _c , j _c ))} (10) EC = EC Return to (3) as'. One schedule can be obtained by repeating the above (3) to (9) for the number of operations. This is called an active schedule. Here, by considering all combinations in G _c of (5), all active schedules can be obtained, but the number thereof is enormous.

[0009]

As a conventional method for solving the job shop scheduling problem, a solution method such as a branch and bound method has been studied. However, since the combination causes an explosion for a large-scale problem, it is optimal. There was a problem that a good solution close to the solution or the optimum solution could not be obtained within an effective time.

An object of the present invention is to obtain a suboptimal solution of a large-scale job shop scheduling problem having complicated constraints,
It is to seek at high speed without causing a combination explosion.

[0011]

In order to achieve the above object, in the job shop scheduling problem solving method of the present invention, a solution is a process of each job on each machine, and a list of work end times is stored in the internal state. Expressed by the individual possessed by, the means for randomly generating the initial population and each individual in the initial population or the population in the process of processing are selected in pairs, and the partial schedule is generated based on that. For the partial schedule, a set of work candidates to be scheduled next is determined, and an operation of determining the work to be scheduled next based on the information of the two individuals previously selected from the set of candidates is scheduled. Continuously, until the completion of the above, there is a means for outputting two new individuals and a means for selecting the initial population or the output population based on the evaluation value to obtain a suboptimal solution. And wherein the Rukoto.

[0012]

According to the job shop scheduling problem solving method of the present invention, an individual solution is represented by a vector consisting of a set of processing end times of respective works. The initial population is constructed as a set of individuals randomly generated by the GT method. Then, each individual in the individual group is paired in pairs, these two individuals are input to the schedule calculation unit, and two new schedules are obtained as outputs from the schedule calculation unit. In this way, the crossover processing of the genetic algorithm is realized, and the genetic algorithm can be applied to the job shop scheduling problem.

The processing in the schedule calculation section is as follows. However, the two individuals that are input to the schedule calculation unit are mom and dad. 1. First, a conflict set is generated based on the GT method. 2. Next, the work to be processed next is selected from the conflict set as follows. (A) If a random number of 0 to 1 is generated, and this random number is smaller than a predetermined parameter (called a mutation ratio), the work to be processed next is arbitrarily selected from the conflict set. (B) If not, first, with probability 1/2, mom, da
Select one of d. Suppose mom is selected now. mo
Find the corresponding component in m and find the smallest one.
This is the work to be processed next. The same applies when dad is selected. 3. This is repeated until the schedule is completed.

By repeating the above 1 to 2 twice, two schedules are obtained. Note that (a) in the processing of the upper schedule calculation unit corresponds to mutation.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 shows a block diagram of an embodiment of the present invention.
In FIG. 1, 1 is an input unit for inputting problem data and parameters of a genetic algorithm, 2 is an initial population generation unit for generating a random schedule constituting an initial population,
3 is a schedule calculation unit that generates a new schedule from the two original schedules, 4 is a pair of each individual in the population, and is input to the schedule calculation unit 3.
A crossover processing unit that receives two new schedules from the schedule calculation unit 3 as each new individual, 5 is a selection processing unit that executes selection, 6 is problem data, parameters of a genetic algorithm, and individuals in the middle of processing and final results A memory for storing groups, and a control unit 7 for controlling the operation of each of these units.

FIG. 2 shows an overall processing flowchart of FIG.

First, the number of jobs N, the number of machines M, the technical order of each work, the processing time, the number of individuals P, which is a parameter of the genetic algorithm, the mutation rate Mr, all the problem data from the input unit 1. The end condition of the process is input, and the memory 6
(Step 11). The end condition of all processing is
It is given in the form of "end when the number of repetitions of a series of processing reaches Loop times or the Conv percentage of individuals in the population becomes the same individual".

Next, the initial population generation unit 2 generates P random populations (random schedule group) (step 12). This is performed by the initial population generation unit 2 calling the schedule calculation unit 3 described later as a subroutine, and receiving the schedules generated by the schedule calculation unit 3 and the respective evaluation values. At this time, the initial population generation unit 2 provides the schedule calculation unit 3 with an empty schedule pair having no value as an input. The generated initial population is stored in the memory 6.

Next, the selection processing unit 5 executes selection based on the evaluation value, as a result, obtains a new population, and the memory 6
(Step 13). The selection method may be the same as the conventional method.

As a result of selection by the selection processing unit 5, if the termination condition is satisfied (YES in step 14), the population on the memory 6 is output and all the processing is terminated.

On the other hand, if the end condition is not satisfied (NO in step 14), then the crossover processing unit 4 makes a pair of each individual of the individual group on the memory 6, and the schedule calculation unit 15 makes this pair. To the schedule calculation section 15 as an output and receive a new individual as an output (step 1
5). This process is repeated twice for each pair, and as a result, a new individual and two evaluation values are obtained for each pair. Then, of the four individuals combined with the two individuals given as inputs, the top two having the highest evaluation value are newly stored in the memory 6 together with the evaluation value. This process is repeated for all pairs of individuals in the population. Then, the process returns to the selection processing unit 13.

FIG. 3 is a processing flowchart of the schedule calculation unit 3. Here, the input schedule storage unit 2
6, the conflict set storage unit 27 and the partial schedule storage unit 28 are prepared on the memory 6.

The schedule calculation unit 3 first receives two individuals (schedule) as inputs from the initial population generation unit 2 and the crossover processing unit 4 (step 21). The two input individuals are assumed to be mom and dad here.
The input individual (schedule) is stored in the input schedule storage unit 26. Next, the conflict set is obtained by the GT method and stored in the conflict set storage unit 27 (step 22). Next, the work to be processed next is selected from this conflict set as follows (step 23). When Case1; mom and dad are empty, the work to be processed next is arbitrarily selected from the conflict set. Case2; A random number of 0 to 1 is generated, and it is set as r. r
If <Mr, the work to be processed next is arbitrarily selected from the conflict set. Case3: In the cases other than the above, first, with a probability of 1/2, mom, d
Select ad. If mom is selected, the one with the earliest work end time in mom among all work of the conflict set is obtained, and that work is processed next. The same applies when dad is selected. FIG. 4 shows the state of the process for selecting the next work. The processing end time of the work selected in this processing is stored in the partial schedule storage unit 28. Step 22, above
The processing of 23 is repeated until the schedule is completed (NO in step 24). When the schedule is completed (YES in step 24), this schedule and the maximum value of the components of the schedule are output as the total work time (step 2).
5).

The operation of the embodiment will be described below with reference to a concrete example.

Here, as shown in FIG. 5, the number of jobs is 4,
Consider a job shop scheduling problem with four machines.

First, the problem data of FIG. 5 and the size of the population (here, 4
Input), mutation (here 0)
Enter from.

Next, the initial population generation unit 2 generates four random individuals (random schedule). Of the four generated individuals, as an example, the data structure of two individuals is shown in FIG.
Shown in. These two individuals are designated as mom and dad. In the case of the example in FIG. 6, the evaluation values of mom and dad are 24 and 24, respectively.
Is.

Next, the selection processing unit 5 selects the population.
The details of the selection processing unit 5 are the same as those of the conventional method, and therefore will be omitted. Here, it is assumed that the two individuals in FIG. 6 remain in the population after selection.

Next, the crossover processing unit 4 pairs two individuals of each individual group. Here, the two individuals mom and da in FIG.
Suppose d is paired. The crossover processing unit 4 passes mom and dad to the schedule calculation unit 3 as inputs. As a result, the scheduling process of the schedule calculation unit 3 starts.

In the schedule calculation unit 3, first, as shown in FIG. 7, a vector array kid1 for storing a new schedule to be output and an array cut for storing work that can be immediately processed among unscheduled works are initialized. To do. Since no job is scheduled at the beginning, kid1 is empty (that is, the partial schedule is empty), and cut stores the work whose technical order is first with respect to each work. In cut, each work is represented by (i, j), which represents the work on the machine that processes work i at the j-th position. The subscript is the earliest completion time. The array cut in FIG. 7 shows the first column in FIG.

Now, let us say that the schedule work has advanced to some extent and the tenth work is now scheduled. Fig. 8 shows the current status of the partial schedule and the array cu.
Indicates the state of t.

First, the conflict set conf is obtained. Figure 8
In the cut, the earliest completion time is (3, 3) ₁₃
However, the whole work that is processed by the same machine as this (machine 2 in this example) and the processing time overlaps is shown in FIG.
Is.

The work to be processed next is selected as follows. First, it is checked whether (mom, dad) is empty.
If nothing is stored in (mom, dad), that is, when it is empty, simply select one from conf. In the example of FIG. 8, (mom, dad) is not empty, so the following is performed.

(Mom, da with a given probability of 1/2)
Select one from d). Now suppose that dad was chosen. Next, the value of the corresponding component in dad for each cut operation is examined. For example, da for work (1,3)
9 is obtained by referring to the (1,3) component of d. The value thus obtained is the value in the subscript of conf _dad in FIG. So, of these, we investigate the one with the smallest value,
The corresponding work, (1,3) in the example of FIG. 8, is scheduled at its earliest completion time 14. As a result, the partial schedule shown in FIG. 9 is obtained.

Next, cut is updated. Work to be processed on the same machine 2 as the selected work (1, 3) (3, 3)
As for (4, 4), the earliest completion time is changed so that the machining is the current state or immediately after the machining of the work (1, 3) is finished, whichever comes later. Also, the work (1,3) is removed from the cut, and instead, the work (1,4) whose technical sequence is immediately after is processed immediately after the machining of (1,3) or (1,4). The machine 3 which is a machine to be machined is set to be either one of the machines immediately after the machining of the last scheduled work (3, 1). As a result, the cut shown in FIG. 9 is obtained.

The above process is repeated until all the work is completed, and the finally obtained schedule is kid1 in FIG.
Is.

Further, by repeating the above scheduling process again, the schedule kid of FIG.
Assume that 2 is obtained.

The crossover processing unit 4 outputs the two individuals kid1 and kid2 shown in FIGS. 10 and 11 as the output from the schedule calculation unit 3.
I received it, mom, dad, this kid2, kid2 in FIG.
Is passed to the selection processing unit 5. mom, dad, kid1, kid2
Evaluation value = total working time is 24, 24, 2 in this order.
As a result of selection, the top two of these four individuals survive in the next generation in the order of smaller total work time. For example, in this case, kid1 and mom are stored in the memory 6 as the constituent elements of the new population, and the process is performed again by the crossover processing unit 4.
Go to.

The above processing is repeated until a predetermined number of repetitions is reached or the whole group of individuals becomes the same individual. The solution finally obtained is shown in FIG. 12 as an example.

[0041]

As described above, according to the present invention,
The genetic algorithm can be applied to the job shop scheduling problem, and it is possible to quickly obtain a good solution of a large-scale problem.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an embodiment of the present invention.

FIG. 2 is an overall processing flowchart of FIG.

FIG. 3 is a processing flowchart of a schedule calculation unit in FIG.

FIG. 4 is a detailed flowchart of a next work selection process in the schedule calculation unit.

FIG. 5 is an example of problem data.

FIG. 6 is an example of a data structure of two individuals.

FIG. 7 shows an initial state of a partial schedule.

FIG. 8 is an example of a state of a partial schedule during processing.

FIG. 9 is also an example of a state of a partial schedule in the middle of processing.

FIG. 10 is an example of a state of a partial schedule finally obtained.

FIG. 11 is also an example of the state of the finally obtained partial schedule.

FIG. 12 is an example of a final solution.

[Explanation of symbols]

 1 input unit 2 initial population generation unit 3 schedule calculation unit 4 crossover processing unit 5 selection processing unit 6 memory 7 control unit

Claims (1)

[Claims] 1. A suboptimal solution of a problem that minimizes the total work time when a plurality of jobs to be processed in a predetermined order and on a plurality of machines for a predetermined time are given. A method for automatically generating a solution, expressing the solution as a list of work end times, which is the processing of each work on each machine, in an internal state, and randomly generating an initial population, Select each pair of individuals from the initial population or the population in the process of processing, select a partial schedule based on the pair, and determine the set of candidates for work to be scheduled next for the partial schedule. , Means for continuously determining the work to be scheduled next based on the information of the two individuals previously selected from the set of candidates until the schedule is completed, and outputting two new individuals, The initial population or And a means for obtaining a sub-optimal solution by selecting the output population based on the evaluation value.