CN112330221A

CN112330221A - Job shop scheduling optimization method with sufficient necessary condition neighborhood structure

Info

Publication number: CN112330221A
Application number: CN202011373398.5A
Authority: CN
Inventors: 李新宇; 桂林; 高亮
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2020-11-30
Filing date: 2020-11-30
Publication date: 2021-02-05

Abstract

The invention belongs to the field of relevant technologies of workshop scheduling and discloses a job workshop scheduling optimization method with a sufficient necessary condition neighborhood structure. The method comprises the following steps: and acquiring a scheduled critical path from the current solution of the job shop scheduling problem, and adjusting the processing sequence of the procedures in the critical path block according to sufficient necessary conditions to acquire a plurality of different processing sequences. And calculating the total processing time of each processing sequence, and taking the processing sequence with the shortest total processing time as the current scheduling sequence. The sufficient requirements are as follows: (1) the absence of a path from js (u) to v is a sufficient necessary condition that a neighborhood solution generated by processing after u moves to v is a feasible solution; (2) the absence of a u to jp (v) path is a sufficient prerequisite for the neighborhood solution generated by the process to be a feasible solution before v moves to u. By the method and the device, the solving quality is effectively improved and the solving time is shortened when the scheduling problem of the job shop is solved.

Description

Job shop scheduling optimization method with sufficient necessary condition neighborhood structure

Technology neighborhood

The invention belongs to the technical field related to workshop scheduling, and particularly relates to a job workshop scheduling optimization method with a sufficient necessary condition neighborhood structure.

Background

The workshop scheduling problem refers to reasonably allocating production resources, so that the production efficiency is improved, the production cost is reduced and the like. A job-shop scheduling problem (JSP) is a classic shop scheduling problem, which is described as having n workpieces, each workpiece has m processes and needs to be processed on m different machines, the machine sequence of different workpieces flowing through the machine sequence in the processing process is different, and the processing sequence and processing time of the workpiece on each machine need to be arranged, so that some indexes are optimal.

JSP is an NP-hard problem, and for small scale problems it is possible to use an exact solution, but for large scale problems it is difficult to use an exact algorithm to obtain a satisfactory solution in a limited time. Therefore, in order to improve the solution efficiency and the solution quality of the problem, the scholars generally use an intelligent optimization algorithm, wherein the intelligent optimization algorithm with efficient local search can greatly improve the solution quality and the solution efficiency, and the neighborhood structure is one of the keys of the local search.

In existing studies, neighborhood structures are generally divided into two types: a code-based neighborhood structure and a critical path-based neighborhood structure. For JSP, most of them use neighborhood structures based on critical paths, which are the longest path from the very beginning of processing to the end of processing all workpieces, and there are three neighborhood structures based on critical paths now commonly used, which are named N5, N6, N7, Nowicki et al (Nowicki, E., & Smutnicki, C. (1996) a fast tab search for the job tile. Management Science,42(6),797-813.) -N5 neighborhood structure, Balas et al (Balas E, varied porosity a. bound local search with shifting tile for job tile mapping [ J ]. Management, 44(2): 262-275G, N6 neighborhood structure, Zhang et al (Zhang mapping, J.),275: Zhang et al, neighborhood structures of Zhang et J. (Zhang, J.), 2007,34(11): 3229-3242) proposes an N7 neighborhood structure, and the problem in the above method is that: the obtained neighborhood solution quantity is limited, the searching time is long, and the precision is low.

Disclosure of Invention

Aiming at the defects or improvement requirements in the prior art, the invention provides a job shop scheduling optimization method with a sufficient necessary condition neighborhood structure, provides a novel neighborhood structure, adjusts the sequence of the key path blocks on the key path blocks through the novel neighborhood structure, can obtain all feasible scheduling sequences, and can quickly and accurately search all feasible scheduling sequences to obtain the scheduling sequence with the shortest total processing time.

To achieve the above object, according to the present invention, there is provided a job shop scheduling optimization method having a neighborhood structure of sufficient requirements, the method comprising the steps of:

acquiring a scheduled critical path from a current solution of a job shop scheduling problem, adjusting the processing sequence of procedures in a path block on the critical path according to sufficient necessary conditions for acquiring feasible solutions, so as to acquire feasible neighborhood solutions of various different processing sequences, calculating the processing time of each feasible neighborhood solution, taking the neighborhood solution with the shortest total processing time as the current solution, and acquiring a required optimal neighborhood solution after multiple iterations, wherein the sufficient necessary conditions comprise the following two conditions:

(1) processing after u moves to v creates sufficient requirements for a feasible processing sequence: if the path from js (u) to v does not exist, u is moved to v and then processing is feasible, and if the path from js (u) to v exists, u is moved to v and then processing is not feasible;

(2) processing before v shifts to u creates sufficient requirements for a feasible processing sequence: if a path from u to jp (v) does not exist, moving v to a position before u for machining is feasible, and if a path from u to jp (v) exists, moving v to a position before u for machining is infeasible;

wherein u and v are different processes on the same machine, and u is processed before v, js (u) is a process after u when the same workpiece is processed, and jp (v) is a process before v when the same workpiece is processed.

It is further preferred that when u is the first pass, and there is no js (u) to v path, the intermediate solution set resulting from moving u to v post-processing has a greater probability of improving the current scheduling order than would otherwise be obtained.

Further preferably, when u is the first process and there is no path for u to point to jp (v), moving v to the intermediate solution set resulting from the processing before u has a greater probability of improving the current scheduling order than an intermediate solution set otherwise obtained.

Further preferably, when v is a tail procedure, and there is no path for js (u) to point to v, moving u to v post-processing results in an intermediate solution set that has a greater probability of improving the current scheduling order than would otherwise be obtained.

Further preferably, when v is a tail procedure, and there is no path for u to point to jp (v), moving v to a previous process of u yields an intermediate solution set that has a greater probability of improving the current scheduling order than an intermediate solution set otherwise obtained.

Further preferably, the adjusting is performed according to sufficient requirements for obtaining a feasible solution, wherein the adjusting is performed on the sequence of the processing procedures in the critical path blocks on the critical path blocks.

Further preferably, the determination as to whether or not a path from js (u) to v exists or whether or not a path from u to jp (v) exists is performed by performing a determination from an analysis map.

Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:

1. compared with the conventional neighborhood structure, the neighborhood structure with sufficient necessary conditions is adopted to change the processing sequence of the procedures on the provided key path block, all feasible neighborhood solutions on the key path block can be found through the neighborhood structure, all feasible scheduling sequences can be obtained, the effect of searching quality of an algorithm is improved, and the scheduling sequence with the shortest total processing time can be quickly and accurately obtained;

2. by adopting the sufficient necessary conditions for generating feasible solutions, the neighborhood solution generated after the working procedure processing sequence on the machine is changed is ensured to be the feasible solution, and the constraint condition is the sufficient necessary condition, so that the maximum neighborhood solution generated by the change of a single working procedure can be obtained, and the search efficiency is improved;

3. the method only changes the processing sequence of the procedures on the key path, and the processing procedure of the changed processing sequence inevitably has the first procedure or the last procedure of the key path block, so that the neighborhood solution which is not improved on the current solution can be reduced by using the method, and the searching efficiency and the searching directionality are improved;

4. the fully and necessarily adjusted neighborhood structure adopted in the invention can obtain the most neighborhood solutions generated by single process change by changing the sequence of the processes in the key path block, and removes a plurality of neighborhood solutions which are not improved on the current solution on the basis, especially when the process u is a first process or the process v is a last process, the generated intermediate solution set has higher probability of improving the current scheduling sequence than the intermediate solution set obtained by other methods;

5. for the rectangular problem in JSP, namely when the proportion of the number of workpieces to be processed to the number of processing machines is large, in the later stage of searching, the number of key path blocks in a key path is small, the number of processes contained in the key path blocks is large, when other neighborhood structures are used, only a small number of neighborhood solutions can be searched, so that the solving quality is reduced, and when the solving method disclosed by the invention is used, more feasible neighborhood solutions can be searched, so that the solving quality is ensured.

Drawings

FIG. 1 is a flow chart of a method for obtaining all neighborhood solutions satisfying sufficient preconditions when solving JSP;

FIG. 2 is a schematic diagram of an extracted graph constructed in accordance with a preferred embodiment of the present invention;

FIG. 3 is a schematic illustration of a possible solution in an extracted graph constructed in accordance with a preferred embodiment of the present invention;

FIG. 4 is a schematic illustration of the infeasible interpretation of an extracted graph constructed in accordance with a preferred embodiment of the present invention;

FIG. 5 is a schematic illustration of a Gantt chart constructed in accordance with a preferred embodiment of the present invention;

FIG. 6 is a schematic view showing the state of the initial solution process u and process v in the preferred embodiment 1 of the present invention;

FIG. 7 is a schematic view showing the state of the process u and the process v after adjustment using sufficient requirements in preferred embodiment 1 of the present invention;

FIG. 8 is a schematic view showing the state of the initial solution process u and process v in the preferred embodiment 2 of the present invention;

FIG. 9 is a schematic view showing the state of the process u and the process v after adjustment using sufficient requirements in preferred embodiment 2 of the present invention;

FIG. 10 is a schematic view showing the state of the initial solution process u and process v in the preferred embodiment 3 of the present invention;

FIG. 11 is a schematic view showing the state of the process u and the process v after adjustment using sufficient requirements in preferred embodiment 3 of the present invention;

FIG. 12 is a diagram illustrating the states of the initial solution process u and the initial solution process v according to the preferred embodiment 4 of the present invention;

FIG. 13 is a schematic view showing the state of the steps u and v after adjustment using sufficient requirements in preferred embodiment 4 of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

As shown in fig. 1, a job shop scheduling optimization method with sufficient requirement neighborhood structure includes the steps of:

for the current solution of the scheduling problem of the job shop, acquiring a scheduled key path according to the current solution, adjusting the sequence of the processing procedures in a path block in the key path by adopting sufficient necessary conditions to obtain a plurality of processing sequences, calculating the processing time corresponding to each processing sequence, wherein the processing sequence with the shortest time is a required sufficient necessary condition neighborhood solution; the critical path is the longest path from the beginning to the end of all the workpieces, and the critical path block is a process combination which is adjacent on the critical path and is processed on the same machine; and critical processes refer to processes on critical paths.

u and v are two procedures on the same key path block in a feasible solution, u is processed before v, and when a path pointing to v by js (u) does not exist in an analytic graph of the feasible solution, u is moved to v and then processed to generate a neighborhood solution of the feasible solution; when there is no path for u to point to jp (v) in the analytic graph of the feasible solution, move v to u before processing yields a neighborhood solution of the feasible solution.

The analysis graph is an expression form of a feasible solution in the job shop scheduling problem; js (u) represents a next process of the same workpiece as u, and if u is the last process of the workpiece, js (u) does not exist; jp (v) represents a step immediately preceding the workpiece with v, and if v is the first step of the workpiece, jp (v) does not exist.

In the job-shop scheduling problem, the scheduling result has two expression forms: the extraction graph expression form expresses the scheduling problem by means of basic knowledge of a graph network, and is specifically shown in the following figure 2:

in fig. 2, there are three workpieces, each workpiece has three processes, each node represents a process, where s and e are virtual nodes, i.e. all workpieces start to be processed from s and end to e; o is_i,jThe ith process of the jth workpiece is shown, and the process sequence O is that each workpiece is processed from the first process to the next_1,1Point to O_2,1From step O with solid arrows_1,1To O_2,1The dashed lines in the figure connect the processes processed on the same machine, what the job shop scheduling problem needs to decide is the process sequence of different processes on the same machine, that is, the process sequence of the processes connected by the dashed lines in fig. 2 is determined, and when the dashed line arrow points, an infeasible solution may occur, that is, the determined solution cannot be executed in the actual production process.

FIG. 3 shows a feasible solution after the decision, and in the analysis diagram of the feasible solutionThe absence of a closed loop allows a feasible solution to be performed during actual production, and FIG. 4 is an infeasible solution after decision making because a closed loop (O) is generated in the solution's analysis graph_1,1-O_2,1-O_1,3-O_2,3-O_1,1) And after the closed ring is produced, in actual production such a machining sequence cannot be performed because of O_1,1Need to be at O_2,1Before, O_2,3Need to be at O_1,1Prior processing, O_1,3Need to be at O_2,3Prior working, i.e. O_1,3Need to be at O_2,1Prior processing, but in FIG. three there is O_2,1Point to O_1,3Arrow of (2), i.e. O_2,1Need to be at O_1,3Prior processing, which contradicts the foregoing, in actual production, such a solution cannot be performed, i.e., the solution is an infeasible solution.

In the analysis diagram, the path is another process that can be found by an arrow in the analysis diagram, that is, the path exists between the two processes, otherwise, the path relationship does not exist, and the analysis diagram that is feasible to be solved by fig. 3 is taken as an example, in the analysis diagram, the O exists_1,3Point to O_3,2The path of (A) is represented by (O)_1,3-O_2,1-O_3.2) (ii) a But in O_1,1And O_3,3There is no path in between.

In the gantt chart, during the process from the start of all the processes to the end of all the processes, one path composed of the processes without time gaps is called a critical path, such as the one composed of the processes (O) in fig. 5_1.2-O_2.3-O_1.1-O_2.1-O_3.1) The composed path is then a critical path, and on the critical path, a block composed of adjacent processes processed on the same machine is called a critical path block, as shown in fig. 5, where O exists_1.2-O_2.3-O_1.1、O_2.1And O_3.1Three critical path blocks.

The specific embodiment is as follows:

and solving the critical path of the current solution to obtain a critical path block in the critical path. Starting from the first critical path block, if the critical path block only contains one process, selecting the next critical path block, otherwise obtaining a feasible neighborhood solution according to the following implementation scheme.

Preferably, when u is the first process on the critical path block and there is no path where js (u) points to v in the analytic graph of the feasible solution, moving u to v and post-processing to generate a neighborhood solution of the feasible solution;

wherein the first process refers to a first process on the critical path block;

preferably, when v is a tail process on the critical path block and there is no path where js (u) points to v in the analytic graph of the feasible solution, moving u to v and post-processing to generate a neighborhood solution of the feasible solution;

wherein, the last process refers to the last process on the critical path block;

preferably, when u is the first process on the critical path block and there is no path for u to point to jp (v) in the analytic graph of the feasible solution, moving v to u and then processing a neighborhood solution generating the feasible solution;

preferably, when v is the last process on the critical path block and there is no path for u to point to jp (v) in the analytic graph of the feasible solution, moving v to u is preceded by processing to produce a neighborhood solution of the feasible solution.

The invention will now be further illustrated with reference to specific examples.

Example 1

As shown in fig. 6, the process u is the first machining process on the critical path block, and v is the same critical path block as u and is machined after u. And (5) using transverse traversal or other methods to check whether a js (u) -to-v path exists, and if not, moving u to be processed after the procedure v to obtain a feasible neighborhood solution, as shown in FIG. 7.

Example 2

As shown in fig. 8, the process u is the first machining process on the critical path block, and v is the same critical path block as u and is machined after u. Using a transverse traversal or other means to check whether a path from u to jp (v) exists, if not, moving v to process before the process u to obtain a feasible neighborhood solution, as shown in fig. 9.

Example 3

As shown in fig. 10, a process v is the last process on the critical path block, and u is a process that is processed before v and is the same critical path block as v. And (5) using transverse traversal or other methods to check whether a js (u) -to-v path exists, and if not, moving u to be processed after the procedure v to obtain a feasible neighborhood solution, as shown in FIG. 11.

Example 5

As shown in fig. 12, a process v is the last process on the critical path block, and u is a process that is processed before v and is the same critical path block as v. Using a transverse traversal or other means to check whether a path from u to jp (v) exists, if not, moving v to process before process u to obtain a feasible neighborhood solution, as shown in fig. 13.

In order to prove the practical application effect of the invention, 80 examples of TA data set are selected in JSP standard test example for simulation test. The TA data set is a standard calculation example which is commonly used internationally and used for comparing the advantages and disadvantages of the JSP algorithm. Experiment the present invention was compared with N5, N6, N7 and the new neighborhood was denoted NS. The experiment uses a tabu search algorithm as an integral framework, other experiment parameters are the same except that the neighborhoods are different in the experiment, each neighborhood is started by the same initial solution, 10 times of operation are carried out on each calculation example, and the optimal value and the average value are taken for comparison. The scale of the example is represented by n × m (n represents the number of workpieces to be machined, m represents the number of machining steps included in each workpiece), the optimum value is represented by Cbest, the average value is represented by Cavg, the experimental data is shown in table 1, and the statistical results are shown in table 2 by integrating the examples of the same scale. The data bolded in NS indicates the best results in the four neighborhoods.

TABLE 1 TA01-80 calculation results

TABLE 2 statistics of different scale examples

From the above experimental results, in 80 examples of the TA data set, the neighborhood structure of the present invention can obtain 70 optimal C compared to the other three neighborhood structures_bestAnd 61C_avgMeanwhile, in the statistical data of the same-scale calculation example, the neighborhood structure of the invention has the most advantages, which shows that the optimization and the stability of the neighborhood structure of the invention are better than those of other three neighborhood structures.

It will be readily understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.

Claims

1. A job shop scheduling optimization method with sufficient necessary condition neighborhood structure is characterized by comprising the following steps:

for the current scheduling sequence of a job shop, a sufficient necessary condition neighborhood structure is adopted to adjust the processing sequence in a path block on a scheduled key path, so as to obtain a plurality of different processing sequences, the total processing time corresponding to each processing sequence is calculated, the processing sequence with the shortest total processing time is taken as the current scheduling sequence, and the scheduling sequence with the shortest total processing time is obtained after multiple iterative adjustments, so that the optimization of the shop scheduling is realized, wherein the sufficient necessary condition neighborhood structure comprises the following two steps:

2. The method of claim 1, wherein when u is a first process and there is no js (u) to v path, moving u to v postprocessing yields an intermediate solution set that has a greater probability of improving the current scheduling order than an intermediate solution set otherwise obtained.

3. The method of claim 1, wherein when u is a prime and there is no path for u to point to jp (v), moving v to u results in an intermediate solution set that is processed before u with a greater probability of improving the current scheduling order than an intermediate solution set otherwise obtained.

4. The method of claim 1, wherein when v is a tail process and there is no path for js (u) to point to v, moving u to v post-processing results in an intermediate solution set that has a greater probability of improving the current scheduling order than would otherwise be obtained.

5. The method of claim 1, wherein when v is a tail process and there is no path for u to point to jp (v), moving v to u before processing results in an intermediate solution set that has a greater probability of improving the current scheduling order than an intermediate solution set otherwise obtained.

6. The method as claimed in claim 1, wherein the adjustment of the processing sequence in the critical path blocks according to the sufficient requirements for obtaining feasible solution is performed, wherein the adjustment is performed on the sequence of the processing steps in the critical path blocks on the critical path blocks.

7. The method for optimizing work shop scheduling having a neighborhood structure of sufficient requirements according to claim 1, wherein the determination of whether a js (u) to v path exists or whether a u to jp (v) path exists is made by a determination from an extraction graph.