CN103729694A - Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure - Google Patents

Abstract

The invention discloses a method for solving the flexible job-shop scheduling problem with an improved GA based on a polychromatic set hierarchical structure. According to the method, an original process-machine tool contour matrix is split into matrixes of relation of process-benchmark, benchmark-equipment model, equipment model-asset number by establishing equipment benchmarks and setting process constraint, equipment constraint, machine tool constraint and unique constraint, and the data size of a constraint model is effectively reduced; furthermore, by optimizing chromosome lengths reasonably and setting blending operation of batch benchmarks, the time and space complexity of chromosomes is effectively reduced, and then the solving speed and practicality of the algorithm can be greatly improved.

Description

An Improved GA Method for Solving Flexible Shop Scheduling Based on Multicolor Set Hierarchy

technical field

The invention belongs to the technical field of flexible workshop scheduling, and relates to an improved genetic algorithm, in particular to a method for solving flexible workshop scheduling based on an improved GA of a multi-color set hierarchical structure.

Background technique

The core idea of Flexible Job-Shop Scheduling Problem (FJSP) is that multiple batches of multiple types of parts can be processed and produced on the same type of equipment. Before formal processing, the process of each component is uniquely determined, but the process route is uncertain. Each process has a variety of processing equipment options, that is, each component to be processed has multiple process routes to choose from. And the selection of equipment should be based on the balance of equipment capabilities. Compared with the traditional workshop scheduling problem, the FJSP problem is a more complicated NP-hard problem. Solving this kind of problem requires a higher complexity of the algorithm, but because it is closer to the actual situation of production, it has become the current domestic and foreign Research focus in the field of scheduling.

In recent years, scholars have also carried out a lot of research on flexible workshop scheduling; in the existing technology, "Zhou Huiren, Zheng Pier, An Xiaohui, etc. A new method for solving Job Shop scheduling optimization based on genetic algorithm [J]. Journal of System Simulation, 2009, 21(11): 3295-3306" and "Pezzella F.A genetic algorithm for the flexible Job-Shop scheduling problem[J]. Computers and Operations Research, 2007, 21(9): 54-61" in order to improve the search speed of GA, A method of improving the coding method and optimizing the chromosome is proposed, which greatly reduces the time and space complexity of the GA algorithm, but its scheduling situation is too theoretical and does not consider environmental changes, so it is not flexible.

In "Zhang Guohui, Gao Liang, Li Peigen, etc. Improved Genetic Algorithms to Solve Flexible Job Shop Scheduling Problems [J]. Chinese Journal of Mechanical Engineering, 2009, 45(7): 145-151", combined with the characteristics of FJSP problems, using appropriate strategies to improve The chromosome coding method, crossover operator and mutation operator are improved, which greatly improves the accuracy of the algorithm, but the solution speed does not increase.

In "Ji Shuxin, Qian Jixin, Sun Youxian. Coding Research in Genetic Algorithms for Job Shop Scheduling [J]. Information and Control, 1997, 26(5): 393-400", in order to eliminate GA, it can only be applied to group technology JSS Due to the limitations of the method, the JSS linkage gene coding method is proposed. Although the solution efficiency is improved, the space complexity of the chromosome is still high.

"Pan Quanke, Zhu Jianying. Job Shop Optimization Based on Petri Net and Hybrid Algorithm [J]. Computer Integrated Manufacturing System, 2007, 13(3): 580-584", "Chen Weimin, Wang Bo, Wei Yuke. Genetic Algorithm of Petri Net Application research in Job-Shop problem [J]. Journal of Harbin University of Science and Technology, 2008, 13 (1): 59-62" and "Ju Quanyong, Zhu Jianying. Research on dynamic shop scheduling system based on hybrid genetic algorithm [J]. China Mechanical Engineering, 2007, 18(1): 40-43", first established the timed transition Petri net model of JSP, and then applied genetic algorithm (Genetic algorithm, GA), simulated annealing (Simulated Annealing, SA), particle swarm One of the Particle Swarm Optimization (PSO) algorithms or a combination of the two algorithms can solve this problem, but the solution algorithm used still has high time and space complexity, and cannot effectively improve the solution speed and accuracy of the algorithm at the same time.

"Fu Weiping, Liu Dongmei, Lai Chunwei, Wang Wen. An improved genetic algorithm based on multi-color sets to solve multi-variety flexible scheduling problems [J]. Computer Integrated Manufacturing Systems, 2011, 17(5): 1004-1011" and "Liu Dongmei, Fu Wei Ping. Improved Genetic Algorithm to Solve the Flexible Workshop Scheduling Problem[J]. In Northwest University Journal, 2011, 41(4): 611-616, the multi-color set theory, which is easier to describe the logical relationship of data, is used to exclude infeasible solutions , greatly reducing the GA search solution domain, and at the same time, a single-layer encoding method is proposed to represent the double constraints in the scheduling problem, which reduces the time and space complexity of the algorithm. However, the algorithm described in this document can only generate chromosomes in simple cases (choose one of the equipment corresponding to the process), which is far from the actual application; and the segmented coding used by the chromosome is generated based on the maximum number of processes as the benchmark unit, which is As a result, when the algorithm deals with large-scale multi-process scheduling problems in practice, the chromosomes are too long and there are too many invalid data, which needs further improvement.

Contents of the invention

The purpose of the present invention is to overcome the shortcoming of above-mentioned prior art, provide a kind of method based on the improved GA of multi-color set hierarchical structure to solve the method of flexible shop scheduling, this method has introduced the constraint description method of multilevel, the original huge confinement matrix Segmentation reduces the amount of redundant data in the constraint model and increases the possibility of practical application of the algorithm; in addition, it improves the coding method of chromosomes, removes a large number of invalid genes, further optimizes the algorithm from the perspective of space complexity, and improves the convergence speed.

In order to achieve the above object, the technical solution adopted in the present invention comprises the following steps:

1) Establish a mathematical model of the flexible workshop scheduling problem;

2) Establish a shop scheduling constraint model based on the PST hierarchy;

3) According to the procedure-benchmark, benchmark-equipment number, equipment number-asset number contour Boolean matrix, generate a process-equipment real number contour matrix, and then generate a genetic recessive coding sequence table, the column label corresponds to the machine tool code, and the row label corresponds to the implicit Among them, the content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece, by searching the corresponding process-baseline, benchmark-equipment number, equipment number-asset number enclosing the Boolean matrix, thus Find the machine tool code corresponding to a specific process, and then select the corresponding machine tool code as the dominant code of the chromosome according to the availability characteristics of the machine tool.

In the step 1), the specific method of establishing the mathematical model of the flexible shop scheduling problem is as follows:

J_e为工件e的工序数；X为所有工件的加工次序，S_egk表示工件e的第g道工序在设备k上加工的开始时间；E_egk为工件e的第g道工序在设备k上的加工结束时间；T_egk为工件e的第g道工序在设备k上的持续加工时间，且k∈I_eg则有E_egk=S_egk＋T_egk；E_p表示最后工序的完工时间；MS表示所有工件的最后完工时间；FJSP can be described as, assuming that M is the number of processing equipment, N is the number of workpieces to be processed, P is the number of processes, and I is the set of all equipment; _Ieg represents the set of available equipment for the gth process of the workpiece e,

J _e is the process number of workpiece e; X is the processing sequence of all workpieces, S _egk represents the start time of the g-th process of workpiece e being processed on equipment k; E _egk is the g-th process of workpiece e on equipment k The processing end time; T _egk is the continuous processing time of the gth process of the workpiece e on the equipment k, and k∈I _eg has E _egk =S _egk + T _egk ; E _p represents the completion time of the last process; MS represents The final completion time of all workpieces;

When the j-th process of workpiece i and the g-th process of workpiece e are executed on the same equipment, if process j is processed before process g, Q _ijeg = 1, otherwise Q _ijeg = 0; if the g-th process of workpiece e If a procedure is processed on machine k, then X _egk =1, otherwise X _egk =0;

If there are S possible processing sequences in a certain FJSP, and the processing sequence with the shortest total operation time is required, first obtain the operation time corresponding to each processing sequence x(x∈{1,...,S}); obviously, the sequence The completion time of the last processing procedure in x is the final completion time of all workpieces, then

MS=E _p (1)

The objective function F(x) is

F(x)=min(MS _x )=min((E _p ) _x ) (2)

X=1,...,S

STS _egk -E _e(g-1)n ≥0

e=1,...,N;g=1,...,J _e ;X _egk =1,X _e(g－1)n =1 (3)

_Segk － _Eigk≥0

e=1, . . . , N; g=1, . . . , J _e ; X _ijk =1, X _egk =1, Q _ijeg =1 (4).

In the step 2), the constraint relationship of the shop-shop scheduling constraint model is:

First, set the equipment benchmark. Each equipment benchmark contains several equipment models with similar processes. Each equipment model contains several specific equipment of this type. Each specific equipment corresponds to the corresponding asset number. The processing is completed on the specific equipment, so the constraint relationship between the process and the specific equipment can be established indirectly through the constraint relationship between the process and the benchmark, the constraint relationship between the equipment benchmark and the equipment model, and the constraint relationship between the equipment model and the asset number, so as to realize the The huge process machine tool contour matrix is divided into small relational matrices to reduce the scale and data volume of the matrix and improve the solution speed of the algorithm.

In step 3), according to the availability characteristics of the machine tool, select the corresponding machine tool code as the dominant code of the chromosome, specifically:

3.1) Establish a constraint model based on the hierarchical structure of the Boolean matrix:

Use the hierarchical structure surrounding Boolean matrix of benchmark and equipment model, equipment model and asset number, autocorrelation, process equipment, and process equipment real numbers as a constraint model to generate a genetic recessive coding sequence table, and the operation of GA is within the scope of the constraint model conduct;

3.2) Chromosome coding:

3.3) Chromosome decoding:

According to the corresponding information in the chromosome, search the process-equipment real number contour matrix to determine the processing time parameters of all processes on each machine tool;

3.4) Select operation:

The chromosomes corresponding to the individuals with the best fitness value in the previous generation population are directly selected into the next generation population;

3.5) Cross operation:

Randomly select two parent chromosomes, two random numbers 0<a<b<N, where N is the number of chromosome genes, and find out the segments corresponding to a and b on the two parent chromosomes to exchange with each other;

3.6) Variation.

The specific method of the chromosome coding is:

First determine the chromosome length as the sum of the effective number of processes of each job:

(a) When it is a single-piece multi-variety production mode:

There are n types of workpieces each, and the length of the GA chromosome is Where L _g is the number of processes corresponding to the gth part;

(b) When it is a multi-piece multi-variety production mode:

There are n types of workpieces, a total of J pieces J=n ₁ +n ₂ +...+n _i +...+n _n , where n ₁ , n ₂ ,..., n _i ,..., n _n are respectively Indicates the number i∈n of the i-th type of workpieces, and each type of workpiece has p _i processes, it is necessary to encode the processing order of the workpieces first, and randomly sort the processing order of the workpieces to generate dominant chromosomes;

When the number of parts of the same type is less than 100, merge them into one task; finally, generate recessive chromosomes according to the matrix of benchmarks and equipment models, equipment models and asset numbers;

When the number of parts of the same kind exceeds 100, the batch strategy is adopted, and the individual tasks after batching are randomly sorted.

The specific method of the variation is:

3.6.1) Set the mutation rate and determine the gene bits that need to be mutated;

3.6.2) Search the benchmark and equipment model, equipment model and asset number matrix, find out that this gene bit can replace the code of the machine tool, and generate a new chromosome;

3.6.3) Calculate the objective function of the new chromosome, compare the objective function values corresponding to the old and new chromosomes, and then select the better one to enter the next generation.

Compared with the prior art, the present invention has the following beneficial effects:

According to the process-reference, reference-equipment number, equipment number-asset number enclosing Boolean matrix, the present invention generates a process-equipment real number enclosing matrix, and then generates a genetic recessive coding sequence table, the column label corresponds to the machine tool code, and the row label corresponds to the implicit Among them, the content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece, by searching the corresponding process-baseline, benchmark-equipment number, equipment number-asset number enclosing the Boolean matrix, thus Find the machine tool code corresponding to a specific process, and then select the corresponding machine tool code as the dominant code of the chromosome according to the availability characteristics of the machine tool. The random execution process of the improved GA algorithm of the present invention in encoding, decoding and mutation is carried out within the constraints of the procedure-reference, reference-equipment number, equipment number-asset number confinement matrix, and is a kind of random execution within the controllable range. , its role is to reduce the amount of data in the constraint model and remove invalid information to narrow the search range of the understanding space, and ultimately improve the accuracy and speed of the algorithm.

Further, the method for encoding chromosome gene bits adopted in the present invention removes invalid gene bits, reduces the space and time complexity of the algorithm, and thus improves the search efficiency of the GA.

Description of drawings

Fig. 1 is a hierarchical constraint relationship diagram of the present invention;

Fig. 2 is a PS hierarchical structure model diagram of task assignment of the present invention;

Fig. 3 is the hereditary convergence curve figure of example 1 of the present invention;

Fig. 4 is the scheduling Gantt chart of the example 1 of the present invention;

Fig. 5 is the genetic convergence curve figure of the example 2 of the present invention;

Fig. 6 is the scheduling result Gantt chart of the example 2 of the present invention;

Fig. 7 is a flowchart of the present invention.

Detailed ways

Below in conjunction with accompanying drawing and embodiment the present invention is described in further detail:

Example:

1) Mathematical model of flexible shop scheduling problem

J_e为工件e的工序数；X为所有工件的加工次序，S_egk表示工件e的第g道工序在设备k上加工的开始时间；E_egk为工件e的第g道工序在设备k上的加工结束时间；T_egk为工件e的第g道工序在设备k上的持续加工时间，且k∈I_eg则有E_egk=S_egk＋T_egk；E_p表示最后工序的完工时间；MS表示所有工件的最后完工时间；FJSP can be described as, assuming that M is the number of processing equipment, N is the number of workpieces to be processed, P is the number of processes, and I is the set of all equipment; _Ieg represents the set of available equipment for the gth process of the workpiece e,

J _e is the process number of workpiece e; X is the processing sequence of all workpieces, S _egk represents the start time of the g-th process of workpiece e being processed on equipment k; E _egk is the g-th process of workpiece e on equipment k The processing end time; T _egk is the continuous processing time of the gth process of the workpiece e on the equipment k, and k∈I _eg has E _egk =S _egk + T _egk ; E _p represents the completion time of the last process; MS represents The final completion time of all workpieces;

When the j-th process of workpiece i and the g-th process of workpiece e are executed on the same equipment, if process j is processed before process g, Q _ijeg = 1, otherwise Q _ijeg = 0; if the g-th process of workpiece e If a procedure is processed on machine k, then X _egk =1, otherwise X _egk =0;

If there are S possible processing sequences in a certain FJSP, and the processing sequence with the shortest total operation time is required, first obtain the operation time corresponding to each processing sequence x(x∈{1,...,S}); obviously, the sequence The completion time of the last processing procedure in x is the final completion time of all workpieces, then

MS=E _p (1)

The objective function F(x) is

F(x)=min(MS _x )=min((E _p ) _x ) (2)

X=1,...,S

STS _egk -E _e(g-1)n ≥0

e=1,...,N;g=1,...,J _e ;X _egk =1,X _e(g－1)n =1 (3)

_Segk － _Eigk≥0

e=1,...,N; g=1,...,J _e ;X _ijk =1, X _egk =1, Q _ijeg =1 (4)

2) FJSP constraint model based on PST hierarchy

2.1 Introduction to polychromatic set theory

Multicolor set theory is a new system modeling theory and a mathematical tool to help information processing. Since its appearance, this theory and method have been widely promoted and applied in the former Soviet Union and the current Russian business circles, especially aerospace companies. The core idea of this theory is to apply the same mathematical model to simulate different objects (products, production systems, design and process, etc.), describe the hierarchical structure and complex relationship between elements, and organize and process them at the collection layer and logic layer Information, dealing with the actual value of low-level data at the quantitative level.

2.2 Analysis of actual production constraints in the workshop

For general manufacturing enterprises, the actual production work will be affected and restricted by a large number of factors such as people, machines, materials, methods, and the environment. Therefore, there are many factors that need to be considered in the actual workshop scheduling work. The ordinary PST is used to describe this Constraint relations will lead to a large amount of data in the individual color, uniform color, and body contour matrix. How to timely change multi-faceted influences into the contour matrix describing the relationship between elements is an important bottleneck in the application of multi-color set theory and intelligent algorithms to solve scheduling problems. The hierarchical structure model of PST provides an effective way to solve this bottleneck.

Combined with the actual experience analysis of a large number of workshop scheduling, it is found that if the corresponding equipment reference and equipment model are set for the equipment in the workshop, the process can be associated with the equipment reference sequence, the equipment reference can be associated with the equipment code, and the equipment code can be associated with the specific equipment in the workshop. The asset number is associated with each other, and finally the corresponding relationship between the process and the equipment is established indirectly, which brings great convenience to the equipment management and workshop scheduling work of the enterprise. If a single confinement matrix is used to describe the corresponding relationship between procedures and equipment, it will inevitably lead to too large a matrix and lack of practicability.

2.3 Shop Scheduling Constraint Model Based on PST Hierarchy

Based on the above analysis and considering various influencing factors in the actual production of the workshop, the present invention sets four kinds of constraints in the scheduling process: the process constraint means that the processes must be scheduled according to the actual processing technology; the benchmark constraint means that a The process can only be processed on the equipment of several specified benchmark types; the machine tool constraint means that each benchmark type corresponds to several fixed machine tool models; the unique constraint means that any process of each workpiece can only be processed on one machine at a fixed time Processing on the machine. The constraint relationship is to first set the equipment benchmark, each equipment benchmark includes several equipment models of similar technology, each equipment model includes several specific equipment of this type, and each specific equipment corresponds to the corresponding asset number, And the process must be processed on specific equipment, so the constraint relationship between the process and the specific equipment can be indirectly established through the constraint relationship between the process and the benchmark, the constraint relationship between the equipment benchmark and the equipment model, and the constraint relationship between the equipment model and the asset number. , so as to realize the division of the huge process machine tool contour matrix into small relational matrices, so as to reduce the scale and data volume of the matrix, and improve the solution speed of the algorithm. The specific hierarchical structure is shown in Figure 1.

The contour matrix in the upper left corner of Figure 1 reflects the process constraints and reference equipment type constraints of the parts, that is, which reference equipment type can be processed by each process, which can be reflected by the matrix, and those without values cannot be processed. The upper right corner matrix reflects the machine tool constraints of the benchmark equipment type and the specific equipment model. If there is 1 among them, it proves that the reference device type includes the device model. The lower corridor matrix reflects the corresponding relationship between the equipment model of the M workshop and the specific machine tool, where the value indicates the processing time of the corresponding process on the machine tool. On this basis, its task allocation model can be further drawn as shown in Figure 2.

The following will introduce the establishment process of the PST hierarchy constraint model through the FJSP of the three workpieces. The processing task information table is shown in Table 1, where the columns represent the equipment information, the rows represent the workpiece process information, and the data in the table represent the row correspondence. The process is listed in the corresponding processing time on the machine tool, and the equipment benchmarks J1, J2, J3 are set according to the relevant information and process similarity criteria in Table 1, the equipment models are S1, S2, S3, and the asset numbers are M1, M2, M3, M4, M5 , M6, that is, the 6 equipments processed this time, and the constraint relationship between them is shown in formulas (5) and (6).

Table 1 Processing task information table

The point of C _ij indicates the equipment model included in the benchmark represented by the point horizontally. From this matrix, the relationship between benchmarks and device models can be found.

The point where C _ij =1 represents the asset number of all equipment in this workshop corresponding to the equipment model represented by the horizontal direction.

In summary, the autocorrelation matrix [F(a)×F(a)] of the node set can be obtained as shown in Table 2:

Table 2 [F(a)×F(a)]

According to the relevant data in Table 1 and the equipment reference corresponding to the set workpiece and the relationship between the nodes recorded in Table 2 [F(a)×F(a)], the contour matrix [A×F(A)] can be obtained and body circumference array [A×A(F)] are shown in Table 3 and Table 4. Among them, F1-F6 represent different process names of lathe, pliers, boring, drilling, milling, and planing; J1, J2, and J3 represent three different equipment benchmarks. And in this example, there is a one-to-one correspondence with the process. a1-a15 represent the sequence of three workpieces; M1-M6 represent the machine tool to be processed. Among them, the point of C _ij =1 indicates that the element represented by the abscissa is directly related to the color represented by the ordinate.

Table 3 Process-Equipment Boolean Confinement Matrix [A×F(A)]

The real part matrix in Table 4 [A×A(F)] can be used as the basis for further recessive chromosome coding. From this matrix, the equipment that can process each process and the time required to process the work in this equipment can be obtained.

Table 4 Process-Equipment Real Contour Matrix [A×A(F)]

Based on this, the genetic recessive coding sequence table is generated as shown in Table 5. The column label corresponds to the machine tool code, and the row label corresponds to the recessive gene bit. The content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece. , to search the relative process-benchmark, benchmark-equipment number, equipment number-asset number confinement matrix, so as to find the machine tool code corresponding to a specific process, and then select the appropriate machine tool code according to the availability characteristics of the machine tool (occupied or idle). as a dominant code for a chromosome.

Table 5 Genetic recessive coding sequence list

3) Improved GA operation under the hierarchy constraint model

As shown in Figure 7, Figure 7 is a flowchart of the improved genetic algorithm of the present invention;

3.1 Constraint Model Based on Hierarchical Confinement Boolean Matrix

The improved GA of the present invention uses the hierarchical structure surrounding Boolean matrix of benchmark and equipment model, equipment model and asset number, autocorrelation, process equipment, and process equipment real numbers as a constraint model, and the operations of GA are all carried out within the scope of the constraint model, specifically The operation is as follows.

3.2 Chromosome coding

First determine the chromosome length as the sum of the effective number of processes of each workpiece

(a) When it is a single-piece multi-variety production mode: there are n types of workpieces each, and the length of the GA chromosome improved by the present invention is Among them, L _g is the number of processes corresponding to the g-th part, and n is the number of workpieces scheduled for this batch. Taking the above 3×6 single-room scheduling as an example, the chromosomes generated are as follows:

1 5 4 3 4 6 2 3 4 2 6 3 1 2 4 1

1-6 represent the processing machine information of workpiece 1; 7-11 represent the processing machine information of workpiece 2; 12-15 represent the processing machine information of workpiece 3.

(b) When it is a multi-piece multi-variety production mode:

When it is a multi-variety production mode: there are n types of workpieces and a total of J pieces (J=n ₁ +n ₂ +...+n _i +...+n _n , where n ₁ , n ₂ ,..., n _i , ..., n _n respectively represent the number of workpieces of the i type (i∈n), each type of workpiece has p _i processes, the processing order of the workpieces needs to be coded first, if there are A, B, and C types of workpieces For each of 3 pieces, the processing order of the workpieces is first randomly sorted to generate dominant chromosomes.

According to the learning curve theory, repeated operations can increase the proficiency of employees and shorten the processing time of a single part. Therefore, the same type of parts batch production coding strategy is adopted in the research of the present invention. When the quantity of the same kind of parts is less than 100 pieces, combine them into one task. The above example can be coded as follows (A*3 means that the processing time of each process is multiplied by the coefficient, that is, the number of parts).

A ₁₁ 3 … A _1m 3 B ₁₁ 3 … B _1m 3 C _k1 ·3 … C _km 3

Finally, recessive chromosomes are generated according to the benchmark and equipment model, equipment model and asset number confinement matrix.

If it exceeds 100, the batching strategy is adopted, because if the number of a workpiece is too large, the processing of subsequent parts will be affected after a batch is synthesized. Because the delivery time of parts in each batch is different, in order to meet other parts can also arrive at the designated warehouse within the specified delivery time, for example, take 100 pieces as the critical point of batching. Suppose there are 150 pieces of workpiece A, 211 pieces of workpiece B, and 50 pieces of workpiece C, then:

A·100 C·50 B·100 B·11 A·50 B·100

The individual tasks after batching are randomly sorted.

3.3 Chromosome decoding

According to the corresponding information in the chromosome, search the genetic recessive coding sequence table in Table 5 to determine the processing time and other parameters of all processes on each machine tool.

3.4 Select operation

The chromosomes corresponding to the individuals with the best fitness value in the previous generation population are directly selected into the next generation population.

3.5 Cross-operation

Randomly select two parent chromosomes, two random numbers 0<a<b<N (N is the number of chromosome genes), and find out the segments corresponding to a and b on the two parent chromosomes to exchange with each other.

3.6 Variation

3.6.1 Set the mutation rate and determine the gene bits that need to be mutated.

3.6.2 Search the process-benchmark, benchmark and equipment model, equipment model and asset number encircling the matrix, find the code of the machine tool that can replace the gene bit, and generate a new chromosome.

3.6.3 Calculate the objective function of the new chromosome, compare the objective function values corresponding to the old and new chromosomes, and then select the better one to enter the next generation.

According to the procedure-benchmark, benchmark-equipment number, equipment number-asset number confinement Boolean matrix, a process-equipment real number confinement matrix is generated, and then a genetic recessive coding sequence table is generated, the column label corresponds to the machine tool code, and the row label corresponds to the recessive gene Wherein, the content in the table is the processing time of the procedure, and the recessive gene code bit corresponds to the procedure number of the workpiece, by searching the corresponding procedure-benchmark, benchmark-equipment number, equipment number-asset number surrounding the Boolean matrix, so as to find the corresponding According to the machine tool code for a specific process, and then according to the availability characteristics of the machine tool, the corresponding machine tool code is selected as the dominant code of the chromosome. The random execution process of the improved GA algorithm of the present invention in encoding, decoding and mutation is carried out within the constraints of the procedure-reference, reference-equipment number, equipment number-asset number confinement matrix, and is a kind of random execution within the controllable range. , its role is to reduce the amount of data in the constraint model and remove invalid information to narrow the search range of the understanding space, and ultimately improve the accuracy and speed of the algorithm. The method for encoding chromosome gene bits used in the present invention removes invalid gene bits, reduces the space and time complexity of the algorithm, and improves the search efficiency of GA. The specific data can be obtained from Table 3.

Principle of the present invention:

Genetic algorithm is a kind of evolutionary algorithm (Evolutionary Algorithms), which finds the optimal solution by imitating the process of inheritance and selection in nature. It is suitable for solving complex problems and has been widely used in research in various fields. However, from the perspective of optimization algorithm and usage requirements, the academic community has never stopped improving and optimizing the algorithm to reduce the time and space complexity of the algorithm.

Algorithm optimization direction

The single-layer encoding method can reduce the space complexity of genetic encoding to a certain extent; at the same time, when dealing with batch scheduling problems, the product type is encoded as a segment of chromosome as a whole, and each process of the product is based on recessive chromosome segments. reflected in the perimeter matrix.

Although the single-layer coding method has certain advantages and is conducive to production scheduling, there are a large number of invalid gene bits in the chromosome. Because it defines the chromosome length as max(m _i )×n (max(m _i ) is the maximum number of processes contained in n types of workpieces). In this way, the length of the entire chromosome is largely determined by the workpiece with the largest number of procedures in each batch of tasks. Chromosome length directly affects the efficiency of the genetic algorithm in the iterative process and increases the space complexity of the algorithm.

Optimization of single-layer encoding

1) Chromosome length optimization

The chromosome length of the present invention is Among them, L _g is the process number of the corresponding part, and n is the number of workpieces scheduled for this batch.

Before improvement (take 3 parts, the maximum number of processes is 6 as an example):

1 4 6 7 0 0 2 3 4 0 0 0 1 3 5 1 7 3

Improved:

1 4 6 7 2 3 4 1 3 5 1 7 3

From the above, it can be found that the length of the chromosomes of only three artifacts has been significantly shortened. From the perspective of algorithm optimization, the space complexity of the algorithm can be significantly reduced when there is a large amount of data. The improved algorithm of the present invention is compared with it as shown in Table 6.

Table 6 Algorithm optimization comparison

Among them, G represents the genetic algebra of the genetic algorithm; Z is the number of chromosomes initialized in the mating pool; m _i is the number of processes contained in the i-th type of workpiece; M is the number of equipment; J is the number of benchmark equipment (much smaller than the actual number of equipment) .

2) Batch according to actual needs

When scheduling multiple pieces and varieties: Assume there are j pieces of n types of workpieces (J=n ₁ +n ₂ +...+n _i +...+n _n , where n ₁ , n ₂ ,...,n _i ,..., n _n respectively represent the number of workpieces of the i type, and i∈n), and each type of workpiece has p _i processes.

The method adopted in the prior art is as follows, if there are 3 workpieces of each type A, B, and C, the processing sequence of the workpieces is randomly sorted to generate dominant chromosomes.

A C A A B C B B C

Then according to the process-machine tool contour matrix, recessive chromosomes are generated. Among them, A ₁₁ is the first process of A-type products, and so on. As shown in the table below.

A ₁₁ … A _1m C ₁₁ … C _1m A ₂₁ … A _2m … _K … C _km

According to the learning curve theory, repeated operations can increase the proficiency of employees and shorten the processing time of a single part. Therefore, the present invention adopts the batch production coding strategy for the same type of parts. When the quantity of the same kind of parts is less than 100 pieces, combine them into one task. The above example can be coded as follows: A*3 means that the processing time of each process is multiplied by the coefficient, that is, the number of parts.

A·50 B·11 C·50

Finally, recessive chromosomes are generated according to the process-machine tool contour matrix.

A ₁₁ 3 … A _1m 3 B ₁₁ 3 … B _1m 3 C _k1 ·3 … C _km 3

If it exceeds 100, the batching strategy is adopted, because if the number of a workpiece is too large, the processing of subsequent parts will be affected after a batch is synthesized. Because the delivery date of each batch of internal parts is different, in order to meet other parts can also arrive at the designated warehouse within the specified delivery date, 100 pieces are taken as the critical point of batching according to actual experience. Suppose there are 150 pieces of workpiece A, 211 pieces of workpiece B, and 50 pieces of workpiece C, then:

A·100 C·50 B·100 B·11 A·50 B·100

The individual tasks after batching are randomly sorted.

Example simulation

Example 1 simulation:

For the calculation example in Table 1, the parameters of the genetic algorithm are set as follows: the population size is 50, the crossover rate is 0.6, the mutation rate is 0.8, and the maximum number of evolutionary bands is 100. The GA evolution curve is obtained by simulation in the MATILAB7.0 environment: As shown in Figure 3, it can be seen from Figure 3 that the improved GA algorithm can quickly converge from 147 to 134 in the 70th generation, and the Gantt chart of the corresponding scheduling result is shown in Figure 4.

Example 2 simulation and comparison:

In order to further verify the correctness of the algorithm, choose Example 2 for simulation, set 2 process benchmarks, 4 equipment numbers, and 8 specific equipment, and the optimal solution is 121 minutes. It can be seen from the genetic evolution curve in Figure 5 that the improved genetic algorithm can quickly converge from 130 to 121 in the 32nd generation, and its solution speed is obviously faster, and the Gantt chart of the corresponding scheduling result is shown in Figure 6 .

Example 3 simulation and comparison:

In order to compare and verify the algorithm effect more comprehensively. On a computer with a CPU frequency of 2.5G and a memory of 512MB, using VB6.0 as the development platform, the 8×8 instance in the Kacem benchmark problem of flexible job scheduling is selected for solution, and 2 process benchmarks and 4 equipment numbers are set. 8 specific devices, calculated 10 times. Table 7 is the results obtained by the algorithm of the present invention and the evolutionary algorithm (Approach by Localization&Controlled Genetic Algorithhm, AL+CGA), master-slave genetic algorithm, multi-stage genetic algorithm, and ant colony genetic algorithm with local minimization as the distribution model. Compared.

Table 7 Comparison of the solution results of various methods for the Kacem8×8 benchmark problem

Aiming at the traditional multicolor set theory improving the constraint model of the genetic algorithm and the large amount of redundant data in the chromosome, the present invention further proposes to use the multicolor set hierarchical structure model to improve the constraint model of the algorithm, by establishing the equipment benchmark, setting the process Constraints, equipment constraints, machine tool constraints, and unique constraints, the original process-machine tool perimeter matrix is divided into a relationship matrix between benchmark and equipment model, equipment model and asset number, which greatly reduces the amount of redundant data in the constraint model. Through the reasonable optimization of the length of the chromosome and the batch operation of setting the batch benchmark, the time and space complexity of the chromosome is effectively reduced, and the dynamic responsiveness of the algorithm model is also improved. Finally, through the comparison of the simulation results of the same example, It is proved that the improved GA of PST hierarchical structure has improved compared with the traditional PST improved GA in terms of solution accuracy and speed. At the same time, the experiments of the Kacem8×8 benchmark example on the computer with the same configuration have proved that the algorithm of the present invention These performances are all improved compared with various traditional algorithms, which further proves the practicability and superiority of the algorithm in solving flexible job shop scheduling problems.

The above content is only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solutions according to the technical ideas proposed in the present invention shall fall within the scope of the claims of the present invention. within the scope of protection.

Claims (6)

1. the improvement GA based on polychromatic sets hierarchical structure solves a method for Flexible Workshop scheduling, it is characterized in that, comprises the following steps:

1) set up the mathematical model of Markov chain;

2) set up the Job-Shop restricted model based on PST hierarchical structure;

3) according to operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.

2. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 1), the concrete grammar of setting up the mathematical model of Markov chain is:

FJSP can be described to, and supposes that M is the quantity of process equipment, and N is workpiece to be processed quantity, and P is process number, the set that I is all devices; I _egrepresent the available devices set of the g procedure of workpiece e, j _eprocess number for workpiece e; X is the process sequence of all workpiece, S _egkthe start time that the g procedure of expression workpiece e is processed on equipment k; E _egkfor the g procedure of the workpiece e process finishing time on equipment k; T _egkfor the g procedure of workpiece e lasting process time on equipment k, and k ∈ I _egthere is E _egk=S _egk+ T _egk; E _pthe completion date that represents finishing operation; MS represents the last completion date of all workpiece;

When the j procedure of workpiece i and the g procedure of workpiece e are carried out on same equipment, if operation j adds man-hour prior to operation g, Q _ijeg=1, otherwise Q _ijeg=0; If the g procedure of workpiece e is processed on lathe k, X _egk=1, otherwise X _egk=0;

If certain FJSP has the possible processing sequence of S kind, require total the shortest Machining Sequencing of activity duration, first ask for each processing sequence x (x ∈ 1 ..., S}) the corresponding activity duration; Obviously, in order x, the i.e. last completion date of all workpiece of the completion date of last manufacturing procedure, has

MS=E _p （1）

Objective function F (x) is

F(x)=min(MS _x)=min（(E _p) _x） （2）

X=1，…，S

S.T.S _egk－E _e(g－1)n≥0

e=1，…，N;g=1，…，J _e;X _egk=1，X _e(g－1)n=1 （3）

S _egk－E _igk≥0

e=1，…，N;g=1，…，J _e;X _ijk=1，X _egk=1，Q _ijeg=1 （4）。

3. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: described step 2), the restriction relation of Job-Shop restricted model is:

First equipment benchmark is set, several unit types that each equipment benchmark comprises process similarity, each unit type comprises again the concrete equipment of several this kind of models, every concrete equipment is corresponding with corresponding asset number again, and operation finally will complete processing on concrete equipment, therefore just can be by the restriction relation of operation and benchmark, the restriction relation of equipment benchmark and unit type, the restriction relation of unit type and asset number, indirectly set up the restriction relation of operation and concrete equipment, thereby realize huge operation lathe circuit matrix is divided into little relational matrix, to reduce scale and the data volume of matrix, improve the speed that solves of algorithm.

4. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 3), according to the availability aspect of lathe, select corresponding lathe coding to be specially as chromosomal dominant coding:

3.1) set up the restricted model based on hierarchical structure circuit Boolean matrix:

Use the hierarchical structure circuit Boolean matrix of benchmark and unit type, unit type and asset number, auto-correlation, process equipment, process equipment real number as restricted model, produce hereditary recessive code sequence list, the operation of GA is all carried out in the scope of restricted model;

3.2) chromosomal coding:

3.3) chromosomal decoding:

According to the corresponding information of chromosome the inside, search technique-equipment real number circuit matrix, determines parameter process time of all process steps on each lathe;

3.4) select operation:

The corresponding chromosome of individuality that fitness value in previous generation population is best is directly selected to enter population of future generation;

3.5) interlace operation:

Two parent chromosomes of random selection, two random number 0<a<b<N, wherein, N is chromogene number, finds out corresponding a on two parent chromosomes, the fragment between b exchanges each other;

3.6) variation.

5. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described chromosome coding is:

First determine effective process number sum that chromosome length is each workpiece:

(a) when being the production model of the many kinds of single-piece:

Have each of n class workpiece, GA chromosome length is

l wherein _gprocess number for corresponding g part;

(b) when being the pattern of variety production more than many:

There is n class workpiece J part J=n altogether ₁+ n ₂+ ...+n _i+ ...+n _n, n wherein ₁, n ₂..., n _i..., n _nthe quantity i ∈ n that represents respectively i class workpiece, every class workpiece has p _iprocedure, needs first the process sequence of workpiece to be encoded, and workpiece process sequence is carried out randomly ordered, generates dominant chromosome;

When the quantity of part of the same race is less than 100, be merged into a task; Finally, according to benchmark and unit type, unit type and asset number circuit matrix, generate recessive chromosome;

When quantity employing over 100 of part of the same race strategy in batches, between the individual task body after in batches, be randomly ordered.

6. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described variation is:

3.6.1) set aberration rate, determine the gene position that needs variation;

3.6.2) search benchmark and unit type, unit type and asset number circuit matrix, find this gene position can replace the coding of lathe, produces new chromosome;

3.6.3) calculate new chromosomal objective function, the target function value that new and old chromosome is corresponding, and then select preferably to enter the next generation.

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