CN110796355A - Flexible job shop scheduling method based on dynamic decoding mechanism - Google Patents

Flexible job shop scheduling method based on dynamic decoding mechanism Download PDF

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CN110796355A
CN110796355A CN201911005648.7A CN201911005648A CN110796355A CN 110796355 A CN110796355 A CN 110796355A CN 201911005648 A CN201911005648 A CN 201911005648A CN 110796355 A CN110796355 A CN 110796355A
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刘峰
汪孝胜
陶凌峰
李茂盛
高磊
洪鹏
吕向峰
刘哲
金磊
张斌
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Jiangsu Jinling Intellectual Building Research Institute Co Ltd
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Abstract

A flexible job shop scheduling method based on a dynamic decoding mechanism. The invention relates to the technical field of flexible job shop scheduling. The flexible job shop scheduling method based on the dynamic decoding mechanism is provided, which adopts the improved MOGA to solve and is integrated with the improved workpiece priority sequence crossing method, the insertion mutation method and the initialized population strategy, so as to complete the optimal design of the multi-target flexible job shop scheduling. The technical scheme of the invention is as follows: the method comprises the following steps: 1) modeling; 2) initializing a population; 3) genetic manipulation; 4) and updating the external Pareto solution set. Simulation experiments prove that after a dynamic decoding mechanism is applied, the improved algorithm can obtain richer non-dominant solutions and higher-quality non-dominant solutions, and then the optimal design of the multi-target flexible job shop scheduling is completed.

Description

Flexible job shop scheduling method based on dynamic decoding mechanism
Technical Field
The invention relates to the technical field of flexible job shop scheduling.
Background
The scheduling problem of the job shop refers to that n workpieces are machined on m machines, the machining process of each workpiece is determined before machining, each process of each workpiece has a specific machining machine, the machining time of the designated process is also determined, and the purpose of research is to sequence the machining processes of all the workpieces on the machines and optimize specific performance indexes. However, the flexible job-shop scheduling problem is also that n workpieces are processed on m machines, and the job-shop scheduling problem is different in that each workpiece processing procedure has a fixed processing machine and processing time. The flexible job shop schedules the various process processing machines for the problem workpiece to be uncertain, and all processes have more than or equal to one machine that can be selected to process the designated process. It can also be said that job shop scheduling problem is a special case of flexible job shop scheduling problem. The goal of the flexible job shop scheduling problem study is to order all the processes and assign all the processes to designated processing machines to meet certain performance criteria in the manufacturing system to reach optimal values.
In the prior art, when solving the problem, the machine allocation code and the process sequencing code are generally only subjected to genetic operations including crossover operations and mutation operations, so that the diversity of the population is increased and good characters are kept. However, the process of crossover and mutation operations is too random, and the ideal optimization result is not necessarily obtained by changing the crossover and mutation probabilities only. The operation is not dynamically adjusted according to the current state of the population, so that the algorithm is slow in solving speed, poor in solving precision and easy to fall into local optimization.
The Multi-Objective Genetic Algorithm (MOGA) has great advantages in processing Multi-Objective problems, and a high-quality non-dominated solution can be obtained by properly improving the Algorithm. The dynamic decoding mechanism provided by the invention can automatically adjust corresponding parameters according to the current population situation, so that inferior objective function values in the population can be better developed in the following iteration process. And guiding the Pareto solution set obtained by algorithm calculation to iterate towards the front edge of the Pareto, and finally obtaining an ideal optimization result. Therefore, how to select an algorithm for optimization, how to improve the algorithm to adapt to the solution of the problem, and how to design a decoding mechanism of a feasible solution are great technical difficulties at present.
Disclosure of Invention
Aiming at the problems, the invention provides a flexible job shop scheduling method based on a dynamic decoding mechanism, which adopts an improved MOGA (multi-object-oriented genetic algorithm) to solve and integrates an improved workpiece priority crossing method, an insertion mutation method and an initialized population strategy, thereby completing the optimal design of multi-target flexible job shop scheduling.
The technical scheme of the invention is as follows: the method comprises the following steps:
1) and modeling:
1.1), establishing a mathematical model for optimizing the maximum completion time, the total machine load and the maximum machine load of a target, and determining constraint conditions of the mathematical model;
1.2) adopting Pareto to control and process a feasible solution screening problem;
1.3) carrying out discretization treatment on the MOGA, and coding by adopting a coding mode based on a working procedure;
2) initializing a population:
2.1), initializing population control parameters including population number SN and cross probability pcAnd the probability of variation pm；
2.2) adopting a random criterion, a maximum workpiece operation time residual criterion and a maximum workpiece residual procedure criterion to process codes to generate an initialized population;
2.3) decoding by applying a dynamic decoding mechanism, and storing the non-dominant solution in the population to an external Pareto solution set;
3) and genetic manipulation: selecting individuals corresponding to the population by using a championship selection mechanism, judging and then performing genetic operation, wherein the genetic operation is cross operation or mutation operation; applying Pareto to individuals generated after genetic operation to reserve high-quality individuals, and repeating SN times;
4) updating an external Pareto solution set: updating an external Pareto solution set, judging whether a stopping criterion is met, and if so, deriving an external Pareto storage set; if not, returning to the step 3).
The relevant assumed conditions established by establishing the mathematical model in step 1.1) are as follows:
firstly, each machine can only process one workpiece at each moment;
secondly, each procedure can be processed by only one machine;
thirdly, the starting time of all the processing machines can be 0;
fourthly, the starting processing time of all the workpieces can be 0;
fifthly, each workpiece can be processed in the next procedure only after the previous procedure is finished;
sixthly, once the machining is started, the machining cannot be interrupted in all the working procedures;
seventhly, the processing sequence of different procedures of the same workpiece is fixed, and the processing sequence of the procedures among different workpieces is not fixed;
the variable symbols in the mathematical model are shown in table 1:
TABLE 1 variable symbol definitions
Figure BDA0002242679960000021
The three optimization goals are respectively minimizing the maximum completion time, minimizing the total machine load and minimizing the maximum machine load;
the mathematical model and the related constraint conditions are as follows:
Figure BDA0002242679960000032
Figure BDA0002242679960000033
Figure BDA0002242679960000034
Figure BDA0002242679960000035
Figure BDA0002242679960000036
Figure BDA0002242679960000037
Figure BDA0002242679960000038
the formula (1) is an optimization target for minimizing the maximum completion time, represents the time of finishing the last of all the workpieces, and has a close and inseparable relationship with the completion time of all the workpieces and the use efficiency of processing machines, and the use efficiency of the machines can be further improved and the completion time of all the workpieces can be shortened by optimizing the maximum completion time; equation (2) is a goal of minimizing total machine load optimization, representing the total processing load of all machines, to improve economic efficiency by allocating a relatively small processing time of the machine for each process; equation (3) is a minimum maximum machine load optimization objective, representing the maximum processing load among all machines, by optimizing this objective to balance the processing load among all machines to prevent allocation of excessive processing load to a single machine; formula (4) is a calculation method of the machine Mi processing load; the formula (5) represents order constraint between the steps; equation (6) indicates that only one process can be processed by one machine at a time; the expression (7) indicates that only one machine can be selected for processing in the selectable machines for each process.
In the step 1), the flexible job shop scheduling problem solution comprises two parts, namely a process coding part and a machine coding part;
the procedure coding part adopts a procedure-based coding mode; the method can ensure that the requirements of relevant constraints are met and the feasibility of the solution is ensured. In the machine coding part, the machine coding part corresponds to the process coding part one by one, and the dimensions of the process coding part and the machine coding part are the same as the total number of processes needing to be processed.
In step 2), the dynamic decoding mechanism only operates the process codes, and can obtain the machine distribution codes corresponding to the process codes while decoding the process codes; the dynamic decoding mechanism can automatically adjust corresponding parameters according to the situation of the current population, mainly develop inferior objective function values, and iterate in the direction that a Pareto solution set obtained by calculation of a guide algorithm faces the front edge of Pareto;
the three calculation criteria of the dynamic decoding mechanism are: maximum time-out minimum criterion N1, maximum machine load minimum criterion N2, total machine load minimum criterion N3.
The relevant calculation formula of the dynamic decoding mechanism is as follows:
Figure BDA0002242679960000041
Figure BDA0002242679960000042
Figure BDA0002242679960000043
Figure BDA0002242679960000044
Figure BDA0002242679960000045
Figure BDA0002242679960000046
ω1+ω2+ω3＝1 (14)
Figure BDA0002242679960000052
Figure BDA0002242679960000053
fitness＝ω1×F1+ω2×F2+ω3×F3(18)
Figure BDA0002242679960000054
in the above expression, ω1、ω2、ω3Respectively representing the probability of selecting N1, the probability of selecting N2 and the probability of selecting N3 in the decoding process; min (f)1)、min(f2)、min(f3) The minimum value of the three objective functions in the current population is not the minimum value of the three objective functions in the current population, but the minimum value of the three objective functions from iteration to the present, namely the minimum value of the three objective functions in the current external Pareto solution set; max (f)1)、max(f2)、max(f3) At the current iterationIn the process, the maximum values of three objective functions in the population;
a. the molecular parts in the expressions b and c are used for expressing the objective function value f in the population when the algorithm is iterated1、f2、f3And historical optimum min (f)1)、min(f2)、min(f3) The degree of deviation therebetween; when the deviation degree between one objective function value and the optimal objective function value is large, the current objective function value is proved to be far away from the objective function value in the Pareto frontier; therefore, the algorithm should enhance the search for the objective function value in the next iteration process;
after the deviation degrees a, b and c of the three objective function values are calculated, normalization processing is carried out on the three values; when the objective function with large deviation degree is iterated next time, the criterion corresponding to the objective function has higher selected probability, so that the objective function is correspondingly improved; on the contrary, when the objective function with small deviation degree is in the next iteration process, the criterion corresponding to the objective function has lower selected probability. Centralizing min (f) by constantly updating external Pareto solutions1)、min(f2)、min(f3) And max (f) in the current population1)、max(f2)、max(f3) Dynamically adapting to the state of the population in the algorithm; by continuously adopting the dynamic decoding mechanism, the algorithm is iterated towards the direction of a weaker objective function in the three objective functions, so that the optimization aim is fulfilled.
The operation steps of the cross operation in the step 3) are as follows:
a3.1) selecting two individuals from the population by applying a tournament mechanism;
a3.2) randomly dividing all the workpieces encoded in an individual into two sets, J1 and J2 respectively;
a3.3) copying the workpiece containing J1 in the parent individual 1 to the child individual 1 and copying the workpiece containing J2 in the parent individual 2 to the child individual 2 on the basis of keeping the initial positions of the procedures of the parent individual 1 and the parent individual 2;
a3.4) copying the work piece containing J2 in the parent individual 2 to the child individual 1, and copying the work piece containing J1 in the parent individual 1 to the child individual 2.
The operation steps of the variation operation in the step 3) are as follows:
b3.1) selecting an individual from the population using a tournament mechanism;
b3.2) in the process-based coding part, firstly randomly selecting a process;
b3.3) randomly inserting the process in front of another process, the other processes moving backwards in sequence while keeping the machine code assigned to all the processes unchanged.
Compared with the prior art, the invention has the following remarkable advantages: the invention designs a flexible job shop scheduling method based on a dynamic decoding mechanism, which adopts a coding mode based on a working procedure and provides a dynamic decoding mechanism, and the mechanism can automatically adjust corresponding parameters according to the current population situation, so that inferior objective function values in the population can be better developed in an iteration process. And solving by adopting an improved MOGA (molecular oxygen gas) and integrating an improved workpiece priority crossing-based method, an insertion mutation-based method and an initialized population strategy. Simulation experiments prove that after a dynamic decoding mechanism is applied, the improved algorithm can obtain richer non-dominant solutions and higher-quality non-dominant solutions, and then the optimal design of the multi-target flexible job shop scheduling is completed.
Drawings
FIG. 1 is a flow diagram of the improved MOGA of the present invention;
FIG. 2 is a Gantt chart of an example problem of the present invention;
FIG. 3 is a schematic diagram of an improved workpiece priority based crossover method of the present invention;
FIG. 4 is a schematic diagram of an insertion mutation-based method according to the present invention;
FIG. 5 is a graph of a Pareto solution set distribution obtained after algorithm optimization according to an embodiment of the present invention;
FIG. 6(a) is a Gantt chart of a first scheduling scheme according to an embodiment of the present invention;
FIG. 6(b) is a Gantt chart of a second scheduling scheme according to an embodiment of the present invention;
FIG. 6(c) is a Gantt chart of a third scheduling scheme according to an embodiment of the present invention;
fig. 6(d) is a gantt chart of a fourth scheduling scheme in accordance with an embodiment of the present invention.
Detailed Description
The present invention, as shown in FIGS. 1-5, 6(a) -6(d), operates according to the following steps:
1) and modeling: the flexible job shop scheduling optimization is to sort all the procedures and distribute all the procedures to designated processing machines so as to meet certain performance indexes and achieve the optimal performance indexes;
1.1), establishing a mathematical model for optimizing the maximum completion time, the total machine load and the maximum machine load of a target, and determining constraint conditions of the mathematical model;
1.2) adopting Pareto to control and process a feasible solution screening problem;
1.3) carrying out discretization treatment on the MOGA, and coding by adopting a coding mode based on a working procedure;
2) initializing a population:
2.1), initializing population control parameters including population number SN and cross probability pcAnd the probability of variation pm；
2.2) adopting a random criterion, a maximum workpiece operation time residual criterion and a maximum workpiece residual procedure criterion to process codes to generate an initialized population;
2.3) decoding by applying a dynamic decoding mechanism, and storing the non-dominant solution in the population to an external Pareto solution set;
3) and genetic manipulation: selecting individuals corresponding to the population by using a championship selection mechanism, judging and then performing genetic operation, wherein the genetic operation is cross operation or mutation operation; wherein, the crossover operation adopts an improved crossover method based on the priority of workpieces, the mutation operation adopts a mutation method based on insertion, and a dynamic decoding mechanism is applied for decoding; specifically, two random numbers X1 and X2 between 0 and 1 are randomly generated. If X1 ≦ pcAnd X2 is not more than pmThen, the cross operation and the mutation operation are carried out; if X1 > pcAnd X2 is not more than pmOnly performing mutation operation; if X1 ≦ pcAnd X2 > pmOnly the cross operation is carried out; if X1 > pcAnd X2 > pmIf the operation is not performed, the cross operation and the genetic operation are not performed; if the crossover operation and the mutation operation are both carried out, the two operations have no sequence relation; applying Pareto to individuals generated after genetic operation to reserve high-quality individuals, and repeating SN times; step 3) aims at carrying out genetic operation to obtain a Pareto solution set with higher quality (obtain more Pareto solutions), wherein the solution set comprises the solution set obtained in the step 2), the Pareto solutions in the solution set obtained in the step 3) have better quality, and the main aim is to obtain the better and more Pareto solutions instead of finding the best solution in the Pareto solution set;
4) updating an external Pareto solution set: updating the external Pareto solution set, and judging whether a stopping criterion is met (the stopping criterion is the iteration number of the algorithm, for example, iter represents the current iteration number, if iter > the iteration number of the algorithm, the iteration is stopped, the operation of the algorithm is completed, and an external Pareto storage set is derived), if so, an external Pareto storage set is derived; if not, returning to the step 3). The final external Pareto solution set is a plurality of optimal solutions, namely a plurality of scheduling methods, and which one is specifically used in the final actual use can be determined by manpower.
The relevant assumed conditions established by establishing the mathematical model in step 1.1) are as follows:
firstly, each machine can only process one workpiece at each moment;
secondly, each procedure can be processed by only one machine;
thirdly, the starting time of all the processing machines can be 0;
fourthly, the starting processing time of all the workpieces can be 0;
fifthly, each workpiece can be processed in the next procedure only after the previous procedure is finished;
sixthly, once the machining is started, the machining cannot be interrupted in all the working procedures;
seventhly, the processing sequence of different procedures of the same workpiece is fixed, and the processing sequence of the procedures among different workpieces is not fixed;
the variable symbols in the mathematical model are shown in table 1:
TABLE 1 variable symbol definitions
Figure BDA0002242679960000081
The three optimization goals are respectively minimizing the maximum completion time, minimizing the total machine load and minimizing the maximum machine load;
the mathematical model and the related constraint conditions are as follows:
Figure BDA0002242679960000091
Figure BDA0002242679960000092
Figure BDA0002242679960000093
Figure BDA0002242679960000094
Figure BDA0002242679960000095
Figure BDA0002242679960000096
Figure BDA0002242679960000097
the formula (1) is an optimization target for minimizing the maximum completion time, represents the time of finishing the last of all the workpieces, and has a close and inseparable relationship with the completion time of all the workpieces and the use efficiency of processing machines, and the use efficiency of the machines can be further improved and the completion time of all the workpieces can be shortened by optimizing the maximum completion time; equation (2) is a goal of minimizing total machine load optimization, representing the total processing load of all machines, to improve economic efficiency by allocating a relatively small processing time of the machine for each process; equation (3) is a minimum maximum machine load optimization objective, representing the maximum processing load among all machines, by optimizing this objective to balance the processing load among all machines to prevent allocation of excessive processing load to a single machine; formula (4) is a calculation method of the machine Mi processing load; the formula (5) represents order constraint between the steps; equation (6) indicates that only one process can be processed by one machine at a time; the expression (7) indicates that only one machine can be selected for processing in the selectable machines for each process.
In the step 1), the flexible job shop scheduling problem solution comprises two parts, namely a process coding part (process sequencing vector) and a machine coding part (machine allocation vector);
the procedure coding part adopts a procedure-based coding mode; the method can ensure that the requirements of relevant constraints are met and the feasibility of the solution is ensured. In the machine encoding part (machine allocation vector), the machine encoding part corresponds to the process encoding part one by one, and the dimensions of the process encoding part and the machine encoding part are the same as the total number of processes to be processed. To elaborate on the expression of this solution, the scheduling problem of 8 processes, 3 workpieces, 3 machines, is exemplified herein, and the processing time of each process is shown in table 2. In Table 2, numeral 1 denotes a step O2,1At machine M2The processing time was 1. Table 3 is a possible solution to the problem, where O2,1Indicating the first machining pass of the workpiece 2 and the pass code has a higher priority. The processing sequence of all the workpieces on the machine under the code is as follows: m1:O3,1→O1,2、M2:O2,1→O3,2→O2,3、M3:O1,1→O2,2→O1,3。
TABLE 2 processing times for the individual procedures in the example problems
Figure BDA0002242679960000101
TABLE 3 expression patterns of feasible solutions
Work Process Oi,j O2,1 O3,1 O1,1 O2,2 O1,2 O1,3 O3,2 O2,3
Workpiece i 2 3 1 2 1 1 3 2
Step j 1 1 1 2 2 3 2 3
Machine k 2 1 3 3 1 3 2 2
Machining time P i,j,k 3 1 2 4 3 2 2 3
In step 2), the dynamic decoding mechanism only operates the process codes, and can obtain the machine distribution codes corresponding to the process codes while decoding the process codes; the dynamic decoding mechanism can automatically adjust corresponding parameters according to the situation of the current population, the inferior objective function value is mainly developed, the Pareto solution set obtained by calculation of the guiding algorithm is iterated towards the front edge direction of the Pareto, and the iteration times are set manually and autonomously;
the three calculation criteria of the dynamic decoding mechanism are: maximum time-out minimum criterion N1, maximum machine load minimum criterion N2, total machine load minimum criterion N3. The method comprises the following specific steps:
maximum completion time minimum criterion N1: first, for each process Oi,jSelecting all machines which can be selected for processing in the procedure; next, the machining operation O on each selectable machine is calculatedi,jCompletion time of (d); finally, the comparison completes process O on each of the alternative machinesi,jAnd selecting the machine with the shortest time for completing the process as the processing machine of the process.
Maximum machine load minimum criterion N2: in the calculation process, when a machine is selected for each process, the current load of each machine is recorded. In the pair process Oi,jWhen the machine is selected, the load capable of processing each machine in the procedure is added to the current load of each machine corresponding to the previous procedure, and the machine with the minimum total load in the current machines is selected as a processing procedure Oi,jThe machine of (1).
Total machine load minimum criterion N3: for each process Oi,jAll machines capable of processing the process are selected, and the machine which is the shortest in time to process the process is selected as the machine for processing the process among the machines.
The relevant calculation formula of the dynamic decoding mechanism is as follows:
Figure BDA0002242679960000111
Figure BDA0002242679960000112
Figure BDA0002242679960000114
Figure BDA0002242679960000115
Figure BDA0002242679960000116
ω1+ω2+ω3＝1 (14)
Figure BDA0002242679960000117
Figure BDA0002242679960000118
Figure BDA0002242679960000119
fitness＝ω1×F1+ω2×F2+ω3×F3(18)
Figure BDA0002242679960000121
in the above expression, ω1、ω2、ω3Respectively representing the probability of selecting N1, the probability of selecting N2 and the probability of selecting N3 in the decoding process; min (f)1)、min(f2)、min(f3) The minimum value of the three objective functions in the current population is not the minimum value of the three objective functions in the current population, but the minimum value of the three objective functions from iteration to the present, namely the minimum value of the three objective functions in the current external Pareto solution set; max (f)1)、max(f2)、max(f3) In the current iteration process, the maximum value of three objective functions in the population;
a. the molecular parts in the expressions b and c are used for expressing the objective function value f in the population when the algorithm is iterated1、f2、f3And historical optimum min (f)1)、min(f2)、min(f3) In-line with the aboveThe degree of deviation therebetween; when the deviation degree between one objective function value and the optimal objective function value is large, the current objective function value is proved to be far away from the objective function value in the Pareto frontier; therefore, the algorithm should enhance the search for the objective function value in the next iteration process;
after the deviation degrees a, b and c of the three objective function values are calculated, normalization processing is carried out on the three values; when the objective function with large deviation degree is iterated next time, the criterion corresponding to the objective function has higher selected probability, so that the objective function is correspondingly improved; on the contrary, when the objective function with small deviation degree is in the next iteration process, the criterion corresponding to the objective function has lower selected probability. Centralizing min (f) by constantly updating external Pareto solutions1)、min(f2)、min(f3) And max (f) in the current population1)、max(f2)、max(f3) Dynamically adapting to the state of the population in the algorithm; by continuously adopting the dynamic decoding mechanism, the algorithm is iterated towards the direction of a weaker objective function in the three objective functions, so that the optimization aim is fulfilled.
The operation steps of the crossover operation (specifically shown in fig. 3) in step 3) are as follows:
a3.1) selecting two individuals from the population by applying a tournament mechanism;
a3.2) randomly dividing all the workpieces encoded in an individual into two sets, J1 and J2 respectively;
a3.3) copying the workpiece containing J1 in the parent individual 1 to the child individual 1 and copying the workpiece containing J2 in the parent individual 2 to the child individual 2 on the basis of keeping the initial positions of the procedures of the parent individual 1 and the parent individual 2;
a3.4) copying the work piece containing J2 in the parent individual 2 to the child individual 1, and copying the work piece containing J1 in the parent individual 1 to the child individual 2.
The operation steps of the variation operation (specifically shown in fig. 4) in step 3) are as follows:
b3.1) selecting an individual from the population using a tournament mechanism;
b3.2) in the process-based coding part, firstly randomly selecting a process;
b3.3) randomly inserting the process in front of another process, the other processes moving backwards in sequence while keeping the machine code assigned to all the processes unchanged.
The first embodiment is as follows:
the invention verifies the dynamic decoding mechanism and improves the effectiveness of the algorithm by solving the workshop processing example of a certain mechanical manufacturing enterprise. The workshop has 9 workpieces to be processed, each workpiece has 8 processing procedures, 6 processing machines are provided, and the specific processing time is shown in table 4. The code for all algorithms was written on the MATLAB R2012a platform and run on a Core-i5(3.2GHz) personal computer. The parameters of the algorithm are set as follows: SN of 100, pcIs 0.8, pm0.2 and 100 iterations.
TABLE 4 example of workshop processing for a machinery manufacturing enterprise
Figure BDA0002242679960000131
Figure BDA0002242679960000141
For this example problem, the improved algorithm runs independently 10 times under the same test environment. The non-dominated solution set obtained after algorithm optimization is shown in table 5, and the Pareto solution set distribution diagram is shown in fig. 5; objective function f in Table 51The gantt charts of the first 4 solutions (data), i.e., the four scheduling schemes, in descending order, are shown in fig. 6(a) to 6 (d).
TABLE 5 non-dominated solution set obtained after algorithm optimization
Figure BDA0002242679960000142
From the calculation results, the improved algorithm adopts a dynamic decoding mechanism for decoding, and is embedded with an improved workpiece priority order crossing-based method, an insertion mutation-based method and an initialization population strategy, so that the searching capability of the algorithm is enhanced, the solving speed and the solving precision are improved, and richer non-dominant solutions and higher-quality non-dominant solutions can be obtained. In conclusion, the dynamic decoding mechanism and the improved algorithm provided by the invention can effectively solve the scheduling problem of the multi-target flexible job shop and can obtain a good optimization effect.

Claims (7)

1. A flexible job shop scheduling method based on a dynamic decoding mechanism is characterized by comprising the following steps:
1) and modeling:
1.1), establishing a mathematical model for optimizing the maximum completion time, the total machine load and the maximum machine load of a target, and determining constraint conditions of the mathematical model;
1.2) adopting Pareto to control and process a feasible solution screening problem;
1.3) carrying out discretization treatment on the MOGA, and coding by adopting a coding mode based on a working procedure;
2) initializing a population:
2.1), initializing population control parameters including population number SN and cross probability pcAnd the probability of variation pm；
2.2) adopting a random criterion, a maximum workpiece operation time residual criterion and a maximum workpiece residual procedure criterion to process codes to generate an initialized population;
2.3) decoding by applying a dynamic decoding mechanism, and storing the non-dominant solution in the population to an external Pareto solution set;
3) and genetic manipulation: selecting individuals corresponding to the population by using a championship selection mechanism, judging and then performing genetic operation, wherein the genetic operation is cross operation or mutation operation; applying Pareto to individuals generated after genetic operation to reserve high-quality individuals, and repeating SN times;
4) updating an external Pareto solution set: updating an external Pareto solution set, judging whether a stopping criterion is met, and if so, deriving an external Pareto storage set; if not, returning to the step 3).
2. The flexible job shop scheduling method based on dynamic decoding mechanism as claimed in claim 1, wherein the relevant assumed conditions established by the mathematical model established in step 1.1) are:
firstly, each machine can only process one workpiece at each moment;
secondly, each procedure can be processed by only one machine;
thirdly, the starting time of all the processing machines can be 0;
fourthly, the starting processing time of all the workpieces can be 0;
fifthly, each workpiece can be processed in the next procedure only after the previous procedure is finished;
sixthly, once the machining is started, the machining cannot be interrupted in all the working procedures;
seventhly, the processing sequence of different procedures of the same workpiece is fixed, and the processing sequence of the procedures among different workpieces is not fixed;
the variable symbols in the mathematical model are shown in table 1:
TABLE 1 variable symbol definitions
Figure FDA0002242679950000021
The three optimization goals are respectively minimizing the maximum completion time, minimizing the total machine load and minimizing the maximum machine load;
the mathematical model and the related constraint conditions are as follows:
Figure FDA0002242679950000022
Figure FDA0002242679950000023
Figure FDA0002242679950000024
Figure FDA0002242679950000025
Figure FDA0002242679950000027
Figure FDA0002242679950000028
the formula (1) is an optimization target for minimizing the maximum completion time, represents the time of finishing the last of all the workpieces, and has a close and inseparable relationship with the completion time of all the workpieces and the use efficiency of processing machines, and the use efficiency of the machines can be further improved and the completion time of all the workpieces can be shortened by optimizing the maximum completion time; equation (2) is a goal of minimizing total machine load optimization, representing the total processing load of all machines, to improve economic efficiency by allocating a relatively small processing time of the machine for each process; equation (3) is a minimum maximum machine load optimization objective, representing the maximum processing load among all machines, by optimizing this objective to balance the processing load among all machines to prevent allocation of excessive processing load to a single machine; formula (4) is a calculation method of the machine Mi processing load; the formula (5) represents order constraint between the steps; equation (6) indicates that only one process can be processed by one machine at a time; the expression (7) indicates that only one machine can be selected for processing in the selectable machines for each process.
3. The flexible job shop scheduling method based on the dynamic decoding mechanism according to claim 2, wherein in step 1), the solution of the flexible job shop scheduling problem comprises two parts, namely a process coding part and a machine coding part;
the procedure coding part adopts a procedure-based coding mode; the method can ensure that the requirements of relevant constraints are met and the feasibility of the solution is ensured. In the machine coding part, the machine coding part corresponds to the process coding part one by one, and the dimensions of the process coding part and the machine coding part are the same as the total number of processes needing to be processed.
4. The flexible job shop scheduling method based on the dynamic decoding mechanism as claimed in claim 1, wherein in step 2), the dynamic decoding mechanism only operates on the process codes, and the machine allocation codes corresponding to the process codes can be obtained while the process codes are decoded; the dynamic decoding mechanism can automatically adjust corresponding parameters according to the situation of the current population, mainly develop inferior objective function values, and iterate in the direction that a Pareto solution set obtained by calculation of a guide algorithm faces the front edge of Pareto;
the three calculation criteria of the dynamic decoding mechanism are: maximum time-out minimum criterion N1, maximum machine load minimum criterion N2, total machine load minimum criterion N3.
5. The flexible job shop scheduling method based on the dynamic decoding mechanism as claimed in claim 4, wherein the calculation formula related to the dynamic decoding mechanism is as follows:
Figure FDA0002242679950000031
Figure FDA0002242679950000033
Figure FDA0002242679950000041
Figure FDA0002242679950000042
Figure FDA0002242679950000043
ω1+ω2+ω3＝1(14)
Figure FDA0002242679950000044
Figure FDA0002242679950000046
fitness＝ω1×F1+ω2×F2+ω3×F3(18)
in the above expression, ω1、ω2、ω3Respectively representing the probability of selecting N1, the probability of selecting N2 and the probability of selecting N3 in the decoding process; min (f)1)、min(f2)、min(f3) The minimum value of the three objective functions in the current population is not the minimum value of the three objective functions in the current population, but the minimum value of the three objective functions from iteration to the present, namely the minimum value of the three objective functions in the current external Pareto solution set; max (f)1)、max(f2)、max(f3) In the current iteration process, the maximum value of three objective functions in the population;
a. the molecular parts in the expressions b and c are used for expressing the objective function value f in the population when the algorithm is iterated1、f2、f3And historical optimum min (f)1)、min(f2)、min(f3) The degree of deviation therebetween; when the deviation degree between one objective function value and the optimal objective function value is large, the current objective function value is proved to be far away from the objective function value in the Pareto frontier; therefore, the algorithm should enhance the search for the objective function value in the next iteration process;
after the deviation degrees a, b and c of the three objective function values are calculated, normalization processing is carried out on the three values; when the objective function with large deviation degree is iterated next time, the criterion corresponding to the objective function has higher selected probability, so that the objective function is correspondingly improved; on the contrary, when the objective function with small deviation degree is in the next iteration process, the criterion corresponding to the objective function has lower selected probability. Centralizing min (f) by constantly updating external Pareto solutions1)、min(f2)、min(f3) And max (f) in the current population1)、max(f2)、max(f3) Dynamically adapting to the state of the population in the algorithm; by continuously adopting the dynamic decoding mechanism, the algorithm is iterated towards the direction of a weaker objective function in the three objective functions, so that the optimization aim is fulfilled.
6. The flexible job shop scheduling method based on the dynamic decoding mechanism according to claim 1, wherein the operation steps of the interleaving operation in step 3) are as follows:
a3.1) selecting two individuals from the population by applying a tournament mechanism;
a3.2) randomly dividing all the workpieces encoded in an individual into two sets, J1 and J2 respectively;
a3.3) copying the workpiece containing J1 in the parent individual 1 to the child individual 1 and copying the workpiece containing J2 in the parent individual 2 to the child individual 2 on the basis of keeping the initial positions of the procedures of the parent individual 1 and the parent individual 2;
a3.4) copying the work piece containing J2 in the parent individual 2 to the child individual 1, and copying the work piece containing J1 in the parent individual 1 to the child individual 2.
7. The flexible job shop scheduling method based on the dynamic decoding mechanism according to claim 1, wherein the operation steps of the variant operation in step 3) are as follows:
b3.1) selecting an individual from the population using a tournament mechanism;
b3.2) in the process-based coding part, firstly randomly selecting a process;
b3.3) randomly inserting the process in front of another process, the other processes moving backwards in sequence while keeping the machine code assigned to all the processes unchanged.
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