Flexible job shop energy-saving scheduling method based on multi-objective evolutionary algorithm

Abstract

The invention relates to the technical field of flexible job shop scheduling control, in particular to a flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm, which comprises the following steps of: constructing a flexible job shop energy-saving scheduling problem model, and defining a job set, a machine set, a process set, a manufacturing span, processing time and energy consumption parameters, and a problem constraint condition is set. According to the method, the problem model is constructed, the multi-objective evolutionary algorithm based on decomposition is correspondingly improved, the corresponding relation between the operation and the machine is defined by using double-layer coding, meanwhile, the crossover operator based on the position is adopted, local optimum is better avoided, weight vectors with repeated sub-problems are adaptively updated, and the problem is solved. And a weight vector neighborhood is updated, and finally a group of Pareto front optimal solutions are generated from an evolution result, so that the energy-saving scheduling problem of the flexible job shop is solved, and the energy consumption is reduced while the minimum manufacturing span is optimized.

Description

Technical Field

[0001] The invention relates to the technical field of flexible job shop scheduling control, and in particular to a flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm. Background Art

[0002] With the rapid development of global economic integration, the competition in the manufacturing industry of various countries is becoming increasingly fierce. At present, manufacturing enterprises tend to be more flexible in production, especially in the Chinese market. Product diversification and rapid changes in market demand have shortened product life cycles, making the profits of traditional large-scale production models gradually decrease. Therefore, flexible manufacturing methods are gradually replacing the past stereotyped models to adapt to market changes and diversified needs. The emerging flexible job shop scheduling method came into being, which is called the production scheduling method of the flexible job shop. It can quickly meet consumer needs and realize a multi-variety small batch production mode. Different from the scheduling scheme of the traditional job shop, the flexible job shop allows the selection of products from multiple machines that meet the requirements. At the same time, the reasonable scheduling of the flexible job shop can also reduce energy consumption, reduce environmental pollution, improve production efficiency, and further increase the competitiveness of the enterprise.

[0003] For example, a flexible workshop robust scheduling method based on a decomposed multi-objective evolutionary algorithm provided by announcement number CN105929690A includes: (1) reading input information such as the job and machine attributes of the flexible job workshop; defining the optimization goal and setting constraints; (2) initializing the parameters of the algorithm; (3) determining the neighborhood of each subproblem, generating an initial parent population, and determining all Pareto non-dominated solutions from the initial population to form an external memory; (4) generating a child population. Perform mating selection, use an adaptive mutation operator and a repair-based crossover operator to reproduce the offspring individuals, and update the external memory; (5) use the generated child population to update the current optimal individual of each subproblem to form a new parent population; (6) if the number of individual target evaluations reaches the maximum, output the external memory, that is, a set of Pareto non-dominated flexible job workshop scheduling solutions; if not reached, jump to (4). The present invention quickly and efficiently implements scheduling tasks in flexible job workshops;

[0004] The announcement number CN110543151B provides a method for solving the energy-saving scheduling problem of a flexible job shop based on an improved NSGA-Ⅱ algorithm. From the four aspects of completion time, total delay time, total equipment load and total system energy consumption, a better scheduling solution is provided to production enterprises. First, a model of the energy-saving scheduling problem of a flexible job shop is constructed; then, an initial population is generated in a random manner, and a second-generation parent population is generated through fast non-dominated sorting, congestion distance calculation and elite selection, and crossover and mutation operations are performed on it to generate a crossover child population; and a local search is performed on the sparse solution to generate a local search child population; the parent population, the crossover child population and the local search child population are merged to obtain a new population; the same operation is performed on the new population to continue updating; finally, a solution is selected from the optimal solution set as the optimal compromise solution by using a weighted method, and output;

[0005] The single-objective flexible job shop energy-saving scheduling method based on the improved gray wolf algorithm provided by announcement number CN114862009A improves the gray wolf algorithm and adopts two-stage encoding to realize the conversion between continuous individual positions and discrete scheduling solutions; designs a population initialization method to ensure the quality and diversity of the population; uses a dual-mode parallel search method to balance the algorithm's global search and local search capabilities during the search process; introduces improved tracking and search operations to improve the accuracy of problem solving, in which the search adopts combined mutation to increase the speed of evolution and break through the local optimal solution. In addition, the better individual of the two sub-individuals obtained by the tracking operation is selected as the new individual according to the fitness value relationship.

[0006] However, when the above technology is actually used:

[0007] CN105929690A adopts a multi-objective evolutionary algorithm based on decomposition, but does not consider the energy saving problem of workshop scheduling, nor does it optimize the algorithm;

[0008] CN110543151B uses an improved NSGA-II algorithm, but the inventive algorithm has poor results in minimizing the manufacturing span, and can calculate smaller instance dimensions;

[0009] CN114862009A adopts a novel grey wolf algorithm, but it is a single-objective optimization. It cannot optimize the minimum manufacturing span while optimizing energy consumption, which is inconsistent with the actual production situation. Summary of the invention

[0010] The purpose of the present invention is to provide a flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm to solve the problem of not considering the energy-saving problem of shop scheduling and not optimizing the minimization of manufacturing span.

[0011] To achieve the above object, the present invention provides the following technical solution: a flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm, comprising the following steps:

[0012] S1. Taking the maximum manufacturing span and total energy consumption as optimization objectives, a flexible job shop energy-saving scheduling problem model is constructed, and the job set, machine set, process set, manufacturing span, processing time and energy consumption parameters are defined, and problem constraints are set. The flexible job shop energy-saving scheduling problem model is:

[0013]

[0014] S2, using a two-layer coding method to represent the mapping relationship between the operation process and the machine selection, the first layer of coding is the machine selection part, and the second layer of coding is the process-based sorting part;

[0015] S3, initialize the population to ensure the diversity and superiority of the initial population;

[0016] S4, construct the neighborhood structure, and perform population evolution through adaptive crossover and mutation operators, adjusting the crossover and mutation probabilities according to the degree of population evolution;

[0017] S5. Use Chebyshev method to decompose sub-problems, decompose the multi-objective optimization problem into a single-objective optimization problem, and find the optimal solution by optimizing the maximum distance;

[0018] S6, traverse the population to obtain non-dominated solutions, and update the weight vector and neighborhood structure, adjust the weight vector according to the non-dominated sorting result, and optimize the weight distribution;

[0019] S7, determine whether the iteration termination condition is met, if not, return to step S4 to continue iteration, if met, output the optimal Pareto front solution.

[0020] Preferably, the flexible job shop energy-saving scheduling problem model in step S1 is defined as follows:

[0021] There exists a job J = {J1, J2, ..., J n}, where each J p There is a set of independent processes O = {O p1 ,O p2 ,…,O pj},O i,j represents the jth process of the ith job, in the machine set M = {M1, M2, ..., M k}Select machine processing, in machine M k Upper processing O i,j Used time T i,j,k The resulting energy consumption can be calculated as follows: EO i,j,k *T i,j,k .

[0022] Preferably, the constraint condition in step S1 is:

[0023] The initial available time of each machine starts from 0;

[0024] Each machine processes only one process at a time;

[0025] Each machine's on / off is subject to a safety time limit, that is, the machine's processing speed remains unchanged during the interval between shutting down and starting up, and the processing energy consumption is set to default;

[0026] The energy consumption of each function of the machine is taken into account;

[0027] Each machine can only process one process at a time;

[0028] Each job can only be processed by one machine at a time;

[0029] All processes are not allowed to be interrupted once they start processing;

[0030] The sequence of different processes in the same operation is fixed.

[0031] Preferably, in the population initialization step S3, the possibility of falling into the local optimum is reduced by the random selection principle, the process is processed on the machine with the smallest current machine load by the local minimum load principle and the global minimum load principle, the diverse population generated by random selection is retained by the non-dominated resettable principle, and the population quality is improved by the non-dominated priority principle.

[0032] Preferably, the adaptive crossover and mutation operations in step S4 adopt a position-based crossover operator (PBX), and the crossover and mutation probabilities are adjusted according to the degree of population evolution to accelerate the convergence of the population.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The present invention constructs a problem model and makes corresponding improvements based on a decomposed multi-objective evolutionary algorithm, including using two-layer coding to define the correspondence between jobs and machines, and adopting a position-based crossover operator to better avoid falling into local optimality, adaptively updating the weight vectors that generate repeated sub-problems, updating the neighborhood of the weight vectors, exploring the discontinuous areas of sub-problems and the sparse areas of sub-problems to achieve reasonable allocation of computing resources, and finally generating a set of Pareto frontier optimal solutions from the evolutionary results to solve the energy-saving scheduling problem of flexible job shops and reduce energy consumption while optimizing the minimized manufacturing span. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1The overall structure flow chart of the flexible job shop energy-saving scheduling method based on the multi-objective evolutionary algorithm of the present invention;

[0036] Figure 2 It is a double-layer coding schematic diagram of the flexible job shop energy-saving scheduling method based on the multi-objective evolutionary algorithm of the present invention;

[0037] Figure 3 A population initialization flow chart for the flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm of the present invention;

[0038] Figure 4 It is a schematic diagram of a position-based crossover operator in the adaptive crossover and mutation of the flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm of the present invention;

[0039] Figure 5 Schematic diagram of the Pareto optimal frontier of some examples of MOEA\D1, MOEA\D2, MOEA\D3, and MOEA\D-DDWA in the comparative example. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] See also Figure 1-5 The present invention provides a technical solution: a flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm, comprising the following steps:

[0042] S1. Taking the maximum manufacturing span and total energy consumption as optimization objectives, a flexible job shop energy-saving scheduling problem model is constructed, and the job set, machine set, process set, manufacturing span, processing time and energy consumption parameters are defined, and problem constraints are set. The flexible job shop energy-saving scheduling problem model is:

[0043]

[0044] The flexible job shop energy-saving scheduling problem model is defined as follows:

[0045] There exists a job J = {J1, J2, ..., J n}, where each J p There is a set of independent processes O = {O p1 ,O p2 ,…,O pj},O i,jrepresents the jth process of the ith job, in the machine set M = {M1, M2, ..., M k}Select machine processing, in machine M k Upper processing O i,j Used time T i,j,k The resulting energy consumption can be calculated as follows: EO i,j,k *T i,j,k ;

[0046] And the constraints are:

[0047] The initial available time of each machine starts from 0;

[0048] Each machine processes only one process at a time;

[0049] Each machine's on / off is subject to a safety time limit, that is, the machine's processing speed remains unchanged during the interval between shutting down and starting up, and the processing energy consumption is set to default;

[0050] The energy consumption of each function of the machine is taken into account;

[0051] Each machine can only process one process at a time;

[0052] Each job can only be processed by one machine at a time;

[0053] All processes are not allowed to be interrupted once they start processing;

[0054] The sequence of different processes in the same operation is fixed.

[0055] in:

[0056] J n : Code for job n;

[0057] M k : Code of machine k;

[0058] O i,j : The jth process of the i-th job;

[0059] MS i,j :Process O i,j Manufacturing span;

[0060] T i,j,k :Process O i,j Processing time on machine k;

[0061] TI k,u : The uth idle time of machine k;

[0062] TM k,p : The pth processing time of machine k;

[0063] MSPk : Unit starting power on machine k;

[0064] MWP k : Unit preheating power on machine k;

[0065] MSBP k : Unit standby power on machine k;

[0066] MSTP k : The unit setting power on machine k;

[0067] EO i,j,k :Process O i,j The default unit energy consumption on machine k;

[0068] X i,j,k : It is defined as a binary set as follows

[0069]

[0070] C k =C maxk

[0071] X i,j,k Identify the job operations processed on the machine.

[0072] S2, a two-layer coding method is used to represent the mapping relationship between the operation process and the machine selection. The first layer of coding is the machine selection part (MS), and the ranking of each gene is arranged according to the operation process; the second layer is based on the process sorting part (OS), and the number that appears represents the operation code, and the number of times the number appears represents the number of the operation process, such as Figure 2 As shown. Set the initial population number Pop, the current number of iterations P d , the maximum number of iterations P max , crossover, mutation current probability value P cmd , crossover, mutation initial probability value P cmm , the iteration range AWV of weight vector adjustment;

[0073] S3. Initialize the population to ensure the diversity and superiority of the initial population. In the initialization step:

[0074] The random selection principle is beneficial to the distribution range of the initial population and reduces the possibility of falling into the local optimum. n Randomly select, the corresponding O i,j Randomly select a processable machine M k ;

[0075] The principle of local minimum load is conducive to the generation of high-quality solutions for the initial population. n Processing selection, Oi,j Select the machine M that can be processed k It should be the one with the smallest current machine load;

[0076] In the selection of all jobs by the principle of global minimum load, O i,j Select the machine M that can be processed k It should be the one with the smallest current machine load;

[0077] The diversity of the population generated by random selection is retained through the non-dominated resettable principle, and the non-dominated priority principle is used under the load principle to improve the quality of the population. Figure 3 As shown, Pop1, Pop2, and Pop3 are merged to form a new population N', and the non-dominated solution Pop is obtained in N using the fast non-dominated sorting method. n Being dominated by Pop x . Because the initial population Pop x Much more than Pop n , so only some Pop x , Pop removed x The number is supplemented by the random selection principle to achieve partial reset of the initial population, which can be reset repeatedly according to the reset times z. This principle increases the possibility of generating high-quality solutions while expanding the distribution of the initial population;

[0078] S4. Construct a neighborhood structure, and perform population evolution through adaptive crossover and mutation operators, adjusting the crossover and mutation probabilities according to the degree of population evolution. The specific steps of constructing the neighborhood structure are:

[0079] Generate a uniformly distributed weight vector λ = {λ1,λ2,…,λ i}, after WS-transformation in formula (2), the solution mapping vector λ' replaces the weight vector λ of the scalar subproblem. The Euclidean distance between the solution mapping vectors λ' is calculated to construct the neighborhood {λ′ T1 ,λ′ T2 ,…,λ′ Ti}, the Euclidean calculation is as shown in formula (3).

[0080]

[0081] The specific steps of adaptive crossover and mutation are:

[0082] Adaptive mutation and crossover operators produce corresponding probability changes as the population evolves. In the later stages of population evolution, the crossover and mutation probabilities gradually decrease, thereby accelerating the convergence of the population. The crossover rate should satisfy the following equation (4), and the mutation rate is similar.

[0083]

[0084] Among them, P cmax represents the upper limit of the crossover rate, P cmin Represents the lower limit of the crossover rate, L Gen Represents the chromosome length.

[0085] like Figure 4 As shown, a location-based crossover operator (PBX) is adopted;

[0086] S5. Use Chebyshev method to decompose sub-problems. Based on the idea of ​​decomposition, decompose the multi-objective optimization problem of each weight vector into a single-objective optimization problem. Use the Chebyshev method in formula (5) to find the maximum distance of each dimension and optimize the maximum distance during the optimization process. That is, decompose MS and TEC into Max MS or Max TEC .

[0087]

[0088] S6. Traverse the population to obtain non-dominated solutions and convert the parent population P i and the offspring population C i Merge into R i , the population size is N m ={N,N+1,…,2N}. i Perform fast non-dominated sorting to obtain non-dominated solution N p , if N p >N, then according to the sorting level, the higher-ranked ones are placed in the new parent population P first. i , until N is satisfied Pi = N. At the same time, save the optimal point z*;

[0089] Through the above non-dominated sorting results, the mapping weight vector is analyzed. Two update methods are used to update the weight vector. The population generated within a certain iteration range is calculated according to the crowding estimation method to calculate the solution proximity distance as follows:

[0090]

[0091] in, is the Euclidean distance from the solution of the jth subproblem to the solution of the ith subproblem. Equation (7) defines the discontinuous or sparse subproblem. If PFS = 0 exists, it proves that j is an overcrowded subproblem. Delete the crowded subproblem. Adjust the corresponding weight according to the deleted subproblem. The update method adopts a combination of quantitative adjustment of the weight vector and dynamic adjustment of the weight vector. The quantitative adjustment is to adjust the vector at the boundary of the weight vector, and the dynamic adjustment is to adjust the weight vector at the boundary of the weight vector. Region adjustment weight vector.

[0092]

[0093] The specific operations for updating the weight vector and neighborhood structure are:

[0094] S61: Determine the current number of iterations Gen i , when the number of iterations meets Gen i >AWV min Pop∩Gen i <AWV max Pop, then start adjusting the weight vector, otherwise jump to step S4;

[0095] S62: Calculate the Euclidean distance. When PFS=0, according to A j Sort in ascending order, delete Num all Sub-problems of quantity;

[0096] S63: According to A j Sort in descending order and add Num number of sub-problems in the sparse area;

[0097] S64: For Num constant A j =0 sub-problem, if Num constant ≤Num all , add Num constant At the boundary of the weight vector λ s ≈λ b And continue the operation, where λ b The weight vector corresponding to the boundary value of the subproblem. Otherwise, only Num is added all The weight vector of each boundary and jump to step 4;

[0098] S65: For A j ≠0, add a weight vector that can produce good individuals, the number is The weight vector is defined as follows:

[0099]

[0100] S66: At the same time, a new weight vector Num is added to generate good individuals. df =Num all -Num de , along λ j To s Diffusion adds new distribution;

[0101] S67: For λ 1 ,λ 2 ,...,λ m , reconstruct the neighborhood list

[0102] S7: Determine whether the iteration termination condition is met. If not, Then stop adjusting the weight vector. If the maximum number of iterations Max is met p , then the iteration cycle ends and the optimal Pareto front solution is obtained, otherwise Gen i =Gen i +1, continue calculating non-dominated solutions.

[0103] Comparative Example

[0104] All four MOEA\D strategies use double-layer vector encoding. Among them, MOEA / D1 only uses random initialization, MOEA / D2 uses NDRI and the classic sequence-based crossover (POX). MOEA / D3 uses RI and PBX. The international benchmark dataset designed by Brandimarte and dauzere is used. MOEA / D-DDWA is the method described in the present invention. The population number, iteration number, fixed crossover and mutation probability of all algorithms are [100, 100, 0.8, 0.7]. The energy consumption is randomly set each time, and the four algorithms use the same random energy consumption. Each example is run 20 times.

[0105] Comparison of Maximum Manufacturing Span (MSmax) and Minimum TEC (TECmin)

[0106] In Table 1, we can see that MOEA / D-DDWA shows a certain superiority and obtains the optimal solution in most data sets. It is worth mentioning that MOEA / D2 uses RI and MOEA / D3 uses RI and PBX, so there is a certain probability of obtaining the optimal solution, which also shows that the improvement is effective. However, the algorithm has been significantly improved after using DDWA. The completion time, as an unchangeable variable, is better than the results of other inventions.

[0107] Comparing Hypervolume (HV) metrics

[0108] HV index: the volume of the area in the target space enclosed by the non-dominated solution set obtained by the algorithm and the reference point. The larger the HV value, the better the overall performance of the algorithm. HV can evaluate convergence and diversity at the same time without knowing the advantages of the true PF or reference set. HV is expressed as:

[0109]

[0110] Among them, δ represents the Lebesgue measure, L represents the length of the data set, which is used to measure the volume. |S| represents the number of non-dominated solution sets, v i represents the hypervolume formed by the reference point and the i-th solution in the solution set.

[0111] Since the reference point is self-selected, the present invention normalizes the fitness of EP and selects the commonly used (1.2, 1.2) as the reference point. The comparison results are recorded in Table 2. AVG and SD represent the average and standard deviation, respectively. The average (AVG) indicates the quality of the HV index, and the standard deviation (SD) indicates the dispersion of the HV index. In Mk03, compared with other solutions, MOEA / D-DDWA always produces an optimal solution. Therefore, in normalization, it is always used as [0,0] and the reference point to calculate the hypervolume, so AVG is always equal to 0.144 and SD=0. It can be seen that compared with other algorithms, MOEA / D-DDWA not only has the best MS max and TEC min , and also has more non-dominated solutions.

[0112] Obtaining the Pareto optimal frontier can more intuitively show the superiority of the solution, such as Figure 5 The Pareto optimal frontier of some examples is shown. It can be seen that MOEA\D-DDWA produces the minimum manufacturing span and the minimum energy consumption, and the number of solutions is relatively rich, providing more choices.

[0113] Table 1: Comparison of maximum completion time and energy consumption

[0114]

[0115]

[0116]

[0117] Table 2: HV index comparison

[0118]

[0119]

[0120]

[0121]

[0122] The present invention constructs a problem model, including the required parameters, decision variables and fitness functions, and makes corresponding improvements based on the decomposed multi-objective evolutionary algorithm (MOEA\D), including using a double-layer coding to define the corresponding relationship between jobs and machines;

[0123] In order to ensure the diversity and superiority of the initial population, four initialization methods are used to ensure the diversity and superiority of the initial population. The population is evolved through adaptive crossover and mutation, and the crossover and mutation probability is reduced in the later stage of population evolution, thereby accelerating the convergence of the population. At the same time, the position-based crossover operator is used to better avoid falling into the local optimum.

[0124] The weight vectors of repeated sub-problems are adaptively updated, the neighborhood of the weight vector is updated, the discontinuous areas and sparse areas of the sub-problems are explored to achieve reasonable allocation of computing resources, and finally a set of Pareto frontier optimal solutions are generated from the evolutionary results, thereby solving the energy-saving scheduling problem of flexible job shops and reducing energy consumption while optimizing the minimized manufacturing span.

[0125] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0126] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the invention, and the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm, characterized by: The following steps are involved: S1. Taking the maximum manufacturing span and total energy consumption as optimization objectives, a flexible job shop energy-saving scheduling problem model is constructed, and the job set, machine set, process set, manufacturing span, processing time and energy consumption parameters are defined, and problem constraints are set. The flexible job shop energy-saving scheduling problem model is: S2, using a two-layer coding method to represent the mapping relationship between the operation process and the machine selection, the first layer of coding is the machine selection part, and the second layer of coding is the process-based sorting part; S3, initialize the population to ensure the diversity and superiority of the initial population; S4, construct the neighborhood structure, and perform population evolution through adaptive crossover and mutation operators, adjusting the crossover and mutation probabilities according to the degree of population evolution; S5. Use Chebyshev method to decompose sub-problems, decompose the multi-objective optimization problem into a single-objective optimization problem, and find the optimal solution by optimizing the maximum distance; S6, traverse the population to obtain non-dominated solutions, and update the weight vector and neighborhood structure, adjust the weight vector according to the non-dominated sorting result, and optimize the weight distribution; S7, determine whether the iteration termination condition is met, if not, return to step S4 to continue iteration, if met, output the optimal Pareto front solution.

2. The flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm according to claim 1 is characterized in that: The flexible job shop energy-saving scheduling problem model in step S1 is defined as follows: There exists a job J = {J1, J2, ..., J n }, where each J p There is a set of independent processes O = {O p1 ,O p2 ,…,O pj },O i,j represents the jth process of the ith job, in the machine set M = {M1, M2, ..., M k }Select machine processing, in machine M k Upper processing O i,j Used time T i,j,k The resulting energy consumption can be calculated as follows: EO i,j,k *T i,j,k .

3. The flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm according to claim 1 is characterized in that: The constraint conditions in step S1 are: The initial available time of each machine starts from 0; Each machine processes only one process at a time; Each machine's on / off is subject to a safety time limit, that is, the machine's processing speed remains unchanged during the interval between shutting down and starting up, and the processing energy consumption is set to default; The energy consumption of each function of the machine is taken into account; Each machine can only process one process at a time; Each job can only be processed by one machine at a time; All processes are not allowed to be interrupted once they start processing; The sequence of different processes in the same operation is fixed.

4. The flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm according to claim 1 is characterized in that: In the population initialization step of step S3, the possibility of falling into the local optimum is reduced by the random selection principle, the process is processed on the machine with the smallest current machine load by the local minimum load principle and the global minimum load principle, the diverse population generated by random selection is retained by the non-dominated resettable principle, and the population quality is improved by the non-dominated priority principle.

5. The flexible job shop energy-saving scheduling method based on a multi-objective evolutionary algorithm according to claim 1 is characterized in that: The adaptive crossover and mutation operations in step S4 adopt a position-based crossover operator (PBX), and adjust the crossover and mutation probabilities according to the evolution degree of the population to accelerate the convergence of the population.

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