Hybrid flow shop scheduling robust optimization method and device based on hybrid genetic algorithm

Abstract

The invention relates to a hybrid flow shop scheduling robust optimization method and device based on a hybrid genetic algorithm, which can realize the improvement of the robustness of a hybrid flow shop scheduling scheme, emphasizes the mean value performance while paying attention to the worst situation, and has relatively strong capabilities of global search and jumping out of a locally optimal solution. The method comprises the following steps: determining a hybrid flow shop scheduling problem mathematical model based on robust optimization; constructing a first optimization algorithm based on a genetic algorithm according to the constraint of the hybrid flow shop scheduling problem; constructing a second optimization algorithm based on a simulated annealing algorithm framework; constructing a scheduling scheme evaluation method based on the stochastic simulation algorithm and considering the worst situation and the average performance; and fusing the first optimization algorithm and the second optimization algorithm to obtain a target optimization algorithm, and performing scheduling scheme optimization based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme.

Description

Technical Field

[0001] The present disclosure relates to the field of industrial technologies, and particularly to a robust optimization method and device for hybrid flow shop scheduling based on a hybrid genetic algorithm. Background Art

[0002] The Hybrid Flow Shop Scheduling Problem refers to a flow shop with multiple stages, where at least one stage consists of multiple machines in a parallel machine mode, and each machine can only process one job at a time, and each job must complete all stages in sequence. At the same time, the processing time of each job may be different when completing each stage. The Hybrid Flow Shop Scheduling Problem is very common in many practical applications. For example, in industries such as end-of-factory distribution, automobile manufacturing, semiconductor production, electronic assembly, and food processing, there are such special hybrid flow shop scheduling layouts.

[0003] In related technologies, the optimization method for the Hybrid Flow Shop Scheduling Problem is to use mathematical methods such as problem properties and integer programming to transform the problem into a mixed integer programming problem for solution. However, the mixed integer programming problem has the characteristics of a small solution scale and a long solution time. Therefore, a robust optimization method for flow shop scheduling that can quickly solve the problem is needed. Summary of the Invention

[0004] To overcome the problems in related technologies, embodiments of the present disclosure provide a robust optimization method and device for hybrid flow shop scheduling based on a hybrid genetic algorithm to solve the defects in related technologies.

[0005] According to the first aspect of the embodiments of the present disclosure, a robust optimization method for hybrid flow shop scheduling based on a hybrid genetic algorithm is provided, including:

[0006] Determine a mathematical model for the hybrid flow shop scheduling problem based on robust optimization;

[0007] Construct a first optimization algorithm based on a genetic algorithm according to the constraints of the hybrid flow shop scheduling problem;

[0008] Construct a second optimization algorithm based on the framework of the simulated annealing algorithm;

[0009] Construct a scheduling scheme evaluation method considering the worst case and average performance based on a stochastic simulation algorithm, where the worst case is used to represent the maximum makespan in each candidate scheduling scheme, the average performance is used to represent the average makespan of each candidate scheduling scheme, and the candidate scheduling scheme is obtained based on the initial solution of the mathematical model of the hybrid flow shop scheduling problem;

[0010] Fuse the first optimization algorithm and the second optimization algorithm to obtain a target optimization algorithm, and optimize the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme, where the scheduling scheme evaluation method is used to calculate the target value of the scheduling scheme, and the reciprocal of the target value is used as the fitness value of the scheduling scheme in the optimization process.

[0011] In one embodiment, the optimizing the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme includes:

[0012] Generate an initial population through a first thread based on the genetic operation in the target optimization algorithm, and record the first optimal solution, where each individual in the initial population and the first optimal solution represent the scheduling scheme of the hybrid flow shop;

[0013] Through a second thread, when the preset simulated annealing trigger condition is met, obtain the initial population from the first thread, and obtain a new population by randomly exchanging gene segments of individuals in the initial population, and record the second optimal solution, where when the simulated annealing trigger condition is not met, the first thread and the second thread execute in parallel;

[0014] Calculate the target values corresponding to the first optimal solution and the second optimal solution respectively based on the scheduling scheme evaluation method, and when the target value corresponding to the second optimal solution is less than the target value corresponding to the second optimal solution, determine the scheduling scheme corresponding to the second optimal solution as the optimal scheduling scheme.

[0015] In one embodiment, the method further includes:

[0016] If the optimal solution has not been improved for a continuous preset number of generations in the genetic operation in the target optimization algorithm, increase the computing resource allocation of the second thread to expand the neighborhood search range of the simulated annealing operation in the target optimization algorithm;

[0017] If the optimization process of the simulated annealing operation in the target optimization algorithm falls into a local optimum, trigger the first thread to execute the diversity mutation operation in the genetic operation, and the diversity mutation operation is used to obtain a new population through different mutation methods.

[0018] In one embodiment, the constructing the first optimization algorithm based on the genetic algorithm includes:

[0019] Adopt a double-layer coding method for scheduling coding. The first layer coding of the double-layer coding is used for the process coding representing the process sequence, and the second layer coding of the double-layer coding is used for the machine coding representing the machine allocation.

[0020] Different mutation operators are adopted for the first - layer coding and the second - layer coding. Among them, the first - layer coding adopts the single - point mutation method to randomly generate a feasible solution at the mutation site, and the second - layer coding adopts the reverse - order mutation method to reverse the coding segment between the mutation points.

[0021] In one embodiment, the construction of the first optimization algorithm based on the genetic algorithm includes:

[0022] A hybrid stopping rule is adopted. The hybrid stopping rule includes an evolution stagnation rule and a maximum iteration number rule. Among them, the evolution stagnation rule is used to regenerate a part of the population individuals to replace the inferior individuals of the current population when the fitness value of the optimal individual stagnates for a certain number of iterations. When the number of times of regenerating the population reaches a certain number and the fitness value of the optimal individual stagnates for a certain number of iterations again, the algorithm iteration is stopped. The maximum iteration number rule is used to stop the algorithm iteration when the iteration number reaches the maximum iteration number. The population individuals are hybrid flow - shop scheduling schemes.

[0023] In one embodiment, the initial solution of the mathematical model of the hybrid flow - shop scheduling problem is generated by a method of mixing multiple initial solutions. Among them, the method of mixing multiple initial solutions includes a random - type initial solution generation and a greedy - type initial solution generation method. The greedy - type initial solution generation method is used to generate the initial solution in the following way:

[0024] When arranging the processing in the first stage, in the order of the processing time in the first stage from short to long, the first workpiece with the shortest processing time in the first stage is preferentially selected, and the first workpiece is arranged on the machine with the smallest completion time in its first stage. Then the second workpiece with the second - shortest processing time in the first stage is selected, and the second workpiece is arranged on the machine with the smallest completion time in its first stage until all the processing workpieces are arranged in the first stage;

[0025] When arranging the processing in the second stage, in the order of the production completion time in the first stage from short to long, first, the workpiece that first completes the production in the first stage is arranged on the machine with the smallest completion time in its second stage, and then the workpiece that second - first completes the production in the first stage is arranged on the machine with the smallest completion time in its second stage until all the workpieces are arranged in all stages.

[0026] In one embodiment, the scheduling - scheme evaluation method is used to obtain the target value in the following way:

[0027] Generate N samples, substitute the N samples into the scheduling scheme to obtain N makespan values. Among them, the N sample features conform to the uncertainty set based on the predicted mean information and the upper and lower bounds of the processing time, and N is a positive integer;

[0028] Calculate the objective value of the scheduling scheme according to the following expression: ;

[0029] where are the weights of the average performance and the worst case respectively, is the completion time of the k-th sample, is the completion time of the k-th sample under the scheduling scheme x, is the maximum completion time of the k-th sample under the scheduling scheme x, and N is the number of samples.

[0030] In one embodiment, the method further includes:

[0031] Determine the fluctuation conditions of the average performance and the worst case according to the distribution robustness of the current solution set during the optimization process;

[0032] In the case where the fluctuation condition of the average performance represents that the fluctuation range is greater than the first preset range, increase the weight of the average performance and decrease the weight of the worst case, where the sum of the adjusted weights of the average performance and the worst case is 1;

[0033] In the case where the fluctuation condition of the average performance represents that the fluctuation range is greater than the second preset range, increase the weight of the worst case and decrease the weight of the average performance, where the sum of the adjusted weights of the average performance and the worst case is 1.

[0034] According to the second aspect of the embodiments of the present disclosure, there is provided a hybrid flow shop scheduling robust optimization device based on a hybrid genetic algorithm, including:

[0035] A determination module, configured to determine a mathematical model of a hybrid flow shop scheduling problem based on robust optimization;

[0036] A first construction module, configured to construct a first optimization algorithm based on a genetic algorithm according to the constraints of the hybrid flow shop scheduling problem;

[0037] A second construction module, configured to construct a second optimization algorithm based on a simulated annealing algorithm framework;

[0038] A third construction module, configured to construct a scheduling scheme evaluation method considering the worst case and the average performance based on a stochastic simulation algorithm, where the worst case is used to represent the maximum maximum completion time among all candidate scheduling schemes, and the average performance is used to represent the average maximum completion time of all the candidate scheduling schemes, and the candidate scheduling schemes are obtained based on the initial solution of the mathematical model of the hybrid flow shop scheduling problem;

[0039] An optimization module is used to fuse the first optimization algorithm and the second optimization algorithm to obtain a target optimization algorithm, and optimize the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme. The scheduling scheme evaluation method is used to calculate the target value of the scheduling scheme, and the reciprocal of the target value is used as the fitness value of the scheduling scheme during the optimization process.

[0040] According to a third aspect of the embodiments of the present disclosure, there is provided an electronic device including a memory and a processor. The memory is used to store computer instructions that can run on the processor, and the processor is used to implement the method according to any one of the first aspects when executing the computer instructions.

[0041] According to a fourth aspect of the embodiments of the present disclosure, there is provided a computer-readable storage medium having a computer program stored thereon, and the program implements the method according to any one of the first aspects when executed by a processor.

[0042] According to a fifth aspect of the embodiments of the present disclosure, there is provided a computer program product including a computer program, and the computer program implements the method according to any one of the first aspects when executed by a processor.

[0043] The technical solutions provided by the embodiments of the present disclosure may include the following beneficial effects:

[0044] The robust optimization method provided by the present disclosure can improve the robustness of the hybrid flow shop scheduling scheme, emphasize the mean performance while paying attention to the worst case, and based on this, design a hybrid genetic algorithm with the characteristics of the fusion algorithm, so that the algorithm can converge quickly, has strong global search and the ability to jump out of local optimal solutions, the algorithm is simple to implement, has a fast solving speed for large-scale problems, and has strong space for personalized transformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0046] Figure 1 is a flowchart of a robust optimization method for hybrid flow shop scheduling based on a hybrid genetic algorithm shown according to an embodiment of the present disclosure;

[0047] Figure 2 is a schematic diagram of a scheduling model shown according to an embodiment of the present disclosure;

[0048] Figure 3 is a schematic diagram of a scheduling encoding shown according to an embodiment of the present disclosure;

[0049] Figure 4It is a schematic diagram of the process of multi-point crossover shown according to an embodiment of the present disclosure;

[0050] Figure 5 It is a schematic diagram of the process of fragment crossover shown according to an embodiment of the present disclosure;

[0051] Figure 6 It is a schematic diagram of the process of single-point mutation shown according to an embodiment of the present disclosure;

[0052] Figure 7 It is a schematic diagram of the process of reverse mutation shown according to an embodiment of the present disclosure;

[0053] Figure 8 It is a schematic diagram of the process of a hybrid genetic algorithm shown according to an embodiment of the present disclosure;

[0054] Figure 9 It is a schematic diagram of a scheduling scheme shown according to an embodiment of the present disclosure;

[0055] Figure 10 It is a schematic diagram of a hybrid flow shop scheduling robust optimization device based on a hybrid genetic algorithm shown in an exemplary embodiment of the present disclosure;

[0056] Figure 11 It is a structural block diagram of an electronic device shown in an exemplary embodiment of the present disclosure. Detailed implementation manners

[0057] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all implementation manners consistent with the present disclosure. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present disclosure as detailed in the appended claims.

[0058] The terms used in the present disclosure are only for the purpose of describing specific embodiments and are not intended to limit the present disclosure. The singular forms "a", "the", and "said" used in the present disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0059] It should be understood that although the terms first, second, third, etc. may be used in the present disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present disclosure, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information.

[0060] The Hybrid Flow Shop Scheduling Problem refers to a flow shop with multiple stages, where at least one stage consists of multiple machines in a parallel machine mode, and each machine can only process one job at a time, and each job must complete all stages in sequence. At the same time, the processing time of each job may be different when it completes each stage. The Hybrid Flow Shop Scheduling Problem is very common in many practical applications. For example, in industries such as factory end distribution, automobile manufacturing, semiconductor production, electronic assembly, and food processing, there are such special Hybrid Flow Shop Scheduling layouts.

[0061] In actual production, there is a certain degree of randomness in the processing process. For example, factors such as processing equipment failures, material shortages, and worker vacations will all lead to randomness in processing time. These random factors make the original scheduling plan unable to adapt to the changes in the actual production process, thus affecting production efficiency and quality.

[0062] In the related art, the optimization method for the Hybrid Flow Shop Scheduling Problem is a method of establishing a stochastic optimization model based on the assumption of the distribution of workpiece processing time for optimization and solution; the robust optimization method in the related art aims to find the optimal solution under the worst-case scenario where the workpiece processing time may occur, but the probability of the worst-case scenario occurring is extremely low, resulting in the processing scheduling plan being too conservative; the robust optimization algorithm in the related art uses mathematical methods such as problem properties and integer programming to transform the problem into a mixed integer programming problem for solution, but the mixed integer programming problem has the characteristics of a small solution scale and a long solution time.

[0063] In view of this, the present disclosure provides a robust optimization method for Hybrid Flow Shop Scheduling based on a hybrid genetic algorithm, aiming to solve the technical problems that the existing robust optimization methods for Hybrid Flow Shop Scheduling cannot be solved quickly, cannot handle random factors better, resulting in large fluctuations in production decisions and overly conservative decisions.

[0064] In a first aspect, at least one embodiment of the present disclosure provides a robust optimization method for Hybrid Flow Shop Scheduling based on a hybrid genetic algorithm. Please refer to Figure 1 , which shows the flow of this method, including steps S101 to S105.

[0065] In step S101, a mathematical model for the Hybrid Flow Shop Scheduling Problem based on robust optimization is determined;

[0066] In step S102, according to the constraints of the Hybrid Flow Shop Scheduling Problem, a first optimization algorithm based on the genetic algorithm is constructed;

[0067] In step S103, a second optimization algorithm based on the simulated annealing algorithm framework is constructed;

[0068] In step S104, a scheduling scheme evaluation method considering the worst case and average performance based on the stochastic simulation algorithm is constructed, where the worst case is used to represent the maximum makespan among all candidate scheduling schemes, and the average performance is used to represent the average makespan of all candidate scheduling schemes, and the candidate scheduling schemes are obtained based on the initial solutions of the mathematical model of the hybrid flow shop scheduling problem;

[0069] In step S105, the first optimization algorithm and the second optimization algorithm are fused to obtain a target optimization algorithm, and the scheduling scheme is optimized based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme, where the scheduling scheme evaluation method is used to calculate the objective value of the scheduling scheme, and the reciprocal of the objective value is used as the fitness value of the scheduling scheme during the optimization process.

[0070] It should be understood that Figure 1 it is only a schematic illustration of an embodiment of the present disclosure. In practical applications, the execution order of steps S102 - S104 can be Figure 1 different. For example, step S103 can be executed first, and then steps S102 and S104. The embodiments of the present disclosure do not limit this.

[0071] Through the above method, it is possible to improve the robustness of the hybrid flow shop scheduling scheme, pay attention to the worst case while emphasizing the mean performance, and based on this, design a hybrid genetic algorithm with the characteristics of the fusion algorithm, so that the algorithm can converge quickly, has strong global search and the ability to jump out of local optimal solutions, the algorithm implementation is simple, the solution speed for large-scale problems is fast, and there is strong room for personalized transformation.

[0072] For the sake of easy understanding, the above steps will be described in detail with examples below.

[0073] First, a mathematical model of the hybrid flow shop scheduling problem based on robust optimization can be constructed through the following steps S1 - S3.

[0074] Step S1: Construct a deterministic model for the hybrid flow shop scheduling optimization with the objective of minimizing the makespan;

[0075] Step S2: Use the predicted mean and upper and lower bounds of the processing time to construct an uncertainty set based on the predicted mean information and upper and lower bounds of the processing time;

[0076] Step S3: Introduce the uncertainty set based on the predicted mean information and upper and lower bounds of the processing time in step S2 to construct a mathematical model of the hybrid flow shop scheduling problem based on robust optimization.

[0077] In one embodiment, in step S1, the objective function of the hybrid flow shop scheduling problem is expressed as follows: (1);

[0078] Wherein, represents the makespan, represents the scheduling scheme.

[0079] In one embodiment, in step S1, the scheduling requirements of the hybrid flow shop are such that the processing of the next workpiece can only start after the processing of the previous workpiece is completed; on the same machine in the same stage, the processing of the next workpiece can only start after the processing of the previous workpiece is completed; the processing of a workpiece in the subsequent stage must start after the processing of the workpiece in the previous stage is completed; at most one workpiece is processed on each machine in each stage; each workpiece must go through all the processing operations, and the scheduling model is as Figure 2 shown. The constraints are expressed by the following formulas (2-6): (2); (3); (4); (5); (6);

[0080] Wherein, expression (2) represents calculating the makespan, represents the makespan; represents the completion time of the processing at the -th processing position on the -th machine in the s-th stage; n represents the total number of workpieces to be processed, represents the total number of machines in the s-th stage;

[0081] Expression (3) means that except for the first processing position, on the k-th machine in the s-th stage, the processing task at the i-th processing position on the k-th machine can only start after the processing of the workpiece at the (i - 1)-th processing position is completed; wherein, represents the processing time of workpiece j on the k-th machine in the s-th stage; represents whether workpiece j is processed at the i-th processing position on the k-th machine in the s-th stage. If so, it is set to 1, otherwise it is set to 0;

[0082] Expression (4) represents a special constraint on the completion time between the processing positions on machine k in the first processing stage and the second processing stage;

[0083] The expression (5) indicates that, except for the first stage, the start of the processing of workpiece j at the s-th stage requires the completion of its processing at the (s - 1)-th stage;

[0084] The expression (6) represents the processing time relationship of workpiece j in the first stage under special constraints.

[0085] In one embodiment, the mathematical model constructed in step S1 must also satisfy the constraints represented by the following expressions (7 - 9): (7); (8); (9);

[0086] Among them, the expression (7) indicates that workpiece j must go through each processing stage;

[0087] The expression (8) indicates that at most one workpiece can be processed simultaneously on any machine at any stage;

[0088] The expression (9) indicates that on any machine at any stage, the processing order of workpieces must be continuous.

[0089] In one embodiment, in step S2, the constructed processing time uncertainty set composed of the mean and upper and lower bounds of the processing time is expressed as follows: (10);

[0090] Among them, the expression (10) indicates that the processing time of job j on the k-th machine at the s-th stage is distributed between its maximum and minimum values, and the expected value of the processing time of job j on the k-th machine at the s-th stage is , where represents the uncertainty set, respectively represent the minimum and maximum values of the processing time of job j on the k-th machine at the s-th stage.

[0091] In one embodiment, in step S3, the constructed robust optimization mathematical model for the hybrid flow shop scheduling problem is expressed as follows: (11);

[0092] Among them, represents the set of all scheduling schemes; represents the processing time matrix of all workpieces on each machine at each processing stage; represents when the processing time of the workpiece is , and the scheduling scheme is the makespan of the system at this time.

[0093] It should be understood that the purpose of the present disclosure is not to construct a mathematical model of the hybrid flow shop scheduling problem based on robust optimization, but to optimize the hybrid flow shop scheduling problem. Therefore, the specific technical details of constructing the mathematical model of the hybrid flow shop scheduling problem based on robust optimization can refer to the related technologies and will not be elaborated here.

[0094] In one embodiment, the construction of the first optimization algorithm based on the genetic algorithm includes: using a double-layer coding method for scheduling coding, where the first layer coding of the double-layer coding is used for process coding representing the process sequence, and the second layer coding of the double-layer coding is used for machine coding representing machine allocation.

[0095] It should be understood that in the genetic algorithm optimization constructed in step S102, the double-layer coding is adopted for the scheduling coding, which can simultaneously describe the processing sequence of workpieces and the machine allocation situation. Compared with the single-layer coding based only on processes, it can more accurately describe the scheduling scheme, thereby improving the optimization efficiency.

[0096] Exemplarily, the coding form can be as Figure 3 shown, representing a hybrid flow shop scheduling problem with 3 workpieces, 2 processes, and 2 devices for each process. The chromosome is [3,1,1,1,2,1;2,2,3,1,1,3], indicating that the processing sequence of the jobs is the first process of workpiece 2, the second process of workpiece 2, the first process of workpiece 3, the first process of workpiece 1, the second process of workpiece 1, and the second process of workpiece 3 in sequence; and the processing machines where they are located are the third machine in the first stage, the first machine in the second stage, the first machine in the first stage, the first machine in the first stage, the second machine in the second stage, and the first machine in the second stage in sequence.

[0097] In one embodiment, the construction of the first optimization algorithm based on the genetic algorithm includes: using a crossover operator that mixes multiple crossover methods, where the crossover operator that mixes multiple crossover methods includes multi-point crossover and segment crossover. The multi-point crossover is used to only exchange the genes at the crossover points, and the segment crossover is used to exchange the gene segments between the crossover points. Correspondingly, the method further includes: repairing the coding after crossover to replace the redundant processing processes with the missing processing processes.

[0098] It should be understood that compared with a single fixed crossover method, the present disclosure uses a crossover operator that mixes multiple crossover methods and combines with a fusion algorithm, which can fully search different scheduling schemes and enhance the global search ability.

[0099] For example, the multi-point crossover is as Figure 4As shown, the first-layer codes of Parent 1 and Parent 2 before crossover are [3, 1, 1, 1, 2, 1] and [2, 1, 2, 3, 1, 1] respectively. The crossover points are the 1st position and the 4th position of the first-layer codes. Only the genes at the crossover points are swapped. After crossover, the first-layer codes of Offspring 1 and Offspring 2 are [2, 1, 1, 3, 2, 1] and [3, 1, 2, 1, 1, 1]. The fragment crossover is as Figure 5 shown. The crossover points are the 1st position and the 3rd position of the second-layer codes respectively. The gene fragments between the crossover points are swapped. Before crossover, the second-layer codes of Parent 1 and Parent 2 are [2, 1, 1, 2, 3, 3] and [2, 2, 1, 1, 3, 3]. After crossover, the second-layer codes of Offspring 1 and Offspring 2 are [2, 2, 1, 2, 3, 3] and [2, 1, 1, 1, 3, 3]. In particular, after crossover, the codes need to be repaired. Offspring 1 lacks the second processing procedure of workpiece No. 1, and Offspring 2 lacks the second procedure of workpiece No. 2. According to the principle of replacing redundant processing procedures with the missing ones, after crossover of the second-layer codes, the missing codes of Parent 1 are repaired to [2, 2, 1, 1, 3, 3] and [2, 1, 1, 2, 3, 3]. In particular, each time crossover occurs, only one crossover method is selected.

[0100] In one embodiment, the construction of the first optimization algorithm based on the genetic algorithm includes: using different mutation operators for the first-layer code and the second-layer code. Among them, the first-layer code adopts the single-point mutation method to randomly generate a feasible solution at the mutation site, and the second-layer code adopts the reverse mutation method to reverse the code segment between the mutation points.

[0101] It should be understood that compared with a single fixed mutation method, the present disclosure adopts different mutation operators for the first-layer code and the second-layer code, and combines with the fusion algorithm, which can fully search different scheduling solutions and improve the global search ability.

[0102] For example, as Figure 6 shown, for the first-layer code, before mutation, the first-layer code is [3, 1, 1, 1, 2, 1], and the mutation point is the 3rd position. A feasible solution is randomly generated at the mutation site, and the mutated first-layer code is [3, 1, 1, 2, 2, 1]. As Figure 7 shown, for the second-layer code, the mutation points are the 1st position and the 3rd position. The code before mutation is [2, 2, 3, 1, 1, 3], and the code segment between the mutation points is reversed. The mutated code segment is [3, 2, 2, 1, 1, 3]. In particular, each time mutation occurs, only one mutation method is selected.

[0103] In one embodiment, in step S102, a hybrid selection algorithm of multiple selection methods is used. It includes an elite retention operator and a roulette selection operator, and the inverse of the target value of the scheduling scheme is used as its fitness value. In the elite retention operator, individuals with fitness values ​​in the top 20% of the population are retained; in the roulette selection operator, the probability of an individual being retained is determined according to the following expression: (12);

[0104] in, is the probability of the i-th individual being selected, is the fitness value of the ith individual.

[0105] In one embodiment, the construction of a first optimization algorithm based on a genetic algorithm includes: adopting a hybrid stopping rule, the hybrid stopping rule includes an evolutionary stagnation rule and a maximum iteration number rule, wherein the evolutionary stagnation rule is used to regenerate a part of the population individuals to replace the poorer individuals of the current population individuals when the fitness value of the best individual stagnates for a certain number of iterations, and when the number of population regenerations reaches a certain number, the fitness value of the best individual stagnates for a certain number of iterations again, the algorithm iteration is stopped, and the maximum iteration number rule is used to stop the algorithm iteration when the number of iterations reaches the maximum number of iterations, and the population individuals are a hybrid flow shop scheduling scheme.

[0106] In one embodiment, the initial solution of the mathematical model of the hybrid flow shop scheduling problem is generated by adopting a method of mixing multiple initial solutions, wherein the method of mixing multiple initial solutions includes a random initial solution generation method and a greedy initial solution generation method, and the greedy initial solution generation method is used to generate the initial solution in the following manner: when arranging the first stage processing, in the order of the processing time in the first stage from short to long, the first workpiece with the shortest processing time in the first stage is preferentially selected, and the first workpiece is arranged on the machine with the shortest completion time in the first stage, and then the second workpiece with the second shortest processing time in the first stage is selected, and the second workpiece is arranged on the machine with the shortest completion time in the first stage, until all the processed workpieces are arranged in the first stage; when arranging the second stage processing, in the order of the production completion time of the first stage from short to long, the workpiece that completes the first stage production first is first arranged on the machine with the shortest completion time in the second stage, and then the workpiece that completes the first stage production second is arranged on the machine with the shortest completion time in the second stage, until all workpieces are arranged in all stages.

[0107] For example, first select the workpiece with the shortest processing time in the first stage and arrange it on the machine with the smallest completion time in its first stage. Then select the workpiece with the second shortest processing time in the first stage and arrange it on the machine with the smallest completion time in its first stage, and so on until all the workpieces to be processed are arranged in the first stage. When arranging the processing in the second stage, first arrange the workpiece that first completes the production in the first stage on the machine with the smallest completion time in its second stage, then arrange the workpiece that second completes the production in the first stage on the machine with the smallest completion time in its second stage, and so on until all the workpieces are arranged in all stages.

[0108] In one embodiment, in step S105, based on the target optimization algorithm and the scheduling scheme evaluation method, the scheduling scheme is optimized to obtain an optimal scheduling scheme, including: generating an initial population by a first thread based on the genetic operation in the target optimization algorithm and recording a first optimal solution, where each individual in the initial population and the first optimal solution represent the scheduling scheme of the hybrid flow shop; when a preset simulated annealing trigger condition is satisfied, a second thread obtains the initial population from the first thread and obtains a new population by randomly exchanging gene segments of individuals in the initial population, and records a second optimal solution, where when the simulated annealing trigger condition is not satisfied, the first thread and the second thread execute in parallel; calculating the objective values corresponding to the first optimal solution and the second optimal solution respectively based on the scheduling scheme evaluation method, and when the objective value corresponding to the second optimal solution is less than the objective value corresponding to the second optimal solution, determining the scheduling scheme corresponding to the second optimal solution as the optimal scheduling scheme.

[0109] It should be understood that when the simulated annealing trigger condition is not satisfied, the first thread and the second thread execute in parallel, and when the simulated annealing trigger condition is satisfied, the first thread and the second thread execute serially, thereby improving the algorithm optimization efficiency and thus improving the efficiency of hybrid flow shop scheduling.

[0110] Exemplarily, the simulated annealing trigger condition may be that the optimal solution has not been improved for a preset number of consecutive generations in the genetic operation of the target optimization algorithm, such as not being improved for 5 consecutive generations. Of course, it may also be other conditions, and the embodiments of the present disclosure do not limit this.

[0111] In one embodiment, if the optimal solution has not been improved for a continuously preset number of generations in the genetic operation of the target optimization algorithm, the computing resource allocation of the second thread is increased to expand the neighborhood search range of the simulated annealing operation in the target optimization algorithm; if the optimization process of the simulated annealing operation in the target optimization algorithm falls into a local optimum, the first thread is triggered to execute the diversity mutation operation in the genetic operation, and the diversity mutation operation is used to obtain a new population through different mutation methods. Thus, dynamic load balancing of computing resources during the optimization process can be achieved, thereby further improving the optimization efficiency and the efficiency of hybrid flow shop scheduling.

[0112] Exemplarily, the continuously preset number of generations can be, for example, 5 consecutive generations, and the embodiments of the present disclosure do not limit this. Different mutation methods can include the mutation methods described above, or other mutation methods in related technologies, and the embodiments of the present disclosure do not limit this.

[0113] In one embodiment, in step S103, the scheduling scheme evaluation method is used to obtain the target value in the following manner:

[0114] Generate N samples, substitute the N samples into the scheduling scheme to obtain N makespans, where the characteristics of the N samples conform to the uncertainty set based on the predicted mean information and upper and lower bounds of the processing time, and N is a positive integer;

[0115] Calculate the target value of this scheduling scheme according to the following expression: (13);

[0116] Wherein, are the weights of the average performance and the worst case respectively, is the makespan of the k-th sample, is the makespan of the k-th sample under the scheduling scheme x, is the makespan of the k-th sample under the scheduling scheme x, and N is the number of samples.

[0117] In one embodiment, the average performance and the fluctuation of the worst case can also be determined according to the distribution robustness of the current solution set during the optimization process; in the case where the fluctuation of the average performance represents that the fluctuation range is greater than the first preset range, the weight of the average performance is increased, and the weight of the worst case is decreased, where the sum of the weights of the average performance and the worst case after adjustment is 1; in the case where the fluctuation of the average performance represents that the fluctuation range is greater than the second preset range, the weight of the worst case is increased, and the weight of the average performance is decreased, where the sum of the weights of the average performance and the worst case after adjustment is 1. Thus, dynamic adjustment of the weights can be achieved, thereby realizing dynamic optimization of the scheduling scheme and improving the accuracy of the hybrid flow shop scheduling.

[0118] In one embodiment, in step S103, it is possible to determine whether to accept the current optimal solution according to the Metropolis acceptance criterion, and the Metropolis acceptance criterion expression is as follows: (14);

[0119] where respectively represent the historical optimal solution and the current optimal solution, respectively represent the objective values of the historical optimal solution and the current optimal solution, T represents the initial temperature, and p represents the probability of not accepting the current optimal solution.

[0120] In one embodiment, a hybrid genetic algorithm provided by the present disclosure is as Figure 8 shown, and the scheduling scheme provided by the hybrid flow shop scheduling robust optimization method based on the hybrid genetic algorithm proposed by the present disclosure is as Figure 9 shown.

[0121] First, refer to Figure 8 , and generate an initial solution. It should be understood that the initial solution is the initial scheduling scheme, that is, the individual in the genetic algorithm. Based on the initial solution, it is determined whether the termination condition is satisfied. If not, new individuals are obtained through any of the above-mentioned crossover, mutation, etc. methods, and then the objective value of each individual is calculated by the scheduling scheme evaluation method considering the worst case and the average performance based on the stochastic simulation algorithm. Then, the reciprocal of the objective value is used as the fitness value. Next, screening is performed according to the fitness value to obtain the optimal solution until the termination condition is satisfied, and the optimal scheduling scheme is obtained.

[0122] Thus, it is possible to improve the robustness of the hybrid flow shop scheduling scheme, pay attention to the worst case while emphasizing the average performance, and design a hybrid genetic algorithm that integrates the characteristics of the algorithm, so that the algorithm can converge quickly, has strong global search and the ability to jump out of local optimal solutions. The algorithm is simple to implement, has a fast solving speed for large-scale problems, and has strong room for personalized transformation.

[0123] According to the second aspect of the embodiments of the present disclosure, a robust optimization device for hybrid flow shop scheduling based on a hybrid genetic algorithm is provided. Please refer to Figure 10 The robust optimization device 1000 for hybrid flow shop scheduling based on a hybrid genetic algorithm includes:

[0124] A determination module 1001, configured to determine a mathematical model of a hybrid flow shop scheduling problem based on robust optimization;

[0125] A first construction module 1002, configured to construct a first optimization algorithm based on a genetic algorithm according to the constraints of the hybrid flow shop scheduling problem;

[0126] A second construction module 1003, configured to construct a second optimization algorithm based on a simulated annealing algorithm framework;

[0127] A third construction module 1004, configured to construct a scheduling scheme evaluation method that considers the worst case and average performance based on a stochastic simulation algorithm, where the worst case is used to represent the maximum makespan in each candidate scheduling scheme, and the average performance is used to represent the average makespan of each candidate scheduling scheme, and the candidate scheduling schemes are obtained based on the initial solutions of the mathematical model of the hybrid flow shop scheduling problem;

[0128] An optimization module 1005, configured to fuse the first optimization algorithm and the second optimization algorithm to obtain a target optimization algorithm, and optimize the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme, where the scheduling scheme evaluation method is used to calculate the objective value of the scheduling scheme, and the reciprocal of the objective value is used as the fitness value of the scheduling scheme during the optimization process.

[0129] In some embodiments of the present disclosure, the optimization module 1005 is specifically configured to:

[0130] Generate an initial population based on the genetic operations in the target optimization algorithm through a first thread, and record a first optimal solution, where each individual in the initial population and the first optimal solution represent the scheduling scheme of the hybrid flow shop;

[0131] When the second thread meets the preset simulated annealing trigger condition, it obtains the initial population from the first thread, and obtains a new population by randomly exchanging gene segments of individuals in the initial population, and records the second best solution. Wherein, when the simulated annealing trigger condition is not met, the first thread and the second thread execute in parallel;

[0132] Calculate the objective values corresponding to the first best solution and the second best solution respectively based on the scheduling scheme evaluation method, and when the objective value corresponding to the second best solution is less than the objective value corresponding to the second best solution, determine the scheduling scheme corresponding to the second best solution as the optimal scheduling scheme.

[0133] In some embodiments of the present disclosure, the apparatus 1000 further includes a first adjustment module for:

[0134] If the optimal solution has not been improved for a continuous preset number of generations in the genetic operation of the target optimization algorithm, increase the computing resource allocation of the second thread to expand the neighborhood search range of the simulated annealing operation in the target optimization algorithm;

[0135] If the optimization process of the simulated annealing operation in the target optimization algorithm falls into a local optimum, trigger the first thread to execute the diversity mutation operation in the genetic operation, and the diversity mutation operation is used to obtain a new population through different mutation methods.

[0136] In some embodiments of the present disclosure, the first construction module 1002 is specifically configured to:

[0137] Use a two-layer coding method for scheduling coding. The first layer coding of the two-layer coding is used to represent the process coding of the process sequence, and the second layer coding of the two-layer coding is used to represent the machine coding of the machine allocation.

[0138] In some embodiments of the present disclosure, the first construction module 1002 is specifically configured to:

[0139] Use a crossover operator that mixes multiple crossover methods, where the crossover operator that mixes multiple crossover methods includes multi-point crossover and segment crossover. The multi-point crossover is used to only exchange genes at the crossover points, and the segment crossover is used to exchange gene segments between the crossover points;

[0140] The apparatus 1000 further includes:

[0141] A repair module for repairing the coding after crossover to replace redundant processing procedures with missing processing procedures.

[0142] In some embodiments of the present disclosure, the first construction module 1002 is specifically configured to:

[0143] A double-layer coding method is used for scheduling coding, wherein the first layer of the double-layer coding is used to represent the process code of the process sequence, and the second layer of the double-layer coding is used to represent the machine code of the machine allocation;

[0144] Different mutation operators are used for the first layer coding and the second layer coding, wherein the first layer coding adopts a single-point mutation method to randomly generate a feasible solution at the mutation site, and the second layer coding adopts a reverse mutation method to reverse the coding segments between the mutation sites.

[0145] In some embodiments of the present disclosure, the first building module 1002 is specifically used to:

[0146] A hybrid stopping rule is adopted, wherein the hybrid stopping rule includes an evolutionary stagnation rule and a maximum iteration number rule. The evolutionary stagnation rule is used to regenerate a part of the population individuals to replace the poor individuals of the current population individuals when the fitness value of the best individual stagnates for a certain number of iterations. When the number of population regeneration reaches a certain number, the fitness value of the best individual stagnates for a certain number of iterations again, and the algorithm iteration is stopped. The maximum iteration number rule is used to stop the algorithm iteration when the number of iterations reaches the maximum number of iterations. The population individuals are a hybrid flow shop scheduling scheme.

[0147] In some embodiments of the present disclosure, the initial solution of the hybrid flow shop scheduling problem mathematical model is generated by adopting a method of mixing multiple initial solutions, wherein the method of mixing multiple initial solutions includes a random initial solution generation method and a greedy initial solution generation method, and the greedy initial solution generation method is used to generate an initial solution through the following modules:

[0148] A first scheduling module is used to, when scheduling the first stage processing, preferentially select the first workpiece with the shortest processing time in the first stage in the order of the processing time in the first stage from short to long, and schedule the first workpiece on the machine with the shortest completion time in the first stage, then select the second workpiece with the second shortest processing time in the first stage, and schedule the second workpiece on the machine with the shortest completion time in the first stage, until all the processing workpieces are scheduled in the first stage;

[0149] The second scheduling module is used to schedule the second stage processing in the order of the first stage production completion time from short to long. First, the workpiece that completes the first stage of production is scheduled on the machine with the shortest completion time of its second stage. Then, the workpiece that completes the first stage of production is scheduled on the machine with the shortest completion time of its second stage, until the scheduling of all workpieces is completed in all stages.

[0150] In some embodiments of the present disclosure, the scheduling scheme evaluation method is used to obtain a target value through the following modules:

[0151] A generation module, configured to generate N samples, substitute the N samples into the scheduling scheme, and obtain N makespan times, where the N sample features conform to an uncertainty set based on the predicted mean information and upper and lower bounds of the processing time, and N is a positive integer;

[0152] A calculation module, configured to calculate the target value of the scheduling scheme according to the following expression: (13);

[0153] Wherein, are the weights of the average performance and the worst case respectively, is the completion time of the kth sample, is the completion time of the kth sample under the scheduling scheme x, is the makespan time of the kth sample under the scheduling scheme x, and N is the number of samples.

[0154] In some embodiments of the present disclosure, the device 1000 further includes a second adjustment module, configured to:

[0155] Determine the fluctuation conditions of the average performance and the worst case according to the distribution robustness of the current solution set during the optimization process;

[0156] In the case where the fluctuation condition of the average performance characterizes that the fluctuation range is greater than the first preset range, increase the weight of the average performance and decrease the weight of the worst case, wherein the sum of the weights of the adjusted average performance and the worst case is 1;

[0157] In the case where the fluctuation condition of the average performance characterizes that the fluctuation range is greater than the second preset range, increase the weight of the worst case and decrease the weight of the average performance, wherein the sum of the weights of the adjusted average performance and the worst case is 1.

[0158] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments of the method in the first aspect, and will not be elaborated herein.

[0159] According to the third aspect of the embodiments of the present disclosure, please refer to Figure 11 , which exemplarily shows a block diagram of an electronic device. The electronic device 700 may include: a processor 701, a memory 702. The electronic device 700 may further include one or more of a multimedia component 703, an input / output (I / O) interface 704, and a communication component 705.

[0160] Among them, the processor 701 is used to control the overall operation of the electronic device 700 to complete all or part of the steps in any of the above methods. The memory 702 is used to store various types of data to support the operation of the electronic device 700. These data may include, for example, instructions for any application or method operating on the electronic device 700, as well as application-related data, such as contact data, messages sent and received, pictures, audio, video, and so on. The memory 702 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disc. The multimedia component 703 may include a screen and an audio component. Among them, the screen can be, for example, a touch screen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signal can be further stored in the memory 702 or sent through the communication component 705. The audio component also includes at least one speaker for outputting audio signals. The I / O interface 704 provides an interface between the processor 701 and other interface modules. The above other interface modules can be a keyboard, a mouse, buttons, etc. These buttons can be virtual buttons or physical buttons. The communication component 705 is used for wired or wireless communication between the electronic device 700 and other devices. Wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination of one or more of them. Therefore, the corresponding communication component 705 may include: a Wi-Fi module, a Bluetooth module, and an NFC module.

[0161] In an exemplary embodiment, the electronic device 700 may be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components for performing any of the above methods.

[0162] In one embodiment, there is also provided a computer-readable storage medium including program instructions, and when the program instructions are executed by a processor, the steps of any of the above methods are implemented. For example, the computer-readable storage medium may be the memory 702 including the program instructions, and the above program instructions may be executed by the processor 701 of the electronic device 700 to complete any of the above methods.

[0163] In one embodiment, there is also provided a computer program product, which includes a computer program capable of being executed by a processor, and when the computer program is executed by the processor, the steps of any of the above methods are implemented.

[0164] The preferred embodiments of the present disclosure have been described in detail above in conjunction with the accompanying drawings. However, the present disclosure is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present disclosure, various simple modifications can be made to the technical solutions of the present disclosure, and these simple modifications all fall within the protection scope of the present disclosure.

[0165] In addition, it should be noted that, in the above specific embodiments, the various specific technical features described can be combined in any suitable manner without conflict. To avoid unnecessary repetition, the present disclosure will not separately describe various possible combination methods.

[0166] Furthermore, any combination can be made between various different embodiments of the present disclosure as long as it does not violate the idea of the present disclosure, and it should also be regarded as the content disclosed by the present disclosure.

Claims

1. A robust optimization method for hybrid flow shop scheduling based on a hybrid genetic algorithm, characterized in that Including: Determine the mathematical model of the hybrid flow shop scheduling problem based on robust optimization; Construct a first optimization algorithm based on the genetic algorithm according to the constraints of the hybrid flow shop scheduling problem; Construct a second optimization algorithm based on the simulated annealing algorithm framework; Construct a scheduling scheme evaluation method considering the worst case and average performance based on the stochastic simulation algorithm, where the worst case is used to characterize the maximum makespan in the scheduling scheme, and the average performance is used to characterize the average makespan of the scheduling scheme. The initial scheduling scheme is obtained based on the initial solution of the mathematical model of the hybrid flow shop scheduling problem; Fuse the first optimization algorithm and the second optimization algorithm to obtain the target optimization algorithm, and optimize the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain the optimal scheduling scheme, where the scheduling scheme evaluation method is used to calculate the objective value of the scheduling scheme, and the reciprocal of the objective value is used as the fitness value of the scheduling scheme in the optimization process.

2. The robust optimization method for hybrid flow shop scheduling based on hybrid genetic algorithm according to claim 1, characterized in that The optimizing the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain the optimal scheduling scheme includes: Generate an initial population based on the genetic operations in the target optimization algorithm through a first thread, and record the first optimal solution, where each individual in the initial population and the first optimal solution represent the scheduling scheme of the hybrid flow shop; Through a second thread, when the preset simulated annealing trigger condition is satisfied, obtain the initial population from the first thread, and obtain a new population by randomly exchanging gene segments of individuals in the initial population, and record the second optimal solution. When the simulated annealing trigger condition is not satisfied, the first thread and the second thread execute in parallel; Calculate the objective values corresponding to the first optimal solution and the second optimal solution respectively based on the scheduling scheme evaluation method, and when the objective value corresponding to the second optimal solution is less than the objective value corresponding to the second optimal solution, determine the scheduling scheme corresponding to the second optimal solution as the optimal scheduling scheme.

3. The robust optimization method for hybrid flow shop scheduling based on the hybrid genetic algorithm according to claim 2, characterized in that The method further includes: If the optimal solution is not improved in a continuous preset number of generations in the genetic operations in the target optimization algorithm, increase the computing resource allocation of the second thread to expand the neighborhood search range of the simulated annealing operation in the target optimization algorithm; If the optimization process of the simulated annealing operation in the target optimization algorithm falls into a local optimum, trigger the first thread to execute the diversity mutation operation in the genetic operations, and the diversity mutation operation is used to obtain a new population through different mutation methods.

4. The robust optimization method for hybrid flow shop scheduling based on the hybrid genetic algorithm according to claim 2, wherein The constructing the first optimization algorithm based on the genetic algorithm includes: Adopt a double-layer coding method for scheduling coding. The first layer coding of the double-layer coding is used for the operation coding representing the operation sequence, and the second layer coding of the double-layer coding is used for the machine coding representing the machine allocation; Different mutation operators are used for the first layer coding and the second layer coding, wherein the first layer coding adopts a single-point mutation method to randomly generate a feasible solution at the mutation site, and the second layer coding adopts a reverse mutation method to reverse the coding segments between the mutation sites.

5. The robust optimization method for hybrid flow shop scheduling based on the hybrid genetic algorithm according to any one of claims 1-4, characterized in that, The constructing of a first optimization algorithm based on a genetic algorithm comprises: A hybrid stopping rule is adopted, which includes an evolutionary stagnation rule and a maximum iteration number rule. The evolutionary stagnation rule is used to regenerate a part of the population individuals to replace the poor individuals of the current population individuals when the fitness value of the best individual stagnates for a certain number of iterations. When the number of population regeneration reaches a certain number, the fitness value of the best individual stagnates for a certain number of iterations again, and the algorithm iteration is stopped. The maximum iteration number rule is used to stop the algorithm iteration when the number of iterations reaches the maximum number of iterations. The population individuals are the scheduling plan of the hybrid assembly line workshop.

6. The robust optimization method for hybrid flow shop scheduling based on hybrid genetic algorithm according to any one of claims 1-4, characterized in that, The initial solution of the hybrid flow shop scheduling problem mathematical model is generated by a method of mixing multiple initial solutions, wherein the method of mixing multiple initial solutions includes a random initial solution generation method and a greedy initial solution generation method, and the greedy initial solution generation method is used to generate an initial solution in the following manner: When arranging the first stage of processing, in the order of the processing time in the first stage from short to long, the first workpiece with the shortest processing time in the first stage is preferentially selected, and the first workpiece is arranged on the machine with the shortest completion time in the first stage, and then the second workpiece with the second shortest processing time in the first stage is selected, and the second workpiece is arranged on the machine with the shortest completion time in the first stage, until all the processing workpieces are arranged in the first stage; When arranging the second stage of processing, the workpiece that completes the first stage of production is arranged in order from short to long. The workpiece that completes the first stage of production is arranged on the machine with the shortest completion time of its second stage. Then the workpiece that completes the first stage of production is arranged on the machine with the shortest completion time of its second stage, until all workpieces are arranged in all stages.

7. The robust optimization method for hybrid flow shop scheduling based on hybrid genetic algorithm according to any one of claims 1-4, characterized in that The scheduling scheme evaluation method is used to obtain the target value in the following way: Generate N samples, substitute the N samples into the scheduling plan, and obtain N maximum completion times, wherein the N sample characteristics conform to the uncertainty set based on the processing time prediction mean information and upper and lower bounds, and N is a positive integer; The target value of the scheduling scheme is calculated according to the following expression: ； wherein, are the weights of the average performance and the worst case respectively, is the completion time of the k-th sample, is the completion time of the k-th sample under the scheduling scheme x, is the makespan of the k-th sample under the scheduling scheme x, and N is the number of samples.

8. The robust optimization method for hybrid flow shop scheduling based on hybrid genetic algorithm according to claim 7, wherein The method further comprises: Determining the fluctuation of the average performance and the worst case according to the distribution robustness of the current solution set during the optimization process; When the fluctuation range of the fluctuation of the average performance is greater than the first preset range, increase the weight of the average performance and reduce the weight of the worst case, wherein the sum of the weights of the average performance and the worst case after adjustment is 1; In the case where the fluctuation range characterized by the fluctuation of the average performance is greater than the second preset range, increase the weight of the worst case and decrease the weight of the average performance, where the sum of the adjusted weights of the average performance and the worst case is 1.

9. A robust optimization device for hybrid flow shop scheduling based on a hybrid genetic algorithm, characterized in that Including: A determination module, configured to determine a mathematical model for the hybrid flow shop scheduling problem based on robust optimization; A first construction module, configured to construct a first optimization algorithm based on a genetic algorithm according to the constraints of the hybrid flow shop scheduling problem; A second construction module, configured to construct a second optimization algorithm based on a simulated annealing algorithm framework; A third construction module, configured to construct a scheduling scheme evaluation method considering the worst case and the average performance based on a stochastic simulation algorithm, where the worst case is used to characterize the maximum makespan in each candidate scheduling scheme, and the average performance is used to characterize the average makespan of each candidate scheduling scheme, and the candidate scheduling schemes are obtained based on the initial solutions of the mathematical model of the hybrid flow shop scheduling problem; An optimization module, configured to fuse the first optimization algorithm and the second optimization algorithm to obtain a target optimization algorithm, and optimize the scheduling scheme based on the target optimization algorithm and the scheduling scheme evaluation method to obtain an optimal scheduling scheme, where the scheduling scheme evaluation method is used to calculate the objective value of the scheduling scheme, and the reciprocal of the objective value is used as the fitness value of the scheduling scheme in the optimization process.

10. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory is used to store computer instructions that can be run on the processor, and the processor is used to implement the steps of the method according to any one of claims 1-8 when executing the computer instructions.

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