A Distributed Hybrid Flow Shop Scheduling Method for Rocket Tank Production

Abstract

The present invention relates to the technical field of workshop production scheduling, and particularly to a distributed hybrid flow shop scheduling method for rocket tank production. Taking the minimization of the maximum completion time of products as the objective function, a distributed hybrid flow shop scheduling model including the assembly process is constructed. This method designs a genetic algorithm framework with multi-layer coding, and introduces an elite selection strategy and a neighborhood search operator into it. The elite selection strategy ensures that high-quality individuals are retained during the iteration process, accelerating the convergence speed of the algorithm; the network diagram method is used to identify the critical path, and the neighborhood search is carried out on the critical workpieces to optimize the production scheduling bottleneck, improve the quality of the solution, and avoid falling into local optima. The present invention can not only greatly improve the production scheduling efficiency of rocket tanks, but also has good applicability and universality, and can be widely applied to other types of distributed hybrid flow shop scheduling environments.

Description

Technical Field

[0001] The present invention relates to the technical field of workshop production scheduling, and particularly to a distributed hybrid flow shop scheduling method for rocket tank production. Background Art

[0002] Under the background of the continuous update and iteration of the intelligent manufacturing level and the rocket tank production process, the manufacturing tasks of the tank body and the tank bottom structure in the rocket tank production process are undertaken by multiple distributed factories. These factories have different process advantages and processing capabilities, and the availability limitations of the factories need to be considered when selecting factories for task orders. In addition, in each factory, there are multiple devices available at each process stage, which makes it particularly important to establish a systematic method to coordinate the production resources distributed at different locations. Each factory not only needs to efficiently complete its own production tasks, but also needs to achieve seamless connection with the subsequent assembly process to ensure the smooth operation of the overall production process.

[0003] The current research on workshop scheduling mainly focuses on single workshops or simple flow shop models, and less considers the complex distributed hybrid flow shop scheduling problem with an assembly process. Traditional exact algorithms, such as branch and bound, branch and price, etc., although they can find the optimal solution, have a high computational complexity when facing large-scale orders and often cannot obtain a solution within a reasonable time. Therefore, more and more research begins to tend to use meta-heuristic algorithms, such as genetic algorithms and particle swarm optimization, etc. These algorithms show advantages in solving large-scale engineering problems and can find satisfactory approximate solutions in a short time. However, meta-heuristic algorithms also have the problem of being easily trapped in local optimal solutions, and further strategy improvements are urgently needed to improve the global search ability. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a distributed hybrid flow shop scheduling method for rocket tank production, which solves the technical problem that existing algorithms are easily trapped in local optimal solutions in the distributed hybrid flow shop scheduling problem with a complex assembly process.

[0005] To solve the above technical problems, the present invention provides the following technical solutions: A distributed hybrid flow shop scheduling method for rocket tank production, the method includes the following processes:

[0006] Obtain the basic information including product information and factory information for the production of each component structure of the rocket tank;

[0007] Based on the basic information, construct a distributed hybrid flow shop scheduling model including the assembly process, and the distributed hybrid flow shop scheduling model includes an objective function and constraint conditions;

[0008] An improved genetic algorithm that introduces an elite selection strategy and a neighborhood search operator is used to solve the distributed hybrid flow shop scheduling model to obtain a scheduling plan; if the improved genetic algorithm reaches the termination condition, it ends and visualizes the output results.

[0009] Furthermore, the description of the product information is: the workpieces corresponding to each tank product of the rocket tank.

[0010] Furthermore, the description of the factory information is:

[0011] The tank products are organized for production in f distributed factories, and each factory s ∈ S = {1, 2, …, f} is a hybrid flow shop with different processing technologies and capabilities;

[0012] The workpiece i ∈ N = {1, 2, …, n} can and can only choose one of the factories for processing, and there are factory availability restrictions. The set of alternative factories for the workpiece i is characterized as

[0013] In the hybrid flow shop, the workpiece needs to go through j ∈ J s = {1, 2, …, h s} stages. Each stage j has at most m sj ≥ 1 parallel machines with the same performance for production, and its equipment set is characterized as M sj = {1, 2, …, m sj}. Each workpiece has to go through all the processing stages in the factory and at most one device is selected for processing at each stage. The processing time of the workpiece i in the j-th stage of the factory s is p isj ;

[0014] After processing, it enters the assembly stage, which is carried out by a work team. Each product l ∈ L = {1, 2, …, q}, n ≥ q can only start assembly after all the workpieces belonging to it are processed. The parameter g il is a 0-1 parameter, taking 1 means the workpiece i belongs to the product l, otherwise it is 0. The assembly stage needs to consider the order of the products, and the assembly time is p l .

[0015] Furthermore, the objective function is to minimize the maximum completion time of the product, characterized as minC max , where:

[0016]

[0017] In the formula, c l is the assembly completion time of the product l; l ∈ L = {1, 2, …, q}.

[0018] Furthermore, the constraint conditions are:

[0019] Ensure that each workpiece is assigned to a factory for processing, i.e.:

[0020]

[0021] Ensure that there is exactly one piece of equipment for processing at each stage of the factory for each workpiece, i.e.:

[0022]

[0023] Ensure that there is a sequential relationship in the processing of workpieces on the equipment, i.e.:

[0024]

[0025] Ensure that a workpiece can enter the next stage only after it is completed in the previous stage of the factory, i.e.:

[0026]

[0027] Ensure that the completion time of a workpiece in the first stage is greater than or equal to its processing time, i.e.:

[0028]

[0029] Ensure the time constraints for workpieces processed sequentially in the same stage, i.e.:

[0030]

[0031] Calculate that the start time of product assembly is later than the completion time of its last workpiece, i.e.:

[0032]

[0033] Ensure the sequential time constraints for products in the assembly stage, i.e.:

[0034]

[0035] Effective inequalities improve the lower bound of the model, i.e.:

[0036]

[0037] Define the value range of variables, i.e.:

[0038]

[0039] In the formula, x is is a 0-1 variable, taking 1 means that workpiece i is assigned to factory s for processing, otherwise taking 0; y isjk is a 0-1 variable, taking 1 means that workpiece i is assigned to the k-th piece of equipment in the j-th stage of factory s for processing, otherwise taking 0; z sjii′kis a 0-1 variable, taking 1 means workpiece i has priority over workpiece i′ to be processed on the k-th device at the j-th stage in factory s, otherwise it is 0; c isj is a continuous variable, representing the completion time of workpiece i at the j-th stage in factory s; v ll′ is a 0-1 variable, taking 1 means product l has priority over product l′ to be processed in the assembly stage, otherwise it takes 0; M is a sufficiently large positive integer.

[0040] Furthermore, the process of obtaining the scheduling plan by solving the distributed hybrid flow shop scheduling model specifically includes:

[0041] Individual coding: For this distributed hybrid flow shop scheduling problem, two-layer coding information is adopted to show the factory to which each workpiece is assigned and the processing priority order in the corresponding factory; the total length of the chromosome is the number of workpieces, the first-layer coding information is the factory number, and each gene in the second-layer coding information represents a random number in the interval [0,1]. According to the first-layer coding information, the set of workpieces to be processed in each factory is determined, and the processing priority of the workpieces in the corresponding factory is obtained by sorting according to the values of the second-layer coding information;

[0042] Individual decoding: In the production stage, equipment is allocated to the workpieces in each factory, and they are sequentially allocated to the earliest available machines according to the processing priority of the workpieces; in the assembly stage, the earliest available assembly time is determined according to the completion times of all the workpieces involved in each product, and the product with the smallest earliest available assembly time among all products is assembled first; after determining the assembly order, start and completion times, the maximum completion time of the product is obtained, which is the fitness value of the individual;

[0043] Initializing the population: Determine the population size pop size , and initialize the population according to the coding rules;

[0044] Updating the elite memory bank: Using the inflection point as the demarcation point of the population, the individuals with fitness values not greater than the inflection point are saved in the elite memory bank;

[0045] Selection operation: Adopt an algorithm combining tournament selection and elite selection as the selection operator;

[0046] Crossover operation: With a crossover probability p c Randomly select two individuals in the population, randomly select two crossover points in the individuals, and perform gene exchange between the two individuals;

[0047] Mutation operation: With a mutation probability p m Select an individual for mutation operation and randomly select any gene position for replacement;

[0048] Improvement of neighborhood search operator based on critical path: Use the critical path method to find a critical path on the network diagram. The length of the path is equal to the objective function value of the chromosome, and the length of the path is the sum of the processing times of all nodes on the path;

[0049] Obtain the workpiece numbers on the critical path, find the corresponding processing factories for the workpieces, reorder the workpieces in the factory according to the assembly order of the products in the critical path. If they belong to the same product, the processing order of the workpieces is random;

[0050] Reassign the second-layer coding information of the chromosome according to the new order of the workpieces;

[0051] Finally, determine whether the fitness value of the individual is better. If it is better, accept the individual;

[0052] Let the maximum number of iterations be MaxGen and the interval generation be GapGen. When the current number of iterations is greater than the maximum number of iterations MaxGen or the optimal value of the population remains unchanged for consecutive GapGen generations, the algorithm terminates.

[0053] Furthermore, the method for determining the inflection point is as follows:

[0054] First, sort the individuals in the population from smallest to largest according to the fitness value to obtain a curve related to the fitness value; second, generate a line by connecting the point with the minimum fitness value and the point with the maximum fitness value; finally, calculate the distance between each point on the curve and the line, and select the point with the largest distance from the line as the inflection point.

[0055] Furthermore, in the selection operation,

[0056] Tournament selection: Randomly select 2 individuals from the population for comparison, and retain the individual with the better fitness value in the next-generation population;

[0057] Elite selection: Set a dynamic elite selection threshold. The threshold is set to a high threshold in the early stage and decreased in the later stage. The threshold update formula is:

[0058] r = (i - MaxGen)^2 / (1 - MaxGen)^2.

[0059] In the formula, MaxGen is the maximum number of iterations;

[0060] In the i-th iteration, randomly generate a random number μ, 0 < μ < 1. If μ < r, select an individual from the elite memory bank and put it into the offspring; otherwise, use the tournament method to select an individual and put it into the offspring.

[0061] With the above technical solutions, the present invention provides a distributed hybrid flow shop scheduling method for rocket tank production, which at least has the following beneficial effects:

[0062] 1. The present invention can not only greatly improve the production scheduling efficiency of rocket tanks, but also has good applicability and generality, and can be widely applied to other types of distributed hybrid flow shop scheduling environments.

[0063] 2. The present invention uses an improved genetic algorithm framework to solve a class of distributed hybrid flow shop scheduling problems for rocket tank product production and assembly. In the model, realistic constraints such as the processing capacity differences of distributed factories and the pre-operation time windows of assembly processes are considered. In the algorithm design, an elite memory bank and an elite selection operator based on inflection points, as well as strategies such as neighborhood search based on the critical path, are added. The effectiveness of the model and algorithm is verified through simulation results.

[0064] 3. The present invention ensures the transmission of high-quality individuals in the early stage and increases the randomness of the algorithm in the later stage by introducing an elite selection threshold; at the same time, after adding the neighborhood search operator of the critical path, by identifying the critical path in the current solution, precise production scheduling optimization is performed on critical workpieces. This operator can make the algorithm more effectively explore a better solution space by fine-tuning critical tasks, thereby enhancing the global search ability. Description of the Drawings

[0065] The drawings described herein are used to provide a further understanding of the present application, and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0066] Figure 1 It is a schematic diagram of the production system implemented in the present invention;

[0067] Figure 2 It is a schematic diagram of the individual coding of the improved genetic algorithm in the present invention;

[0068] Figure 3 It is a schematic diagram of the crossover operator of the improved genetic algorithm in the present invention;

[0069] Figure 4 It is a schematic diagram of the mutation operator of the improved genetic algorithm in the present invention;

[0070] Figure 5 It is a schematic diagram of the directed graph representation of the chromosome scheme in the present invention;

[0071] Figure 6 It is a schematic diagram of the assembly of tank products in the present invention;

[0072] Figure 7 It is a flow chart of the improved genetic algorithm in the present invention;

[0073] Figure 8 It is a Gantt chart of the production scheduling result of the example in the present invention. Detailed implementation manners

[0074] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners. Thereby, the implementation process of how this application uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0075] Since the selection, crossover, and mutation operations in the genetic algorithm are usually random, this may lead to the search process falling into a local optimum. Please refer to Figures 1 - 8 , this embodiment proposes a distributed hybrid flow shop scheduling method for rocket tank production. By introducing an elite memory bank and a neighborhood search operator considering the critical path to enhance the algorithm performance, an elite selection threshold is introduced to ensure the transfer of high-quality individuals in the early stage and increase the randomness of the algorithm in the later stage. At the same time, after adding the neighborhood search operator of the critical path, by identifying the critical path in the current solution, precise scheduling optimization of critical workpieces is performed. This operator can fine-tune critical tasks, enabling the algorithm to more effectively explore a better solution space, thereby enhancing the global search ability. The method includes the following steps:

[0076] S1. Obtain the basic information including product information and factory information for the production of each component structure of the rocket tank, which mainly involves basic information such as the production process route, processing time of each process, and processing resources of each distributed factory.

[0077] Specifically, the description of the product information is: the workpiece composition corresponding to each tank product of the rocket tank. This embodiment is a specific example of applying the above method to the production of a certain rocket tank. As Figure 6 shown, the rocket tank is welded by three tank products, namely a thin-walled cylinder (cylinder section) in the middle and hemispherical bodies (tank bottoms) at both ends. The thin-walled cylinder is manufactured in sections according to each cylinder section, and one tank product is welded by multiple workpieces.

[0078] The description of the factory information is: the rocket tank products are organized for production in f distributed factories, and each factory s ∈ S = {1, 2,..., f} is a hybrid flow shop with different processing technologies and capabilities. The workpiece i ∈ N = {1, 2,..., n} can and can only choose one of the factories for processing, and there are factory availability restrictions. The alternative factory set of the workpiece i is characterized as In the hybrid flow shop, the workpiece needs to go through j ∈ J s = {1, 2,..., h s} stages, and each stage j has at most m sj ≥ 1 parallel machines with the same performance for production, and its equipment set is characterized as M sj = {1, 2,..., m sj}, each workpiece has to go through all processing stages in the factory, and at most one device is selected for processing at each stage. The processing time of workpiece i at the j-th stage in factory s is p isj . After processing is completed, it enters the assembly stage. The assembly stage is carried out by a work team. For each product l ∈ L = {1, 2,..., q}, n ≥ q, assembly can only start after all the workpieces belonging to it are processed. The parameter g il is a 0-1 parameter, taking 1 means workpiece i belongs to product l, otherwise it is 0. The assembly stage needs to consider the order of products, and the assembly time is p l . The schematic diagram of the production system is as Figure 1 shown.

[0079] Specifically, the product information and factory information are shown in Table 1 and Table 2.

[0080] Table 1 Product Information Table

[0081]

[0082]

[0083] Table 2 Factory Information Table

[0084]

[0085] As shown in Table 1 and Table 2, the enterprise currently has 3 distributed factories, and there are 3 storage tank products to be processed. Products 1, 2, and 3 are composed of 4, 3, and 4 workpieces respectively. The workpieces can choose factories for processing from the alternative factory set. Each factory is a hybrid flow shop. The number of processing stages of the factory for processing products varies, and there are multiple parallel machines available for selection at each stage. For example, Factory 1 has a total of 3 processes (processing stages). There are 2 parallel machines in the first processing stage, 3 parallel machines in the second stage, and 3 parallel machines in the third stage. After the workpiece selects the corresponding factory, it needs to go through all the processing stages of the factory to complete the production of the workpiece. After all the workpieces corresponding to the product are produced, it enters the assembly process for the final welding of the product. For example, Product 1 needs to be welded in the assembly process after the production of 4 components (workpieces 1-4). The processing times of the products and workpieces in each process are known.

[0086] S2. Build a distributed hybrid flow shop scheduling model including the assembly process based on the basic information. The distributed hybrid flow shop scheduling model includes an objective function and constraint conditions.

[0087] The objective function is to minimize the maximum completion time of the product, characterized as min C max , where:

[0088]

[0089] where c l is the assembly completion time of product l; l ∈ L = {1, 2, …, q}.

[0090] The constraints are as follows:

[0091] Ensure that each workpiece is assigned to one factory for processing, that is:

[0092]

[0093] Ensure that there is exactly one piece of equipment for processing at each stage within the factory, that is:

[0094]

[0095] Ensure the precedence relationship in the processing of workpieces on the equipment, that is:

[0096]

[0097] Ensure that the workpiece can enter the next stage only after it is completed in the previous stage of the factory, that is:

[0098]

[0099] Ensure that the completion time of the workpiece in the first stage is greater than or equal to its processing time, that is:

[0100]

[0101] Ensure the time constraints for workpieces processed successively in the same stage, that is:

[0102]

[0103] Calculate that the assembly start time of the product is later than the completion time of its last workpiece, that is:

[0104]

[0105] Ensure the precedence constraints in time during the assembly stage of the product, that is:

[0106]

[0107] Valid inequalities improve the lower bound of the model, that is:

[0108]

[0109] Define the value range of the variables, that is:

[0110]

[0111] where x isis a 0-1 variable, taking 1 means workpiece i is assigned to factory s for processing, otherwise taking 0; y isjk is a 0-1 variable, taking 1 means workpiece i is assigned to the k-th device in the j-th stage of factory s for processing, otherwise taking 0; z sjii′k is a 0-1 variable, taking 1 means workpiece i has priority over workpiece i′ in the k-th device in the j-th stage of factory s for processing, otherwise being 0; c isj is a continuous variable, representing the completion time of workpiece i in the j-th stage of factory s; v ll′ is a 0-1 variable, taking 1 means product l has priority over product l′ in the assembly stage for processing, otherwise taking 0; p l is the assembly time of product l; p isj is the processing time of workpiece i in the j-th stage of factory s; g il is a 0-1 parameter, taking 1 means workpiece i belongs to product l, otherwise being 0; c l is a continuous variable, the assembly completion time of product l; M is a sufficiently large positive integer, which can be taken as

[0112] S3. Solve the distributed hybrid flow shop scheduling model by using an improved genetic algorithm that introduces an elite selection strategy and a neighborhood search operator to obtain a scheduling plan; if the improved genetic algorithm reaches the termination condition, end and visually output the result. The specific steps of the improved genetic algorithm in step S3 are as follows:

[0113] S31. Individual coding: For this distributed hybrid flow shop scheduling problem, two-layer coding is adopted. The total length of the chromosome is the number of workpieces n. As Figure 2 shown, taking a small-scale example with 3 products, 7 workpieces, and 3 workshops as an example, each individual has a total of 7 gene positions. The first-layer coding information shows the factory to which each workpiece is assigned, and each gene position corresponds to a factory number. In the second-layer coding information, each gene represents a random number in the interval [0,1]. According to the first-layer coding information, the set of workpieces to be processed in each factory is determined, and the processing priorities of the workpieces in the corresponding factory are obtained by sorting according to the values of the second-layer coding information. As Figure 2 shown, the first workpiece is selected to be processed in factory 2, and at the same time, workpiece 5 and workpiece 7 are also processed in factory 2. The processing priorities of the workpieces in the factory are workpiece 1, workpiece 7, and workpiece 5.

[0114] S32. Individual decoding: The machine selects the earliest available machine first strategy. After determining the set of processed workpieces in the factory and the priority of workpiece processing in the factory according to the encoding result, it allocates equipment to the workpieces of each factory, and allocates them to the earliest available machine in turn according to the processing priority of the workpieces. In the assembly stage, the earliest assembly time is determined according to the completion time of all workpieces involved in each product. The product with the smallest earliest assembly time among all products is assembled first. After determining the assembly sequence, start time and completion time, the maximum completion time of the product is obtained, that is, the fitness value of the individual.

[0115] S33. Initialize the population: Determine the population size pop size , and initialize the population according to the encoding rules.

[0116] S34. Elite memory bank update: Use the inflection point as the demarcation point of the population, and the individuals with fitness values not greater than the inflection point are saved in the elite memory bank. First, sort the individuals in the population from smallest to largest according to the fitness value to obtain a curve related to the fitness value. Secondly, generate a line by connecting the point with the smallest fitness value and the point with the largest fitness value. Calculate the distance between each point on the curve and the straight line, and select the point with the largest distance from the straight line as the inflection point.

[0117] S35. Selection operation: Adopt an algorithm that combines tournament selection and elite selection.

[0118] Tournament selection method: Select randomly 2 individuals from the population through the tournament method, compare them, and retain the individual with the better fitness value in the next generation population.

[0119] Elite selection strategy: Set a dynamic elite selection threshold, set the threshold as high as possible in the early stage to ensure the preservation of the elite population; lower the threshold in the later stage to avoid the algorithm falling into local optimum. The threshold update formula is:

[0120] r = (i - MaxGen)2(1 - MaxGen)2.

[0121] It means that in the i-th iteration, a random number μ is randomly generated, 0 < μ < 1. If μ < r, select an individual from the elite memory bank and put it into the offspring; otherwise, select an individual using the tournament method and put it into the offspring.

[0122] S36. Crossover operation: With a certain crossover probability p c Randomly select two individuals in the population, randomly select two crossover points in the individuals, and perform gene exchange between the two individuals. As Figure 3 shown, exchange the chromosome genes between crossover point 1 and crossover point 2 to obtain two new individuals.

[0123] S37. Mutation operation: With a certain mutation probability pm Select an individual for mutation operation, and randomly select any gene position for replacement. As Figure 4 shown, select the 3rd workpiece for mutation, move it from Factory 3 to Factory 1 for processing, and at the same time regenerate a random number within [0,1].

[0124] S38. Improvement of the neighborhood search operator based on the critical path: After determining the chromosome scheme according to the decoding rule, use a directed network graph to represent the scheme. The nodes represent the production stages (processes) of the workpieces, and the directed arcs represent the sequential constraint relationships. As Figure 5 shown, taking a small-scale example with 2 products and 7 workpieces as an example, the product nodes are (0,1) and (0,2) respectively, and other nodes (i,j) represent the jth processing stage of workpiece i. The sequential constraints include the inter-process sequence (such as (1,1) → (1,2)), the assembly sequence between products (such as (0,1) → (0,2)), the processing sequence on the machine (such as (4,1) → (6,1)), and the sequential constraint of the last process of the product and the workpiece (such as (4,3) → (0,1)). Use the critical path method to find a critical path on the network graph, and the length of the path (the sum of the processing times of all nodes on the path) is equal to the objective function value of the chromosome. Obtain the serial numbers of the workpieces on the critical path, find the processing factories corresponding to the workpieces, reorder the workpieces in the factory according to the assembly sequence of the products in the critical path. If they belong to the same product, the processing order of the workpieces is random. Next, reassign the second-layer coding information of the chromosome according to the new order of the workpieces. Finally, judge whether the fitness value of the individual is better. If it is better, accept the individual.

[0125] S39. Determine that the maximum number of iterations of the algorithm is MaxGen and the interval generation is GapGen. When the current number of iterations is greater than the maximum number of iterations or the optimal value of the population remains unchanged for consecutive GapGen generations, the algorithm terminates.

[0126] In this embodiment, the flowchart of using the improved genetic algorithm to solve the distributed hybrid flow shop scheduling model is as Figure 7 shown. In this example, the parameter settings are as follows: the population size pop size is 100, the crossover probability p c is 0.9, the mutation probability p m is 0.1, the maximum number of iterations MaxGen is 100, and the interval generation GapGen is 20. Use Python 3.10 to code the above scheduling algorithm, and calculate the critical path through the networkx library and the forward topological sorting strategy.

[0127] The calculation results are output through a Gantt chart, as Figure 8The production scheduling results of the instances are shown. The assembly stage is the product number, and the workpieces are processed in a mixed-flow manner on various devices in the distributed factory, showing the corresponding workpiece numbers in Table 1. The equipment numbers (3, 3, 2) in the figure represent the second device in the third stage of Factory 3. The optimal objective function value is 25, that is, the assembly time for completing the last product in the assembly stage is 25.

[0128] To evaluate the overall performance of the scheduling algorithm, simulation experiments were conducted for comparison. As shown in Table 3, the comparison results of different algorithms under 8 instances are presented. Gurobi is the solution result of a commercial solver, and the solution time limit for the model is 3600s. "UB" and "LB" in the table represent the upper bound and lower bound of the solver respectively, "Gap" represents the relative difference between the upper and lower bounds of the model within the limited solution time, "Time" represents the solution time of the model. If the model does not find the optimal solution within the solution time limit, then "(Time)" represents the earliest time when the solver obtains the current upper bound "UB".

[0129] EGANS represents the algorithm proposed in the present invention, and GA represents the classical genetic algorithm without elite selection and neighborhood search strategies. Among them, "best" and "avg" respectively represent the best solution and the average expected value obtained by running the algorithm independently 10 times, and "Time" represents the average solution time of running the algorithm independently 10 times.

[0130] Table 3 Comparison Results of Algorithms

[0131]

[0132]

[0133] Through the result comparison, it can be found that the EGANS algorithm proposed in the present invention has a similar solution quality to the Gurobi solver for simple small-scale instances, and the solution time is significantly lower for more complex large-scale instances. The EGANS algorithm is significantly better than the GA algorithm in terms of solution quality within the effective time, indicating that the proposed elite memory selection and neighborhood search algorithms have good effects and can effectively improve the solution quality of the algorithm.

[0134] The present invention aims to minimize the maximum completion time of the product and constructs a distributed hybrid flow shop scheduling model including the assembly process. This method designs a genetic algorithm framework with multi-layer coding and introduces an elite selection strategy and a neighborhood search operator into it. The elite selection strategy ensures that high-quality individuals are retained during the iteration process, accelerating the convergence speed of the algorithm. The network diagram method is used to identify the critical path, and the scheduling bottleneck is optimized by performing neighborhood search on critical workpieces, improving the quality of the solution and avoiding falling into local optima. The present invention can not only significantly improve the scheduling efficiency of rocket tanks, but also has good applicability and generality, and can be widely applied to other types of distributed hybrid flow shop scheduling environments.

[0135] Those of ordinary skill in the art can understand that all or part of the steps in the methods of the above embodiments can be completed by instructing relevant hardware through a program. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0136] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and reference can be made to the partial description of the method embodiments for the relevant parts.

[0137] The above embodiments have introduced the present invention in detail. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. At the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A distributed hybrid flow shop scheduling method for rocket tank production, characterized in that: The method includes the following process: Obtain basic information on the production of each component structure of the rocket tank, including product information and factory information; Based on the basic information, a distributed hybrid flow shop scheduling model including the assembly process is constructed. The distributed hybrid flow shop scheduling model includes an objective function and constraint conditions. An improved genetic algorithm with elite selection strategy and neighborhood search operator is used to solve the distributed hybrid flow shop scheduling model to obtain the scheduling solution. If the improved genetic algorithm reaches the termination condition, it ends and the results are output visually. The specific process includes: Individual coding: For the distributed hybrid flow shop scheduling problem, two layers of coding information are used to show the factory to which each workpiece is assigned and the processing priority in the corresponding factory; the total length of the chromosome is the number of workpieces, the first layer of coding information is the factory number, and each gene in the second layer of coding information represents a random number in the interval [0,1]. The set of workpieces to be processed in each factory is determined based on the first layer of coding information, and the processing priority of the workpiece in the corresponding factory is obtained by sorting according to the value of the second layer of coding information; Individual decoding: In the production stage, the workpieces of each factory are allocated to the earliest available machines according to their processing priority. In the assembly stage, the earliest assembly time is determined according to the completion time of all workpieces involved in each product, and the product with the shortest earliest assembly time is assembled first. After determining the assembly sequence and the start and completion time, the maximum completion time of the product is obtained, which is the individual fitness value. Initialize the population: determine the population size pop size , initialize the population according to the encoding rules; Elite memory bank update: using the inflection point as the dividing point of the population, individuals with fitness values ​​not greater than the inflection point are stored in the elite memory bank; Selection operation: An algorithm combining tournament selection and elite selection is used to select operators; Crossover operation: with crossover probability p c Randomly select two individuals in the population, randomly select two crossover points in the individuals, and exchange genes between the two individuals; Mutation operation: with mutation probability p m Select individuals for mutation operation and randomly select any gene position for replacement; Improvement of neighborhood search operator based on critical path: Use the critical path method to find a critical path on the network graph. The length of the path is equal to the objective function value of the chromosome. The length of the path is the processing time of all nodes on the path. Get the workpiece number on the critical path, find the processing factory corresponding to the workpiece, and reorder the workpieces in the factory according to the assembly order of the products in the critical path. If they belong to the same product, the order of workpiece processing is random; Reassign the second-level encoding information of the chromosome according to the new order of the workpieces; Finally, determine whether the individual's fitness value is better, and if so, accept the individual; Let the maximum number of iterations be MaxGen and the interval generation be GapGen. The algorithm terminates when the current number of iterations is greater than the maximum number of iterations MaxGen or when the optimal value of the population for consecutive GapGen generations remains unchanged.

2. The distributed hybrid flow shop scheduling method according to claim 1 is characterized in that: The product information is described as follows: each tank product of a rocket tank is composed of multiple corresponding workpieces.

3. The distributed hybrid flow shop scheduling method according to claim 1, characterized in that: The description of the factory information is: The tank products are produced in f distributed factories, each of which s∈S={1,2,…,f} is a mixed flow workshop with different processing technology and capacity; Workpiece i∈N={1,2,…,n} can and can only choose one of the factories for processing, and there is a factory availability restriction. The set of alternative factories for workpiece i is represented as In a mixed flow shop, the workpiece needs to pass through j∈J s ={1,2,…,h s } stages, each stage j has at most m sj ≥1 parallel machines with the same performance are available for production, and the equipment set is represented by M sj ={1,2,…,m sj }, each workpiece must go through all the processing stages in the factory, and at most one piece of equipment is selected for processing in each stage. The processing time of workpiece i in the jth stage of factory s is p isj ; After the processing is completed, the assembly phase begins. The assembly phase is carried out by a work team. Each product l∈L={1,2,…,q},n≥q can only be assembled after all the workpieces belonging to it have been processed. il is a 0-1 parameter, 1 means workpiece i belongs to product l, otherwise it is 0. The order of products should be considered in the assembly stage, and the assembly time is p l .

4. The distributed hybrid flow shop scheduling method according to claim 3 is characterized in that: The objective function is to minimize the maximum completion time of the product, represented by minC max ,in: In the formula, c l is the assembly completion time of product l; l∈L={1,2,…,q}.

5. The distributed hybrid flow shop scheduling method according to claim 4 is characterized in that: The constraints are: Ensure that each workpiece is assigned to a factory for processing, that is: Ensure that the workpiece is processed by only one device at each stage in the factory, namely: Ensure that there is a sequence relationship between the workpieces processed on the equipment, namely: Ensure that the workpiece can enter the next stage only after the previous stage of the factory is completed, that is: Ensure that the completion time of the workpiece in the first stage is greater than or equal to its processing time, that is: Ensure the time constraints of workpieces processed successively at the same stage, namely: Ensure that the assembly start time of the product is later than the completion time of all the component workpieces, that is: Ensure that the products have time constraints in the assembly stage, namely: The effective inequality improves the lower bound of the model, namely: Define the value range of the variable, that is: In the formula, x is is a 0-1 variable, 1 means that job i is assigned to factory s for processing, otherwise it is 0; y isjk is a 0-1 variable, taking 1 to indicate that job i is assigned to the kth equipment in the jth stage of factory s for processing, otherwise it takes 0; z sjii′k is a 0-1 variable, which takes 1 to indicate that job i is processed before job i′ in the kth equipment in the jth stage of factory s, otherwise it takes 0; c isj is a continuous variable, indicating the completion time of job i in the jth stage of factory s; v ll′ is a 0-1 variable, taking the value of 1 to indicate that product l is processed before product l′ in the assembly stage, otherwise it takes the value of 0; M is a sufficiently large positive integer.

6. The distributed hybrid flow shop scheduling method according to claim 1, characterized in that: The method for determining the inflection point is: First, sort the individuals in the population from small to large according to their fitness values ​​to obtain a curve related to the fitness values; second, generate a line by connecting the point with the smallest fitness value and the point with the largest fitness value; finally, calculate the distance between each point on the curve and the straight line, and select the point with the largest distance to the straight line as the inflection point.

7. The distributed hybrid flow shop scheduling method according to claim 6 is characterized in that: In the selection operation, Tournament selection: Randomly select two individuals from the population for comparison, and retain the individual with better fitness value to the next generation of population; Elite selection: Set a dynamic elite selection threshold. Set the threshold to a high threshold in the early stage and lower it in the later stage. The threshold update formula is: Where MaxGen is the maximum number of iterations; At the i-th iteration, a random number μ is randomly generated, 0<μ<1. If μ<r, an individual is selected from the elite memory bank and placed in the offspring; Otherwise, use the tournament method to select an individual to be placed in the offspring.

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