Distributed hybrid flow shop scheduling method for rocket tank production

Abstract

The invention relates to the technical field of workshop production scheduling, in particular to a distributed hybrid flow workshop scheduling method oriented to rocket tank production, and aims to construct a distributed hybrid flow workshop scheduling model including an assembly process by taking the maximum completion time of a minimized product as an objective function. According to the method, a multi-layer coding genetic algorithm framework is designed, and an elite selection strategy and a neighborhood search operator are introduced into the framework. The elite selection strategy ensures that high-quality individuals are reserved in the iteration process, and the convergence speed of the algorithm is increased; a network diagram method is adopted to identify key paths, neighborhood search is carried out on key workpieces, the scheduling bottleneck is optimized, the quality of solutions is improved, and local optimum is avoided. The method not only can greatly improve the scheduling efficiency of the rocket tank, 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 in particular to a distributed hybrid flow workshop scheduling method for rocket tank production. Background Art

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

[0003] Current research on workshop scheduling mainly focuses on single workshops or simple flow workshop models, while less consideration is given to complex distributed hybrid flow workshop scheduling problems with assembly processes. Although traditional exact algorithms, such as branch and bound and branch and price, can find the optimal solution, they have high computational complexity when faced with large-scale orders and often cannot be solved within a reasonable time. Therefore, more and more research has begun to tend to adopt meta-heuristic algorithms, such as genetic algorithms and particle swarm optimization, which have shown advantages in solving large-scale engineering problems and can find satisfactory approximate solutions in a relatively 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 global search capabilities. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a distributed hybrid assembly line workshop scheduling method for rocket tank production, which solves the technical problem of distributed hybrid assembly line workshop scheduling for complex assembly processes and the technical problem that the existing algorithms are prone to fall into local optimal solutions.

[0005] In order 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 comprising the following processes:

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

[0007] 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.

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

[0009] Furthermore, the product information is described as: the workpiece composition corresponding to each tank product of the rocket tank.

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

[0011] 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;

[0012] 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

[0013] 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 ;

[0014] 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 are processed. The parameter g 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 .

[0015] Furthermore, the objective function is to minimize the maximum completion time of the product, represented by minC max ,in:

[0016]

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

[0018] Furthermore, the constraint condition is:

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

[0020]

[0021] Ensure that the workpiece is processed by only one piece of equipment at each stage in the factory, namely:

[0022]

[0023] Ensure that there is a sequence relationship between the workpieces processed on the equipment, namely:

[0024]

[0025] Ensure that the workpiece can enter the next stage only after the previous stage of the factory is completed, that is:

[0026]

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

[0028]

[0029] Ensure the time constraints of workpieces processed successively at the same stage, namely:

[0030]

[0031] The assembly start time of the calculated product must be later than the completion time of its last workpiece, that is:

[0032]

[0033] Ensure that the products have time constraints in the assembly stage, namely:

[0034]

[0035] The effective inequality improves the lower bound of the model, namely:

[0036]

[0037] Define the value range of the variable, that is:

[0038]

[0039] 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′kis 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.

[0040] Furthermore, the distributed hybrid flow shop scheduling model is solved to obtain a scheduling solution, and the specific process includes:

[0041] 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;

[0042] 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.

[0043] Initialize the population: determine the population size pop size , initialize the population according to the encoding rules;

[0044] 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;

[0045] Selection operation: An algorithm combining tournament selection and elite selection is used to select operators;

[0046] 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;

[0047] Mutation operation: with mutation probability p m Select individuals 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 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.

[0049] 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;

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

[0051] Finally, determine whether the individual's fitness value is better, and if so, accept the individual;

[0052] 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.

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

[0054] 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.

[0055] Further, in the selection operation,

[0056] 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;

[0057] 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:

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

[0059] Where MaxGen is the maximum number of iterations;

[0060] 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, an individual is selected using the tournament method and placed in the offspring.

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

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

[0063] 2. The present invention adopts an improved genetic algorithm framework to solve a type of distributed hybrid flow shop scheduling problem for the production and assembly of rocket tank products. The model takes into account realistic constraints such as the differences in processing capabilities of distributed factories and the lead time window of the assembly process. The algorithm design incorporates strategies such as an elite memory library and elite selection operator based on inflection points, as well as a neighborhood search based on the critical path. The effectiveness of the model and algorithm is verified through simulation results.

[0064] 3. The present invention introduces an elite selection threshold to ensure the transmission 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, the critical path in the current solution is identified to accurately optimize the production schedule of key workpieces. This operator can fine-tune key tasks, allowing the algorithm to more effectively explore a better solution space, thereby improving the global search capability. BRIEF 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 on 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 individual coding of the improved genetic algorithm in the present invention;

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

[0069] Figure 4 A schematic diagram of a 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 This is a schematic diagram of the assembly of the storage tank product of the present invention;

[0072] Figure 7 A flowchart of the improved genetic algorithm in the present invention;

[0073] Figure 8 This is a Gantt chart of the production scheduling results of the example in the present invention. DETAILED DESCRIPTION

[0074] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods, so that the implementation process of how the present 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 genetic algorithms are usually performed randomly, this may cause the search process to fall into a local optimum. Please refer to Figure 1-Figure 8 This embodiment proposes a distributed hybrid flow shop scheduling method for rocket tank production. It introduces an elite memory library and a neighborhood search operator that considers the critical path to enhance the algorithm performance, introduces an elite selection threshold, ensures the delivery of high-quality individuals in the early stage, and increases the randomness of the algorithm in the later stage. At the same time, after adding the neighborhood search operator of the critical path, the critical path in the current solution is identified to accurately optimize the production schedule of key workpieces. This operator can fine-tune key tasks so that the algorithm can more effectively explore a better solution space, thereby improving the global search capability. The method includes the following steps:

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

[0077] Specifically, the product information is described as follows: the workpieces corresponding to each tank product of the rocket tank are composed. This embodiment is a specific example of applying the above method to the production of a rocket tank, such as Figure 6 As shown, the rocket tank is welded together by three tank products: a thin-walled cylinder in the middle (tank section) and a hemispherical body (tank bottom) at both ends. The thin-walled cylinder is manufactured in sections according to each tube section, and one tank product is welded together by multiple workpieces.

[0078] The description of factory information is: rocket tank products are produced in f distributed factories, each factory s∈S={1,2,…,f} is a mixed flow shop with different processing technology and capabilities. 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 candidate 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. The parameter g 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 The production system diagram is as follows: Figure 1 shown.

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

[0080] Table 1 Product information

[0081]

[0082]

[0083] Table 2 Factory Information

[0084]

[0085] As shown in Table 1 and Table 2, the enterprise currently has 3 distributed factories, with a total of 3 tank products to be processed. Products 1, 2, and 3 are composed of 4, 3, and 4 workpieces respectively. The workpieces can be processed in the selected factories. Each factory is a mixed flow workshop. The number of stages of factory processing products is different. There are multiple parallel machines to choose from in each stage. For example, Factory 1 has a total of 3 processes (processing stages). The first processing stage has 2 parallel machines, the second stage has 3 parallel machines, and the third stage has 3 parallel machines. After selecting the corresponding factory, the workpiece needs to go through all the processing stages of the factory to complete the workpiece production. After all the workpieces corresponding to the product are produced, they enter the assembly process for the final assembly and welding of the product. For example, product 1 needs to be assembled and welded in the assembly process after the production of 4 components (workpieces 1-4). The processing time of the product and workpiece in each process is known.

[0086] S2. A distributed hybrid flow shop scheduling model including the assembly process is constructed based on the basic information. The distributed hybrid flow shop scheduling model includes an objective function and constraints.

[0087] The objective function is to minimize the maximum completion time of the product, represented by min C max ,in:

[0088]

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

[0090] The constraints are:

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

[0092]

[0093] Ensure that the workpiece is processed by only one piece of equipment at each stage in the factory, namely:

[0094]

[0095] Ensure that there is a sequence relationship between the workpieces processed on the equipment, namely:

[0096]

[0097] Ensure that the workpiece can enter the next stage only after the previous stage of the factory is completed, 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 of workpieces processed successively at the same stage, namely:

[0102]

[0103] The assembly start time of the calculated product must be later than the completion time of its last workpiece, that is:

[0104]

[0105] Ensure that the products have time constraints in the assembly stage, namely:

[0106]

[0107] The effective inequality improves the lower bound of the model, namely:

[0108]

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

[0110]

[0111] In the formula, x isis 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, which takes 1 to indicate that product l is processed before product l′ in the assembly stage, otherwise it takes 0; p l is the assembly time of product l; p isj is the processing time of job i in the jth stage of factory s; g il is a 0-1 parameter, 1 means workpiece i belongs to product l, otherwise it is 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, using the improved genetic algorithm that introduces the elite selection strategy and the neighborhood search operator to solve the distributed hybrid flow shop scheduling model to obtain a scheduling solution; if the improved genetic algorithm reaches the termination condition, it ends and visualizes the output results. The specific steps of the improved genetic algorithm in step S3 are:

[0113] S31. Individual coding: Two-layer coding is used for the distributed hybrid flow shop scheduling problem. The total length of the chromosome is the number of workpieces n, such as Figure 2 As shown in the figure, a small-scale example with 3 products, 7 workpieces, and 3 workshops is taken as an example. Each individual has 7 gene bits. The first layer of coding information shows the factory to which each workpiece is assigned. Each gene bit corresponds to a factory number. 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 according to 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, as shown in Figure 2 The first workpiece is selected to be processed in Factory 2. Workpieces 5 and 7 are also processed in Factory 2. The processing priority of workpieces in the factory is Workpiece 1, Workpiece 7 and Workpiece 5.

[0114] S32, Individual decoding: The machine selection adopts the earliest available machine priority strategy. After determining the factory's processing workpiece set and the priority of workpiece processing in the factory based on the encoding results, the workpieces of each factory are allocated to the equipment and are allocated to the earliest available machine in turn according to the workpiece processing priority; in the assembly stage, the earliest available assembly time is determined according to the completion time of all workpieces involved in each product, and the product with the smallest earliest available assembly time is assembled first. After determining the assembly order and the start and completion time, the maximum completion time of the product is obtained, that is, the individual fitness value.

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

[0116] S34, elite memory library update: Use the inflection point as the dividing point of the population, and the individuals with fitness values ​​not greater than the inflection point are stored in the elite memory library. First, sort the individuals in the population from small to large according to the fitness value to obtain a curve related to the fitness value. Secondly, generate a line by connecting the point with the minimum fitness value and the point with the maximum fitness value. 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.

[0117] S35, selection operation: adopt an algorithm that combines tournament selection and elite selection.

[0118] Tournament selection method: Through the tournament selection method, two individuals are randomly selected from the population, compared, and the individual with better fitness value is retained 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 the local optimum. The threshold update formula is:

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

[0121] Indicates that 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, an individual is selected using the tournament method and placed in 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 exchange genes between the two individuals, such as Figure 3 As shown, the chromosome genes between crossover point 1 and crossover point 2 are exchanged to obtain two new individuals.

[0123] S37, mutation operation: with a certain mutation probability pm Select individuals for mutation operation and randomly select any gene position for replacement. Figure 4 As shown, the third workpiece is selected for mutation and moved from factory 3 to factory 1 for processing, and a random number is regenerated in [0,1].

[0124] S38. Improvement of the neighborhood search operator based on the critical path: After determining the chromosome scheme according to the decoding rules, the scheme is represented by a directed network graph, where the nodes represent the production stages (processes) of the workpieces and the directed arcs represent the sequential constraints. Figure 5 As shown in the figure, a small-scale example with 2 products and 7 workpieces is taken as an example. The product nodes are (0, 1) and (0, 2) respectively, and the other nodes (i, j) represent the jth processing stage of workpiece i. The order constraints include the order between processes (such as (1, 1) → (1, 2)), the assembly order between products (such as (0, 1) → (0, 2)), the processing order on the machine (such as (4, 1) → (6, 1)), and the order constraints of the last process of products and workpieces (such as (4, 3) → (0, 1)). The critical path method is used to find a critical path on the network graph. The length of the path (the processing time of all nodes on the path) is equal to the objective function value of the chromosome. The workpiece serial number on the critical path is obtained, and the processing factory corresponding to the workpiece is found. The workpieces in the factory are reordered 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. Next, the second-layer encoding information of the chromosome is reassigned according to the new order of the workpieces. Finally, it is determined whether the fitness value of the individual is better. If it is better, the individual is accepted.

[0125] S39, determining the maximum number of iterations of the algorithm as MaxGen and the number of interval generations as GapGen. When the current number of iterations is greater than the maximum number of iterations or when the optimal value of the population of consecutive GapGen generations remains unchanged, 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 follows: Figure 7 In this example, the parameters are set as follows: Population size pop size is 100, and 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. The above scheduling algorithm is coded using Python 3.10, and the critical path is calculated using the networkx library and the forward topological sorting strategy.

[0127] The calculation results are output through the Gantt chart, such as Figure 8The scheduling results of the example are shown. The assembly stage is the product number. The workpieces are mixed and processed in various equipment in the distributed factory. The corresponding workpiece numbers in Table 1 are shown. The equipment number (3,3,2) in the figure represents the second equipment in the third stage of factory 3. The optimal objective function value is 25, that is, the assembly time of the last product in the assembly stage is 25.

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

[0129] EGANS represents the algorithm proposed in the present invention, GA represents the classical genetic algorithm excluding elite selection and neighborhood search strategies, wherein “best” and “avg” represent the best solution and average expected value obtained by running the algorithm independently 10 times, respectively, and “Time” represents the average solution time of running the algorithm independently 10 times.

[0130] Table 3 Algorithm comparison results

[0131]

[0132]

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

[0134] The present invention takes minimizing the maximum completion time of the product as the objective function and constructs a distributed hybrid flow shop scheduling model including the assembly process. The method designs a multi-layer encoded genetic algorithm framework, 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, which speeds up the convergence of the algorithm; the network graph method is used to identify the critical path, and the production bottleneck is optimized by performing a neighborhood search on the key workpieces, thereby improving the quality of the solution and avoiding falling into the local optimum. The present invention can not only greatly improve the production efficiency of rocket tanks, but also has good applicability and versatility, and can be widely used in other types of distributed hybrid flow shop scheduling environments.

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

[0136] Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0137] The above implementation methods have been described in detail. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on 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 that introduces elite selection strategy and neighborhood search operator is used to solve the distributed hybrid flow shop scheduling model to obtain a scheduling solution; if the improved genetic algorithm reaches the termination condition, it ends and the results are output visually.

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

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 are processed. The parameter g 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: The assembly start time of the calculated product must be later than the completion time of its last workpiece, 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 distributed hybrid flow shop scheduling model is solved to obtain a scheduling solution, and 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.

7. The distributed hybrid flow shop scheduling method according to claim 6 is 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.

8. The distributed hybrid flow shop scheduling method according to claim 6, 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: r=(i-MaxGen)2(1-MaxGen)2. 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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