Solving Method for Integrated Scheduling of Batch Processing and Transportation in Hybrid Flow Shop

Abstract

The present invention relates to the technical field of integrated scheduling of hybrid flow shop production and transportation, and particularly belongs to a solution method for integrated scheduling of batch processing and transportation in a hybrid flow shop. It includes establishing the solution goal of minimizing the makespan and initializing parameters, using a combined heuristic rule to generate P individuals in the population; constructing the main solution; using a variable neighborhood descent search strategy to perform neighborhood search on the main solution, and if an individual with a smaller objective value is found, replacing the individual with the smaller objective value with a new main solution; performing the operation of reconstructing the population; updating the optimal individual, judging whether the termination condition is satisfied, if satisfied, outputting the individual with the smallest objective value, otherwise continuing to optimize. The present invention can improve the overall production efficiency, optimize the resource utilization rate and reduce the production cost.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated scheduling of mixed flow shop production and transportation, and particularly belongs to a solution method for integrated scheduling of batch processing and transportation in a mixed flow shop. Background Art

[0002] In the current production context, with the increasing demand of the manufacturing industry for high efficiency, flexibility, and intelligence, traditional production models face numerous challenges. Especially in complex multi-production-stage and multi-machine parallel processing environments, how to effectively coordinate resources, improve production efficiency, and reduce costs has become a problem to be solved by manufacturing enterprises. To address this challenge, more and more enterprises are continuously optimizing production processes by introducing flexible scheduling and resource allocation methods, thereby enhancing overall production efficiency and promoting the development of the manufacturing industry towards a more intelligent and efficient direction.

[0003] With the rapid development of the manufacturing industry, the integrated scheduling problem of batch processing and transportation in a mixed flow shop has gradually become a research hotspot. This problem involves the coordination between machines, the dynamic scheduling of batches, and the optimization of the transportation link. With the high integration of production and logistics, traditional optimization methods often fail to effectively combine equipment load balancing and transportation efficiency, resulting in insufficient utilization of resources. Therefore, it is necessary to break through the existing limitations and promote the deep coordination of the manufacturing process and logistics scheduling, so as to enhance production capacity and flexibility. Summary of the Invention

[0004] The present invention provides a solution method for integrated scheduling of batch processing and transportation in a mixed flow shop, which solves the technical problem that existing methods are difficult to balance equipment load and transportation efficiency in scenarios where complex production and transportation are closely intertwined, so as to achieve the purpose of enhancing overall production efficiency, optimizing resource utilization rate, and reducing production costs.

[0005] The solution method for integrated scheduling of batch processing and transportation in a mixed flow shop provided by the present invention is characterized by including the following steps:

[0006] S1. Analyze the problem characteristics of the integrated scheduling problem of batch processing and transportation in a mixed flow shop in cold-drawn seamless steel pipe manufacturing, establish the solution goal of minimizing the makespan, and initialize parameters, including the population size P, the maximum number of failures V of the main solution in each neighborhood structure, and the maximum number of failures C of the main solution to update the population;

[0007] S2. Use a combined heuristic rule to generate P individuals in the population;

[0008] S3. Use a cooperation strategy based on a memory mechanism to fully exploit the historical information of existing high-quality individuals in the population to construct the main solution;

[0009] S4. Perform neighborhood search on the main solution using a variable neighborhood descent search strategy through five neighborhood structures. If an individual with a smaller objective value is found, replace the individual with the smaller objective value as the new main solution;

[0010] S5. Reconstruct the population operation. P / 3 individuals in the new population are generated by a combinatorial heuristic rule and perturbed by introducing batch exchange and sub-batch mutation. Another P / 3 individuals are randomly generated, and the remaining P / 3 individuals are selected from the high-quality individuals retained in the original population and perturbed by using batch partial random sorting and sub-batch mutation;

[0011] S6. Update the optimal individual, judge whether the termination condition is satisfied. If satisfied, output the individual with the smallest objective value; otherwise, return to step S3 to continue optimization.

[0012] Furthermore, in the population, each complete individual consists of two parts. The first part is the batch processing sequence, denoted as ∏N = {π1, …, πj, …, πN}, where πj represents the index of the j-th batch and N represents the total number of batches. The batch processing sequence is used to define the processing order of batches. The second part is the batch splitting information, which is represented by a three-dimensional vector ΦS = {Ψ1, …, Ψk, …, ΨS}, where S represents the total number of production stages, and Ψk represents the batch splitting information of all batches in production stage k. Ψk is a two-dimensional batch splitting matrix of size N×e, where N represents the total number of batches and e represents the number of sub-batches included in each batch. The two-dimensional batch splitting matrix Ψk(j, e) represents the number of processing units included in the e-th sub-batch of the j-th batch in production stage k.

[0013] Furthermore, in the population, the allocation rules adopted when allocating machines in each production stage and automatic guided vehicles during transportation are as follows. For the selection of machines in each production stage, the earliest available time rule is used as the allocation criterion, that is, from all available machines in the current production stage, preferentially select the machine that starts processing earliest to process the current batch. For the allocation of automatic guided vehicles, the automatic guided vehicle performs transportation tasks in units of sub-batches and is allocated using the shortest transportation time rule, that is, select the automatic guided vehicle with the shortest transportation time between the current sub-batch location and all available automatic guided vehicles.

[0014] Furthermore, the process of generating P individuals by the combinatorial heuristic rule includes the following steps

[0015] Step 1. Divide each batch πj according to the batch splitting strategy;

[0016] Step 2. Obtain the batch processing sequence ∏N = {π1, …, πj, …, πN} according to the batch sorting rule;

[0017] Step 3: Extract the first two batches from the batch processing sequence, denoted as batch π1 and batch π2 respectively, to form two partial batch processing sequences with different orders. The first one is the partial batch processing sequence with batch π1 in the front and batch π2 in the back; the second one is the partial batch processing sequence with batch π2 in the front and batch π1 in the back. Calculate the objective values of the two partial batch processing sequences respectively, and determine the partial batch processing sequence with the minimum objective value as the current partial batch processing sequence.

[0018] Step 4: Repeat the following steps 4-1 and 4-2 for the subsequent batches, where

[0019] Step 4-1: Insert batch πj into each insertion position in the current partial batch processing sequence. There are j insertion positions in total, and the corresponding partial batch processing sequences are generated respectively, and the objective values are obtained. At this time, the partial batch processing sequence consists of j - 1 batches.

[0020] Step 4-2: Select the partial batch processing sequence that generates the minimum objective value as the current partial batch processing sequence.

[0021] Step 5: Repeat Steps 1 - 4 until P individuals are obtained.

[0022] Furthermore, the batch splitting strategy includes

[0023] Uniform splitting: evenly split the processing units of each batch into each sub-batch;

[0024] Maximum splitting: when each batch is processed on the batch processing machine, there is a maximum number of processing units that the batch processing machine can process. According to the maximum number of processing units that the batch processing machine can carry, allocate the processing units to the sub-batches to the maximum extent.

[0025] Random splitting: randomly divide the processing units of each batch into multiple sub-batches;

[0026] Greedy splitting: for each batch to be divided, when allocating the processing units to each sub-batch, calculate the objective values generated when the processing units are allocated to different sub-batches in turn. Subsequently, select the sub-batch that generates the minimum objective value as the optimal allocation position of the current processing unit.

[0027] Furthermore, the batch sorting rules include: Random sorting, randomly arrange the processing order of all batches;

[0028] First-stage start time sorting: sort in ascending order according to the start time of each batch in the first production stage; First-stage start time and total processing time sorting: add the start time of each batch in the first production stage to the corresponding processing time, and sort in ascending order according to the sum.

[0029] Sort by the total completion time. Assume that each batch is independently processed on the hybrid flow production line, calculate the objective value obtained when all batches are completely processed on the hybrid flow production line, and sort all batches in descending order according to the objective value.

[0030] Furthermore, the process of obtaining the main solution from the population using the cooperation strategy based on the memory mechanism includes the following steps.

[0031] Define the following parameters: T = {1, …, j, …, N}, where T represents the set of batches, j represents the j-th batch, and N represents the total number of batches; ZS = {ZS(1), …, ZS(j), …, ZS(N)}, where ZS represents the batch splitting information of all batches in all production stages, and ZS(j) represents the batch splitting information of batch j in all production stages.

[0032] Create two sets. One is an empty set of selected batches for storing the batch scheduling plan under construction, and the other is a set of batches to be selected. Initially, the set of batches to be selected contains all batches to be scheduled.

[0033] During the process of constructing the main solution, for the batch at the q-th position in the batch processing sequence of the main solution, operate according to the following process.

[0034] With a probability of 90%, randomly select two individuals from the population, compare the objective values of the two individuals, and retain the individual with the smaller objective value. If the batch j at the q-th position of the individual with the smaller objective value does not exist in the set of selected batches, then assign batch j and the batch splitting information ZS(j) of batch j in all production stages to the batch at the q-th position of the main solution, record batch j in the set of selected batches, and remove batch j from the set of batches to be selected at the same time. If the batch j at the q-th position of the individual with the smaller objective value already exists in the set of selected batches, then randomly select an unselected batch g from the set of batches to be selected, g ∈ [1, N], assign batch g to the batch at the q-th position of the main solution, then randomly select an individual from the population, assign the batch splitting information ZS(g) of batch g retained in the individual to the batch at the q-th position of the main solution, record batch g in the set of selected batches, and remove batch g from the set of batches to be selected at the same time.

[0035] With a 10% probability, randomly select an unselected batch j from the set of candidate batches, assign batch j to the batch at the q-th position of the main solution, then randomly select an individual from the population, assign the batch splitting information ZS(j) of the retained batch j in all production stages in the individual to the batch at the q-th position on the main solution, record batch j in the set of selected batches, and simultaneously remove batch j from the set of candidate batches.

[0036] Furthermore, in the implementation process of the variable neighborhood descent search strategy, five neighborhood structures are used to optimize the main solution. The main solution is perturbed through various neighborhood transformation methods. The objective values of the new individuals generated by each perturbation are compared with the current main solution. If the objective value of the new individual is less than the current main solution, the new individual not only replaces the individual with the largest objective value in the population but also replaces the original main solution to become the new main solution and continues to enter the subsequent neighborhood search process. The operation processes of the five neighborhood structures are as follows.

[0037] Batch insertion: Randomly select a batch from the current batch processing sequence, remove the batch from its original position, and then randomly select a position in the batch processing sequence to insert the batch; Batch exchange: Randomly select two different batches from the current batch processing sequence and exchange their positions in the batch processing sequence.

[0038] Sub-batch mutation: Randomly select a production stage from the current batch splitting information, and select a batch with two or more sub-batches from this production stage. Randomly select two different sub-batches from the selected batch, generate a random integer within the range of 1 to 5 as the number of processing units to be adjusted. Subsequently, reduce the number of processing units to be adjusted from one sub-batch and add it to the other sub-batch to achieve the adjustment of the number of processing units of the sub-batch.

[0039] Combination of batch insertion and sub-batch mutation: First, perform batch insertion on the batch processing sequence, and then perform sub-batch mutation on the batch splitting information.

[0040] Combination of batch exchange and sub-batch mutation: First, perform batch exchange on the batch processing sequence, and then perform sub-batch mutation on the batch splitting information.

[0041] Furthermore, the implementation process of the variable neighborhood descent search strategy is as follows. When performing neighborhood search on the main solution, local search starts from the first neighborhood structure, and the consecutive failure count of the current neighborhood structure is set to zero. During the neighborhood structure search process, a new individual is obtained by applying perturbations to the main solution. If the objective value of the new individual is less than that of the main solution, the new individual is assigned to the main solution. At the same time, the consecutive failure count of the current neighborhood structure is reset to zero, and local search resumes from the first neighborhood structure using the new main solution. If the objective value of the new individual is greater than that of the main solution, the consecutive failure count of the current neighborhood structure is incremented by one, and the search continues within the current neighborhood structure until the consecutive failure count of the current neighborhood structure reaches the maximum failure count V. Then, the local search for the main solution switches to the next neighborhood structure, and the above process is repeated until all neighborhood structures have been searched.

[0042] Furthermore, the process of partial random sorting of batches is as follows.

[0043] For partial random sorting of batches, two positions are randomly selected in the batch processing sequence, and the processing order of all batches between these two positions is randomly arranged.

[0044] The solution method for the integrated scheduling of batch processing and transportation in a hybrid flow shop provided by the present invention is an algorithm (KD-VND) that generates an initial population using multiple strategies, continuously mines the historical information of high-quality individuals in the population during the evolution process to optimize the main solution, combines a variable neighborhood descent search strategy to improve the quality and optimization efficiency of the main solution, and thus obtains a high-quality solution. Specifically, the present invention designs an effective complete individual expression scheme that can comprehensively reflect the batch processing sequence and batch splitting information, thereby ensuring the feasibility of the scheduling scheme; when allocating machines during the production stage of an individual and allocating automated guided vehicles during the transportation process, reasonable allocation rules are adopted to ensure the efficient utilization of resources; a combined heuristic rule that integrates multiple batch sorting rules and batch splitting strategies is designed to significantly improve the quality and diversity of the population; a cooperative optimization strategy based on a memory mechanism is also designed, which can fully mine the information characteristics of high-quality individuals in the population and guide the main solution to evolve along a more optimal search path; in terms of local optimization, a variable neighborhood descent search strategy with five neighborhood structures is designed. By dynamically switching the neighborhood structure, the search coverage range is expanded, and the depth exploration ability of the solution is improved; in addition, a population reconstruction operation that combines a combined heuristic rule, random generation, and retention of high-quality individuals is designed. When the search falls into stagnation, the algorithm can be guided to jump out of the local optimum through the population reconstruction operation. In summary, the application of the present invention effectively solves the problem of integrated scheduling of batch processing and transportation in a hybrid flow shop in the manufacture of cold-drawn seamless steel pipes. By optimizing the batch processing sequence, batch splitting scheme, machine allocation, and automated guided vehicle allocation, the goal of continuously reducing the target value is achieved, and it has the positive effects of improving the overall production efficiency, optimizing the resource utilization rate, and reducing the production cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flowchart for the implementation of the present invention;

[0046] Figure 2 is a schematic diagram of a specific individual of the present invention;

[0047] Figure 3 is a schematic diagram of the cooperative strategy based on the memory mechanism of the present invention for generating the main solution;

[0048] Figure 4 is a comparative variance analysis diagram of the present invention and three existing algorithms. DETAILED DESCRIPTION OF THE INVENTION

[0049] As Figures 1-4 shown, the solution method for the integrated scheduling of batch processing and transportation in a hybrid flow shop provided by the present invention is mainly implemented through the following steps.

[0050] Step S1: Analyze the problem characteristics of the integrated scheduling problem of batch processing and transportation in the manufacture of cold-drawn seamless steel pipes, establish the objective of minimizing the makespan, and initialize the parameters, including the population size P, the maximum number of failures V of the main solution in each neighborhood structure, and the maximum number of failures C of the main solution to update the population.

[0051] Step S2: Use a combined heuristic rule to generate P individuals with diversity and high-quality characteristics in the population. In the population, each complete individual consists of two parts. The first part is the batch processing sequence, denoted as ∏N = {π1, …, πj, …, πN}, where πj represents the index of the jth batch and N represents the total number of batches. The batch processing sequence is used to define the processing order of the batches. The second part is the batch splitting information, which is represented by a three-dimensional vector ΦS = {Ψ1, …, Ψk, …, ΨS}, where S represents the total number of production stages, and Ψk represents the batch splitting information of all batches at production stage k. Ψk is a two-dimensional batch splitting matrix of size N×e, where N represents the total number of batches and e represents the number of sub-batches included in each batch. The two-dimensional batch splitting matrix Ψk(j, e) represents the number of processing units included in the e-th sub-batch of the jth batch at production stage k. For example Figure 2As shown, the exemplary embodiment of the present invention shows an individual structure including three batches (π1, π2, π3) at three production stages (Ψ1, Ψ2, Ψ3). Specifically, the batch processing sequence ∏3 = {π1, π2, π3}, indicating that the batches are processed in the order of π1, π2, and π3 successively. The batch splitting information Φ3 = {Ψ1, Ψ2, Ψ3} corresponds to the batch splitting situations at the three production stages respectively. In this example, each batch is divided into 3 sub-batches, that is, the number of sub-batches e is 3. Taking production stage 1 as an example, the dimension of the corresponding two-dimensional batch splitting matrix Ψ1 is 3×3, and the elements in the matrix represent the number of processing units included in each sub-batch of each batch in production stage 1. For example, the first row of the two-dimensional batch splitting matrix Ψ1 indicates that the first sub-batch of batch π1 contains 3 processing units, the second sub-batch contains 5 processing units, and the third sub-batch contains 3 processing units, and so on. The second row represents the batch splitting information of batch π2 in production stage 1, and the third row represents the batch splitting information of batch π3 in production stage 1. Similarly, Ψ2 and Ψ3 respectively represent the sub-batch splitting information of each batch under production stage 2 and production stage 3, and each matrix element records the distribution of the number of processing units of each sub-batch of each batch under the corresponding production stage. In addition, the allocation rules adopted when allocating machines for each complete individual in the production stage and allocating automated guided vehicles during transportation are as follows. For the selection of machines in each production stage, the earliest available time rule is used as the allocation criterion, that is, from all available machines in the current production stage, the machine that can start processing earliest is preferentially selected to process the current batch; in terms of the allocation of automated guided vehicles, the automated guided vehicle performs transportation tasks in units of sub-batches and adopts the shortest transportation time rule for allocation, that is, the automated guided vehicle with the shortest transportation time between the current position of the sub-batch and all available automated guided vehicles is selected.

[0052] The process of generating P individuals by the above combined heuristic rule further includes the following operations.

[0053] Step 1, divide each batch πj according to the batch splitting strategy, where the batch splitting strategy includes:

[0054] Uniform splitting, evenly splitting the processing units of each batch into each sub-batch;

[0055] Maximum splitting. The present invention relates to the application of batch processing machines, and batch processing machines have the ability to process multiple processing units simultaneously. However, batch processing machines often suffer from the problem of processing capacity limitation. To address this problem, the present invention introduces the maximum splitting strategy. When each batch is processed on the batch processing machine, there is a maximum number of processing units that the batch processing machine can process. According to the maximum number of processing units that the batch processing machine can carry, the processing units are allocated to the sub-batches to the greatest extent;

[0056] Random splitting, randomly dividing the processing units of each batch into multiple sub-batches;

[0057] Greedy splitting. For each batch to be divided, when allocating processing units to each sub-batch, calculate the objective values generated when the processing units are allocated to different sub-batches in turn. Subsequently, select the sub-batch with the smallest generated objective value as the optimal allocation position for the current processing unit.

[0058] Step 2, obtain the batch processing sequence ∏N = {π1, …, πj, …, πN} according to the batch sorting rule, where the batch sorting rule includes:

[0059] Random sorting, completely randomly arranging the processing orders of all batches;

[0060] First-stage start time sorting, arranging in ascending order according to the start times of each batch in the first production stage;

[0061] First-stage start time and total processing time sorting, adding the start time of each batch in the first production stage to the corresponding processing time, and arranging in ascending order according to the sum;

[0062] Total completion time sorting. Assume that each batch is independently processed on the mixed-flow production line, calculate the objective value obtained when each batch is completely processed on the mixed-flow production line, and sort all batches in descending order according to the objective value.

[0063] Step 3, extract the first two batches from the batch processing sequence, denoted as batch π1 and batch π2 respectively, to form two different-order partial batch processing sequences. The first one is the partial batch processing sequence with batch π1 in the front and batch π2 in the back; the second one is the partial batch processing sequence with batch π2 in the front and batch π1 in the back; calculate the objective values of the two partial batch processing sequences respectively, and determine the partial batch processing sequence with the smallest objective value as the current partial batch processing sequence.

[0064] Step 4, repeat the following steps 4-1 and 4-2 for subsequent batches, where

[0065] Step 4-1: Insert batch πj into each insertion position in the current partial batch processing sequence. There are j insertion positions, generating corresponding partial batch processing sequences respectively, and obtaining the objective values. At this time, the partial batch processing sequence consists of j - 1 batches;

[0066] Step 4-2: Select the partial batch processing sequence with the smallest generated objective value as the current partial batch processing sequence.

[0067] Step 5, repeat Steps 1 - 4 until P individuals are obtained.

[0068] Step S3: Use the collaborative strategy based on the memory mechanism to fully exploit the historical information of existing high-quality individuals in the population and construct the main solution. Among them, the process of obtaining the main solution from the population through the collaborative strategy based on the memory mechanism further includes the following steps.

[0069] (1) Define the following parameters: T = {1, …, j, …, N}, where T represents the batch set, j represents the j-th batch, and N represents the total number of batches; ZS = {ZS(1), …, ZS(j), …, ZS(N)}, where ZS represents the batch splitting information of all batches in all production stages, and ZS(j) represents the batch splitting information of batch j in all production stages.

[0070] (2) Create two sets, an empty selected batch set for storing the batch scheduling plan under construction, and another candidate batch set. Initially, the candidate batch set contains all batches to be scheduled.

[0071] (3) During the process of constructing the main solution, for the batch at the q-th position in the batch processing sequence of the main solution, operate according to the following process:

[0072] (3-1) With a probability of 90%, randomly select two individuals from the population, compare the objective values of the two individuals, and retain the individual with the smaller objective value. If the batch j at the q-th position of the individual with the smaller objective value does not exist in the selected batch set, then assign batch j and the batch splitting information ZS(j) of batch j in all production stages to the batch at the q-th position of the main solution, record batch j in the selected batch set, and at the same time remove batch j from the candidate batch set; if the batch j at the q-th position of the individual with the smaller objective value already exists in the selected batch set, then randomly select an unselected batch g from the candidate batch set, g ∈ [1, N], assign batch g to the batch at the q-th position of the main solution, then randomly select an individual from the population, assign the batch splitting information ZS(g) of batch g retained in the individual to the batch at the q-th position of the main solution, record batch g in the selected batch set, and at the same time remove batch g from the candidate batch set.

[0073] (3-2) With a probability of 10%, randomly select an unselected batch j from the candidate batch set, assign batch j to the batch at the q-th position of the main solution, then randomly select an individual from the population, assign the batch splitting information ZS(j) of batch j retained in the individual to the batch at the q-th position of the main solution, record batch j in the selected batch set, and at the same time remove batch j from the candidate batch set.

[0074] Such as Figure 3As shown, the present invention demonstrates the process of generating the master solution from 4 individuals based on the memory mechanism. Figure 3 In the figure, ①②③④ represent the serial numbers of the individuals, and B represents the objective value of each individual. The individual and the master solution are both illustrated by taking the batch processing sequence and batch splitting information of 4 batches in the same production stage as an example. First, set the selected batch set and the to-be-selected batch set. For the first batch in the master solution, with a probability of 90%, randomly select individual ① and individual ③ from the population. Compare the objective value B1 of individual ① and the objective value B3 of individual ③, and select the individual ③ with the smaller objective value. Put the batch 2 in the first position of the batch processing sequence of individual ③ into the first position of the batch processing sequence of the master solution, and assign the batch splitting information ZS(2) of batch 2 in individual ③ to the batch corresponding to the first position of the master solution. At the same time, add batch 2 to the selected batch set and delete batch 2 from the to-be-selected batch set. Subsequently, for the second batch in the master solution, with a probability of 10%, randomly select the unselected batch 1 from the to-be-selected batch set, put batch 1 into the second position of the batch processing sequence of the master solution, and randomly select individual ②. Assign the batch splitting information ZS(1) of batch 1 in individual ② to the batch corresponding to the second position of the master solution, add batch 1 to the selected batch set, and delete batch 1 from the to-be-selected batch set. Then, for the third batch in the master solution, with a probability of 90%, randomly select individual ① and individual ④ from the population. Compare the objective value B1 of individual ① and the objective value B4 of individual ④, and select the individual ① with the smaller objective value. Put the batch 3 in the third position of the batch processing sequence of individual ① into the third position of the batch processing sequence of the master solution, and assign the batch splitting information ZS(3) of batch 3 in individual ① to the batch corresponding to the third position of the master solution. Add batch 3 to the selected batch set and delete batch 3 from the to-be-selected batch set. Finally, for the fourth batch in the master solution, with a probability of 90%, randomly select individual ② and individual ③ from the population. Compare the objective value B2 of individual ② and the objective value B3 of individual ③, and select the individual ② with the smaller objective value. Put the batch 2 in the fourth position of the batch processing sequence of individual ② into the fourth position of the batch processing sequence of the master solution. However, since batch 2 already exists in the selected batch set, randomly select batch 4 from the to-be-selected batch set and put it into the fourth position of the master solution. Subsequently, randomly select individual ④, assign the batch splitting information ZS(4) of batch 4 in individual ④ to the batch corresponding to the fourth position of the master solution, add batch 4 to the selected batch set, and delete batch 4 from the to-be-selected batch set.

[0075] Step S4: In the implementation process of the variable neighborhood descent search strategy, five neighborhood structures are set to optimize the main solution. Through various neighborhood transformation methods, the main solution is perturbed. For each newly generated individual due to perturbation, its objective value is compared with that of the current main solution. If the objective value of the new individual is less than that of the current main solution, the new individual not only replaces the individual with the largest objective value in the population but also replaces the original main solution to become the new main solution and continues to enter the subsequent neighborhood search process. Among them, the operation processes of the five neighborhood structures are as follows.

[0076] Batch insertion: Randomly select a batch from the current batch processing sequence, remove the batch from its original position, and then randomly select a position in the batch processing sequence to insert the batch.

[0077] Batch exchange: Randomly select two different batches from the current batch processing sequence and exchange their positions in the batch processing sequence.

[0078] Sub-batch mutation: Randomly select a production stage from the current batch splitting information, and select a batch with two or more sub-batches from this production stage. Randomly select two different sub-batches from the selected batch, generate a random integer within the range of 1 to 5 as the number of processing units to be adjusted. Subsequently, reduce the number of processing units to be adjusted from one sub-batch and add it to the other sub-batch to achieve the adjustment of the number of processing units in the sub-batch. The following takes a batch containing three sub-batches as an example for specific illustration: Suppose the number of processing units in sub-batch 1 is 6, the number of processing units in sub-batch 2 is 7, and the number of processing units in sub-batch 3 is 4. When performing sub-batch mutation, select sub-batch 2 and sub-batch 3 to adjust the number of processing units with each other. Suppose a random integer 3 is generated within the range of 1 to 5. Then the number of processing units in sub-batch 2 minus 3, and the number of processing units in sub-batch 3 plus 3. Finally, it becomes that the number of processing units in sub-batch 1 is 6, the number of processing units in sub-batch 2 is 4, and the number of processing units in sub-batch 3 is 7.

[0079] Combination of batch insertion and sub-batch mutation: First, perform batch insertion on the batch processing sequence, and then perform sub-batch mutation on the batch splitting information.

[0080] Combination of batch exchange and sub-batch mutation: First, perform batch exchange on the batch processing sequence, and then perform sub-batch mutation on the batch splitting information.

[0081] The implementation process of the variable neighborhood descent search strategy is as follows. When performing neighborhood search on the main solution, first start local search from the first neighborhood structure and set the consecutive failure count of the current neighborhood structure to zero. During the neighborhood structure search process, a new individual is obtained by applying perturbations to the main solution. If the objective value of the new individual is less than that of the main solution, assign the new individual to the main solution, reset the consecutive failure count of the current neighborhood structure to zero at the same time, and restart local search from the first neighborhood structure using the new main solution. If the objective value of the new individual is greater than that of the main solution, increment the consecutive failure count of the current neighborhood structure by one and continue searching within the current neighborhood structure until the consecutive failure count of the current neighborhood structure reaches the maximum failure count V. Then, switch the local search of the main solution to the next neighborhood structure and repeat the above process until all neighborhood structures have been searched. At this time, perform the collaborative strategy based on the memory mechanism again to obtain a new main solution, and continue to implement the variable neighborhood descent search strategy for the main solution until the termination time of the algorithm is reached.

[0082] Step S5: Reconstruct the population operation. When the maximum failure count of the main solution for updating the population exceeds C, perform the reconstruct population operation. The implementation process of the reconstruct population operation is as follows.

[0083] The new population consists of three parts. Among them, P / 3 individuals are generated by the combinatorial heuristic rule, and batch exchange perturbations are performed on the batch processing sequences in each individual generated by the combinatorial heuristic rule, and sub-batch mutation perturbations are performed on the batch splitting information in the individuals to enhance population diversity. Another P / 3 individuals are completely randomly generated. The randomly generated individuals obtain the batch processing sequence by using random sorting and obtain the batch splitting information of all batches in all production stages by using random splitting. The remaining P / 3 individuals are selected from the high-quality individuals retained in the original population, and batch partial rearrangement perturbations are performed on the batch processing sequences of the high-quality individuals retained in the original population, and sub-batch mutation perturbations are performed on the batch splitting information in the individuals. At this time, the newly generated population uses the collaborative strategy based on the memory mechanism to obtain a new main solution again. Among them, the process of batch partial random sorting is: randomly select two positions in the batch processing sequence and randomly arrange the processing orders of all batches between these two positions.

[0084] Step S6: Update the optimal individual. Judge whether the termination condition is satisfied. If it is satisfied, output the individual with the minimum objective value; otherwise, return to Step S3 to continue optimization.

[0085] To better illustrate the effectiveness of the present invention applied to the integrated scheduling problem of batch processing and transportation in a hybrid flow shop, through the experimental analysis of a series of examples of the present invention, the present invention is further described and illustrated.

[0086] In the present invention, the problem scale is determined by the combination of three factors: the number of production stages S ∈ {3, 5, 8}, the number of batches N ∈ {40, 60, 80, 100}, and the number of automated guided vehicles A ∈ {8, 10, 12}. A total of 36 different problem scale configurations are designed. For each problem scale configuration, 5 test instances are randomly generated, resulting in a total of 180 instances. Each production stage has 1 - 5 machines. The number of processing units per batch is uniformly distributed within the range of [50, 100]. The maximum number of processing units that the batch processing machine can process for each batch is uniformly distributed within the range of [15, 25]. The processing time for a non - batch processing machine to process one processing unit in the production stage where it is located is uniformly distributed within the range of [1, 10]. The time for the production stage machine where the batch processing machine is located to process multiple processing units simultaneously is uniformly distributed within the range of [50, 100]. The start - up time for each batch is uniformly distributed within the range of [50, 100] to simulate the uncertainties in actual production. The transportation time of the automated guided vehicle simulates the actual production environment, and the transportation time of the automated guided vehicle is calculated according to the Manhattan distance formula. In the hybrid flow shop, the x - axis represents the production stage, and the y - axis represents the number of machines corresponding to each production stage. Through the above coordinate system, the position of each machine in the hybrid flow shop layout can be determined. The automated guided vehicle transports sub - batches back and forth between machines. Based on the positional relationship between machines, the Manhattan distance formula can be used to calculate the distance between machines. The Manhattan distance formula is calculated as follows,

[0087]

[0088] represents the machine to the machine the distance between, represents the machine the production stage where it is located, represents represents the machine the production stage where it is located, represents the machine the machine serial number corresponding to it in the production stage, represents the machine the machine serial number corresponding to it in the production stage;

[0089] The transportation time of the automated guided vehicle is calculated based on the Manhattan distance between machines. As the problem scale expands, in order to simulate the increase in logistics transportation time caused by scale growth, the transportation time is adjusted by multiplying by a multiple u. The calculation formula is as follows,

[0090] ,

[0091] The automated guided vehicle goes from the machine to the machine The transportation time between

[0092] The termination time of the KD-VND algorithm of the present invention is set to 100×N×S (milliseconds). For each instance, it is run independently 10 times, so the Relative Percentage Increase (RPI) of each instance can be obtained. Then, the instances are grouped on the same scale to obtain the Average Relative Percentage Increase (ARPI) of each combination.

[0093] Regarding parameter settings, in order to better solve and optimize the integrated scheduling problem of hybrid flow shop batch processing and transportation, the population size P is set to 30, the maximum number of failures V of the main solution in each neighborhood structure is set to 30, and the maximum number of times C that the main solution fails to update the population is set to 100.

[0094] The experimental results and analysis of this instance are as follows. After the KD-VND algorithm completes the parameter settings, systematic experiments are carried out with three comparison algorithms. The three existing algorithms include a Cooperative Variable Neighborhood Descent algorithm (CVND), a Hybrid algorithm that combines Harmony Search and Genetic Algorithm (HHSGA), and an Improved Cooperative Coevolutionary Algorithm (CCEA). To ensure the fairness of the comparison, all algorithms use a unified problem scale, adopt the same objective, and introduce the same machine allocation rules and Automated Guided Vehicle allocation rules. Finally, the solution quality and stability of KD-VND are evaluated based on the average relative percentage increase values obtained by each algorithm under the same problem scale. The comparison results are shown in Table 1:

[0095] Table 1 Comparison results of instances of the present invention and three existing algorithms

[0096]

[0097] As can be seen from Table 1, the ARPI value obtained by KD-VND is the smallest among all problem scales. For example, in the 4th problem scale of 5×40×8, KD-VND is 1.545, while the other algorithms CVND (2.382), CCEA (3.327), and HHSGA (4.335) are significantly larger. Especially in instances with smaller problem scales, such as 3×40×8, 3×60×8, 3×80×8, 3×100×8, etc., the performance of KD-VND is far better than these three comparison algorithms. From the average ARPI value, it can be seen that the average ARPI value of KD-VND is 0.987, which is significantly lower than that of CVND (1.538), HHSGA (3.066), and CCEA (4.212). This shows that KD-VND is superior to these three comparison algorithms in overall performance. In summary, KD-VND shows significant advantages in most problem scales, especially when solving complex production scheduling problems, and can obtain better optimization effects. This result fully verifies the advantage of the KD-VND algorithm of the present invention in average solution performance. Figure 4 It is an analysis of variance diagram for comparing instance algorithms plotted based on the ARPI data obtained from the comparison of instance algorithms in Table 1. From Figure 4 it can be seen that the confidence interval of KD-VND is significantly narrower than that of other comparison algorithms, and there is no overlap with the confidence intervals of the other three comparison algorithms, which further shows that the results obtained by the KD-VND algorithm of the present invention have a smaller degree of dispersion and higher stability, and also further verifies the significant advantages of the KD-VND of the present invention in terms of data stability and centralization.

[0098] In summary, the method proposed by the present invention can effectively solve the integrated scheduling problem of batch processing and transportation in a hybrid flow shop. The present invention is closer to the actual industrial production environment, comprehensively considers the coordination relationship between production and logistics, and realizes the deep coordination of the production and transportation processes by jointly optimizing batch sequencing, batch splitting, machine allocation, and automatic guided vehicle scheduling, improving the overall scheduling efficiency and resource utilization rate.

Claims

1. A solution method for integrated scheduling of batch processing and transportation in a hybrid flow shop, characterized in that, including the following steps, S1. Analyze the problem characteristics of the integrated scheduling problem of batch processing and transportation in the manufacturing of cold-drawn seamless steel pipes, establish the objective of minimizing the makespan, and initialize the parameters, including the population size P, the maximum number of failures V of the main solution in each neighborhood structure, and the maximum number of failures C of the main solution to update the population; S2. Use a combined heuristic rule to generate P individuals in the population; S3. Utilize a cooperation strategy based on a memory mechanism to fully exploit the historical information of existing high-quality individuals in the population and construct the main solution; S4. Through five neighborhood structures, adopt a variable neighborhood descent search strategy to perform neighborhood search on the main solution. If an individual with a smaller objective value is found, replace the individual with the smaller objective value with the new main solution; S5. Reconstruct the population operation. P / 3 individuals in the new population are generated by the combined heuristic rule and perturbed by introducing batch exchange and sub-batch mutation. Another P / 3 individuals are randomly generated, and the remaining P / 3 individuals are selected from the high-quality individuals retained in the original population and perturbed by adopting partial random sorting of batches and sub-batch mutation; S6. Update the optimal individual, judge whether the termination condition is satisfied. If satisfied, output the individual with the smallest objective value; otherwise, return to step S3 to continue optimization.

2. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 1, characterized in that, In a population, each complete individual consists of two parts. The first part is the batch processing sequence, denoted as ∏ N ={π1,…,π j ,…,π N}, where π j represents the index of the j th batch, N represents the total number of batches, and the batch processing sequence is used to define the processing order of batches; the second part is the batch splitting information, which is represented by a three-dimensional vector Φ S ={Ψ1,…,Ψ k ,…,Ψ S}, where S represents the total number of production stages, Ψ k represents the batch splitting information of all batches in the production stage k , Ψ k is a two-dimensional batch splitting matrix of size N × e , where N represents the total number of batches, e represents the number of sub-batches included in each batch. The two-dimensional batch splitting matrix Ψ k ( j,e ) represents the number of processing units included in the k th sub-batch of the j th batch in the production stage e .

3. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 2, characterized in that, In the population, the allocation rules adopted by each complete individual for machine allocation during the production stage and automatic guided vehicle allocation during the transportation process are as follows. For the selection of machines in each production stage, the earliest available time rule is used as the allocation criterion, that is, from all available machines in the current production stage, preferentially select the machine that starts processing earliest to process the current batch; for the allocation of automatic guided vehicles, the automatic guided vehicle performs transportation tasks in units of sub-batches and is allocated using the shortest transportation time rule, that is, select the automatic guided vehicle with the shortest transportation time between the current sub-batch location and all available automatic guided vehicles.

4. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 3, characterized in that The process of generating P individuals by the combined heuristic rule includes the following steps, Step 1, divide each batch π according to the batch splitting strategy j for division; Step 2, obtain the batch processing sequence ∏ according to the batch sorting rule N ={π1,…,π j ,…,π N}; Step 3. Extract the first two batches from the batch processing sequence, denoted as batch π1 and batch π2 respectively, to form two different-order partial batch processing sequences. The first is the partial batch processing sequence with batch π1 in the front and batch π2 in the back; the second is the partial batch processing sequence with batch π2 in the front and batch π1 in the back. Calculate the objective values of the two partial batch processing sequences respectively, and determine the current partial batch processing sequence as the partial batch processing sequence with the smallest objective value; Step 4. Repeat the following steps 4-1 and 4-2 for subsequent batches, where, Step 4-1, insert batch π j into each insertion position in the current partial batch processing sequence. There are j insertion positions, respectively generate the corresponding partial batch processing sequences, and obtain the target values. At this time, the partial batch processing sequence consists of j -1 batches; Step 4-2. Select the partial batch processing sequence that generates the smallest objective value as the current partial batch processing sequence; Step 5. Repeat steps 1-step 4 until P individuals are obtained.

5. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 4, characterized in that, The batch splitting strategy includes, Uniform splitting, evenly splitting the processing units of each batch into each sub-batch; Maximum splitting, where each batch has the maximum number of processing units that the batch processing machine can process when processed on the batch processing machine. According to the maximum number of processing units that the batch processing machine can carry, the processing units are allocated to the sub-batches to the maximum extent; Random splitting, where the processing units of each batch are randomly divided into multiple sub-batches; Greedy splitting, for each batch to be divided, when allocating processing units to each sub-batch, calculate the objective value generated when the processing units are allocated to different sub-batches in turn. Subsequently, select the sub-batch with the minimum generated objective value as the optimal allocation position for the current processing units.

6. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 4, characterized in that The batch sorting rules include, Random sorting, randomly arranging the processing order of all batches; First-stage start time sorting, arranging in ascending order according to the start time of each batch in the first production stage; First-stage start time and total processing time sorting, adding the start time of each batch in the first production stage to the corresponding processing time, and arranging in ascending order according to the added total; Total completion time sorting, assuming that each batch is processed independently on the hybrid flow production line, calculate the objective value obtained when each batch is completely processed on the hybrid flow production line, and sort all batches in descending order according to the objective value.

7. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 5 or 6, characterized in that, The process of obtaining the main solution from the population using a cooperative strategy based on a memory mechanism includes the following steps, Define the following parameters, T = {1, …, j , …, N}, where T represents the set of batches, j represents the j -th batch, N represents the total number of batches, Z S = {Z S (1), …, Z S ( j ), …, Z S ( N )}, where Z S represents the batch splitting information of all batches in all production stages, and Z S ( j ) represents the batch splitting information of batch j in all production stages; Create two sets, an empty set of selected batches for storing the batch scheduling plan under construction, and another set of batches to be selected. Initially, the set of batches to be selected contains all batches to be scheduled; During the process of constructing the main solution, for the batch at the q-th position in the batch processing sequence of the main solution, operate according to the following process, With a 90% probability, randomly select two individuals from the population, compare the objective values of the two individuals, and retain the individual with the smaller objective value. If the batch at the q-th position of the individual with the smaller objective value j does not exist in the set of selected batches, then the batch j , the batch j batch splitting information Z at all production stages S ( j ) is assigned to the batch at the q-th position of the main solution, and the batch j is recorded in the set of selected batches, and at the same time, the batch j is removed from the set of batches to be selected; if the batch at the q-th position of the individual with the smaller objective value j already exists in the set of selected batches, then randomly select an unselected batch from the set of batches to be selected g , g ∈[1, N , assign the batch g to the batch at the q-th position of the main solution, then randomly select an individual from the population, and assign the batch g batch splitting information Z at all production stages S ( g ) to the batch at the q-th position of the main solution, and record the batch g in the set of selected batches, and at the same time, remove the batch g from the set of batches to be selected; With a 10% probability, randomly select an unselected batch from the set of candidate batches j , assign the batch j to the batch at the q-th position of the main solution, then randomly select an individual from the population, and assign the batches j of the batch splitting information Z S ( j ) at all production stages to the batch at the q-th position of the main solution, and record the batch j in the set of selected batches, and at the same time remove the batch j .

8. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 7, characterized in that, The implementation process of the variable neighborhood descent search strategy optimizes the main solution using five neighborhood structures, perturbs the main solution through various neighborhood transformation methods, and compares the objective value of the new individual generated by each perturbation with the current main solution. If the objective value of the new individual is less than the current main solution, the new individual not only replaces the individual with the largest objective value in the population, but also replaces the original main solution to become the new main solution and continues to enter the subsequent neighborhood search process. The operation processes of the five neighborhood structures are as follows, Batch insertion, randomly select a batch from the current batch processing sequence, remove the batch from its original position, and then randomly select a position in the batch processing sequence to insert the batch; Batch exchange, randomly select two different batches from the current batch processing sequence and exchange their positions in the batch processing sequence; Sub-batch mutation, randomly select a production stage from the current batch splitting information, and select a batch with two or more sub-batches from this production stage. Randomly select two different sub-batches from the selected batch, generate a random integer within the range of 1 to 5 as the number of processing units to be adjusted. Subsequently, reduce the number of processing units to be adjusted from one sub-batch and add it to the other sub-batch to achieve the adjustment of the number of processing units in the sub-batch; Batch insertion is combined with sub-batch mutation. First, batch insertion is performed on the batch processing sequence, and then sub-batch mutation is performed on the batch segmentation information; Batch exchange is combined with sub-batch mutation. First, batch exchange is performed on the batch processing sequence, and then sub-batch mutation is performed on the batch segmentation information.

9. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 8, characterized in that, The implementation process of the variable neighborhood descent search strategy is as follows. When performing neighborhood search on the main solution, local search starts from the first neighborhood structure, and the consecutive failure count of the current neighborhood structure is set to zero. During the neighborhood structure search process, a new individual is obtained by applying perturbations to the main solution. If the objective value of the new individual is less than that of the main solution, the new individual is assigned to the main solution. At the same time, the consecutive failure count of the current neighborhood structure is reset to zero, and local search resumes from the first neighborhood structure using the new main solution. If the objective value of the new individual is greater than that of the main solution, the consecutive failure count of the current neighborhood structure is incremented by one, and search continues within the current neighborhood structure until the consecutive failure count of the current neighborhood structure reaches the maximum failure count V. Then, the local search for the main solution switches to the next neighborhood structure, and the above process is repeated until all neighborhood structures have been searched.

10. The solution method for integrated scheduling of hybrid flow shop batch processing and transportation according to claim 9, characterized in that, The process of batch partial random sorting is as follows, For batch partial random sorting, two positions are randomly selected in the batch processing sequence, and the processing order of all batches between these two positions is randomly permuted.

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