A Solving Method for Distributed Heterogeneous Permutation Flow Shop Scheduling Problem

Abstract

The present invention relates to the technical field of distributed flow shop scheduling, and belongs to a method for solving the problem of distributed heterogeneous permutation flow shop scheduling. The method includes: determining to minimize the total weighted completion time as the solution objective, initializing a population, and optimizing the population to obtain an optimized population; using a ternary tournament method to select a solution from the initial population, and sequentially executing 6 local search operators, each local search operator is executed 5 times; replacing the solution with the largest objective value in the optimized population with the new solution to obtain a new population. If there is no improvement for 5 consecutive times, a perturbation mechanism is triggered to update the new population, and the perturbed new population is combined with the new population before perturbation. Each solution in the combined population is sorted in ascending order according to the objective value of the solution, and part of them are selected for continuous iteration; continue to execute the next round of search until the limited maximum time is reached, and output the solution with the smallest objective value. The present invention has the positive effect of improving production efficiency and production line stability.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed flow shop scheduling, and specifically belongs to a method for solving the distributed heterogeneous permutation flow shop scheduling problem. Background Art

[0002] Under the background of the rapid development of the global market economy, enterprises are facing increasingly severe market competition. The traditional centralized production mode gradually exposes the problem of insufficient flexibility and is difficult to meet the market demand for multi-variety and small-batch production. To adapt to this change, the manufacturing mode evolves towards distribution and heterogeneity to improve production efficiency and resource utilization rate. In this transformation process, efficient scheduling methods become the key link to ensure the smooth production process, optimize resource allocation, and enhance the competitiveness of enterprises.

[0003] In recent years, the distributed heterogeneous permutation flow shop scheduling problem has received extensive attention. This problem involves the collaborative production of multiple factories, and it is necessary to comprehensively consider the release time of workpieces, the scheduling constraints of heterogeneous factories, and the optimal strategy for cross-factory task allocation. At the same time, due to the complexity of actual factories, two special types of workpieces need to be considered specifically. One is the workpiece from VIP customers that needs to be given priority, and the other is the infrequently used workpiece that is about to be phased out. Due to the complexity of workpiece sequencing, factory selection, and machine allocation, traditional scheduling methods are difficult to meet the requirements of actual production. Therefore, more efficient optimization strategies are urgently needed to improve the feasibility and adaptability of the scheduling plan, thereby optimizing the overall production performance. Summary of the Invention

[0004] The present invention aims to provide a method for solving the distributed heterogeneous permutation flow shop scheduling problem, which solves the problem that the current research on the distributed heterogeneous permutation flow shop scheduling problem does not conform to the actual production scenario and does not consider special workpieces, so as to achieve the purpose of taking the actual production scenario as the research premise, making production scheduling more reasonable, and effectively improving production efficiency and the stability of the production line.

[0005] A method for solving the distributed heterogeneous permutation flow shop scheduling problem provided by the present invention is characterized by including the following steps.

[0006] Step 1, analyze the characteristics of the distributed heterogeneous permutation flow shop scheduling problem in printed circuit board production and manufacturing, determine the solution goal of minimizing the total weighted completion time, and initialize the parameters, including the population size PSize , time parameters t ;

[0007] Step 2, Initialize the population. Use the rule of the sum of the shortest processing time and the release time, the maximum weight rule, and the minimum release time rule, and combine with the greedy insertion method to generate the first three solutions of the initial population. Use the composite method to generate the fourth solution of the initial population, and generate the remaining PSize - 4 solutions by random method, and apply the backtracking optimization method to the initial population for optimization to obtain the optimized population;

[0008] Step 3, Use the ternary tournament method to select a solution from the initial population, and sequentially execute 6 local search operators, each local search operator is executed 5 times. Among them, after each execution of the local search operator, execute the Q-learning learning mechanism. If the new solution obtained is better than the original solution, increase the Q value; if the new solution obtained is worse than the original solution, decrease the Q value; if the new solution obtained is equal to the original solution, the Q value remains unchanged. After 5 local search operators are executed, sort the Q values corresponding to each local search operator, and select the local search operator with the highest corresponding Q value to execute once. If the objective value of the new solution obtained after the selected local search operator is executed is smaller, retain the new solution;

[0009] Step 4, Replace the solution with the largest objective value in the optimized population with the new solution to obtain a new population. If there is no improvement for 5 consecutive times, trigger the perturbation mechanism to update the new population, and combine the perturbed new population with the new population before perturbation to obtain a combined population with a size of 2 × PSize . Sort each solution in the combined population from smallest to largest according to the objective value of the solution, and select the first ， solutions to continue the iteration; PSize

[0010] Step 5, Iteratively execute Step 3 and Step 4, continue to execute the next round of search until the limited maximum time is reached, output the solution with the smallest objective value, and terminate the execution.

[0011] Furthermore, in Step 2, the rule of the sum of the shortest processing time and the release time is that the priority is determined according to the sum of the total processing time and the release time of the workpiece, and the workpieces are sorted from smallest to largest according to the sum of the total processing time and the release time of the workpiece;

[0012] The maximum weight rule is that the priority is determined according to the weight of the workpiece, and the workpieces are sorted from largest to smallest according to the weight of the workpiece;

[0013] The minimum release time rule is that the priority is determined according to the release time of the workpiece, and the workpieces are sorted from smallest to largest according to the release time of the workpiece;

[0014] ​The greedy insertion method means that for the workpiece sequence sorted by each sorting rule, a workpiece is selected in turn and inserted into the position in all factory sequences that minimizes the objective value of the solution. The process of selecting workpieces and inserting is repeated until all the workpieces in the workpiece sequences sorted by the shortest processing time plus release time rule, the maximum weight rule, and the minimum release time rule are inserted, and the first three solutions are obtained;

[0015] The implementation process of the composite method includes the following steps,

[0016] (1) Sort all workpieces according to the maximum weight rule to obtain the initial workpiece sequence;

[0017] (2) Extract workpieces one by one from the initial workpiece sequence. When extracting each workpiece, check whether there are other workpieces with the same weight as the extracted workpiece;

[0018] (3) If there are no other workpieces with the same weight, directly insert the extracted workpiece into the position in all factory sequences that minimizes the objective value of the solution, and continue to extract the next workpiece;

[0019] (4) If there are other workpieces with the same weight, put the workpieces with the same weight into a new workpiece sequence, re-sort them according to the shortest processing time plus release time rule, and insert the newly sorted workpieces into the positions in all factory sequences that can minimize the objective value of the obtained solution in turn until all the workpieces in the new workpiece sequence are inserted;

[0020] (5) According to the order of the workpieces in the initial workpiece sequence, select a workpiece that has not been extracted by the initial workpiece sequence and the new workpiece sequence, and repeat steps (3) and (4) until all workpieces are inserted, thus generating the fourth solution;

[0021] The random method randomly sorts all workpieces, and then inserts the sorted workpieces into the positions in all factory sequences that minimize the objective value of the solution in turn;

[0022] In the backtracking optimization method, select the solution with the smallest objective value among the solutions in the initial population as the initial candidate set. If there are multiple solutions with the same and smallest objective value, all of them are added to the initial candidate set as the new candidate set. Randomly select a solution from the initial population, sequentially remove the workpieces in it, and re-insert the removed workpieces into the position in all factory sequences that can minimize the objective value of the obtained solution. During the insertion process, if a better solution is generated, replace the original solution with the better solution. If the better solution is not greater than the solution with the smallest objective value in the initial population, add it to the new candidate set to obtain the preferred candidate set, and select the first untested solution from the preferred candidate set. Repeat the process of removing and inserting workpieces. When the solutions obtained three consecutive times are all greater than the solution with the smallest objective value in the initial population, re-select an unselected solution from the preferred candidate set to start exploration. If there is no solution that meets the requirements in the preferred candidate set at this time, end the backtracking process and update the solution with the smallest objective value.

[0023] Further, in step 3, the ternary tournament method means randomly selecting 3 solutions from the initial population, comparing the objective values of the 3 solutions, and determining the one with the smallest objective value among the 3 solutions. If there are multiple solutions with the same and smallest objective value, select the first selected solution with the smallest objective value to execute the local search operator;

[0024] The local search operator includes the critical factory optimization operator, the large impact workpiece optimization operator, the disruption and reconstruction operator, the two-stage optimization operator, the special workpiece optimization operator, and the inter-factory exchange operator. The critical factory refers to the factory with the largest objective value of the solution among all factories. If there are multiple factories with the same objective value of the solution, select the factory with the smallest factory number. The objective value of the solution of a factory means adding the product of the weight of each workpiece assigned to a factory and the corresponding completion time of each workpiece, where

[0025] The operation process of the critical factory optimization operator is to remove all workpieces in the critical factory and randomly insert the removed workpieces into the position in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the solution is improved through the removal and insertion operations, retain the obtained new solution; otherwise, restore the original solution. Perform the removal and insertion operations at most five times, and finally output the best solution among the five removal and insertion operations;

[0026] The operation process of the large impact workpiece optimization operator is to remove the first 50% of the workpieces that have the greatest impact on the objective value of the solution from the current solution and randomly insert them into the position in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the solution is improved through the removal and insertion operations, retain the obtained new solution; otherwise, restore the original solution. Perform the removal and insertion operations at most five times, and finally output the best solution among the five removal and insertion operations;

[0027] The operation process of the destruction and reconstruction operator is as follows: randomly remove a part of the workpieces, and reinsert the removed workpieces into the position in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the obtained solution is improved through the removal and insertion operation, the obtained new solution is retained; otherwise, the original solution is restored. The removal and insertion operation is performed at most five times, and finally the best solution among the five removal and insertion operations is output;

[0028] The operation process of the two-stage optimization operator is divided into two stages. The first stage is the same as the destruction and reconstruction operator. In the second stage, the workpieces in all factories are exchanged in turn. If the exchange operation improves the quality of the solution, the obtained new solution is retained; otherwise, the solution before the exchange is restored. The exchange operation is performed at most five times, and finally the best solution among the five exchange operations is output;

[0029] The operation process of the special workpiece optimization operator is as follows: randomly select a factory, and exchange the positions of two special workpieces and other workpieces in turn. If the obtained solution is improved, it is updated; otherwise, the original solution is restored.

[0030] The operation process of the inter-factory exchange operator is as follows: select the top two factories with the largest objective values of the solutions of the factories, exchange the latter half of the workpieces in the processing sequences of the two factories, respectively, so that the exchanged workpieces are transferred to the new factories, and reinsert them into the position in the new factory sequences that can minimize the objective value of the obtained solution. If the obtained solution is improved, it is updated; otherwise, the original solution is restored;

[0031] The execution process of the Q-learning learning mechanism includes: when performing 5 times of 6 local search operators in step 3, record the results of each local search operator each time. If the obtained new solution is better than the original solution, the Q value is rewarded if the obtained new solution is worse than the original solution, the Q value is punished if the obtained new solution is equal to the original solution, the Q value remains unchanged. After performing the five local searches, sort the Q values corresponding to each local search operator, and select the local search operator with the highest corresponding Q value to execute once. If the objective value of the new solution is better, update the best solution.

[0032] Furthermore, the perturbation mechanism includes two perturbation operators, the shift perturbation operator and the swap perturbation operator. Each time, a perturbation operator is randomly selected for execution. The shift perturbation operator means randomly selecting a workpiece in the current solution and moving the selected workpiece to a different position in the current solution. The swap perturbation operator means randomly selecting two workpieces and swapping the positions of the two selected workpieces in the solution.

[0033] Furthermore, the limited maximum time is t × n × m, n is the total number of workpieces, m is the total number of machines in each factory.

[0034] A method for solving the distributed heterogeneous permutation flow shop scheduling problem provided by the present invention designs an efficient initial population strategy. Through a heuristic method based on problem characteristics, an initial population with high quality and diversity is generated, and a backtracking optimization method is executed on the initial population. The diversity of the selected solutions is ensured through a ternary tournament method, and the quality of the selected solutions is further improved. By combining 6 different local search operator strategies and a Q-learning mechanism, the local search operator with the highest corresponding Q value is dynamically selected for execution, thereby enhancing the search ability and convergence performance of the method. To sum up, the application of the present invention particularly considers the production scenario with special workpieces, can effectively solve the scheduling problem in the production and manufacturing of printed circuit boards, continuously optimize the objective value of the solution, and has the positive effect of improving production efficiency and enhancing the overall performance of the production line. Description of the Drawings

[0035] Figure 1 is the implementation flowchart of the present invention;

[0036] Figure 2 is the implementation flowchart of the composite method of the present invention;

[0037] Figure 3 is the Gantt chart of the embodiment of the present invention;

[0038] Figure 4 is the mean value chart of the present invention and 5 existing comparison algorithms; Detailed Embodiment

[0039] As Figure 1 and Figure 2 shown, a method for solving the distributed heterogeneous permutation flow shop scheduling problem provided by the present invention is mainly implemented through the following steps.

[0040] Step 1, analyze the characteristics of the distributed heterogeneous permutation flow shop scheduling problem in the production and manufacturing of printed circuit boards, determine the solution objective of minimizing the total weighted completion time, and initialize the parameters, including the population size PSize , time parameter t .

[0041] Step 2, initialize the population. Use the rule of the sum of the shortest processing time and the release time, the maximum weight rule, and the minimum release time rule, combine with the greedy insertion method to generate the first three solutions of the initial population, use the composite method to generate the fourth solution of the initial population, and generate the remaining PSize -4 solutions of the initial population through a random method, and apply the backtracking optimization method to the initial population for optimization to obtain the optimized population. Among them:

[0042] The rule of the sum of the shortest processing time and the release time is to determine the priority according to the sum of the total processing time and the release time of the workpiece, and sort the workpieces in ascending order of the sum of the total processing time and the release time of the workpiece;

[0043] The rule of the maximum weight is to determine the priority according to the weight of the workpiece, and sort the workpieces in descending order of the weight of the workpiece;

[0044] The rule of the minimum release time is to determine the priority according to the release time of the workpiece, and sort the workpieces in ascending order of the release time of the workpiece;

[0045] The greedy insertion method means that for the workpiece sequence sorted by each sorting rule, select a workpiece in turn and insert it into the position that makes the objective value of the solution the smallest in all factory sequences. Repeat the process of selecting workpieces and inserting until all the workpieces in the workpiece sequences sorted by the rule of the sum of the shortest processing time and the release time, the rule of the maximum weight, and the rule of the minimum release time are inserted, and the first three solutions are obtained;

[0046] The implementation process of the composite method includes the following steps,

[0047] (1) Sort all workpieces according to the rule of the maximum weight to obtain the initial workpiece sequence;

[0048] (2) Extract workpieces one by one from the initial workpiece sequence. When extracting each workpiece, check whether there are other workpieces with the same weight as the extracted workpiece;

[0049] (3) If there are no other workpieces with the same weight, directly insert the extracted workpiece into the position that makes the objective value of the solution the smallest in all factory sequences, and continue to extract the next workpiece;

[0050] (4) If there are other workpieces with the same weight, put the workpieces with the same weight into a new workpiece sequence, re-sort them according to the rule of the sum of the shortest processing time and the release time, and insert the newly sorted workpieces into the position that can make the objective value of the obtained solution the smallest in all factory sequences in turn until all the workpieces in the new workpiece sequence are inserted;

[0051] (5) According to the order of the workpieces in the initial workpiece sequence, select a workpiece that has not been extracted by the initial workpiece sequence and the new workpiece sequence, and repeat steps (3) and (4) until all workpieces are inserted, so as to generate the fourth solution;

[0052] The random method randomly sorts all workpieces, and then inserts the sorted workpieces into the position that makes the objective value of the solution the smallest in all factory sequences in turn;

[0053] In the backtracking optimization method, select the solution with the smallest objective value among the solutions in the initial population as the initial candidate set. If there are multiple solutions with the same and smallest objective value, all of them are added to the initial candidate set as the new candidate set. Randomly select a solution from the initial population, sequentially remove the workpieces therein, and re-insert the removed workpieces into the positions in all factory sequences that can minimize the objective value of the obtained solution. During the insertion process, if a better solution is generated, replace the original solution with the better solution. If the better solution is not greater than the solution with the smallest objective value in the initial population, add it to the new candidate set to obtain the preferred candidate set, and select the first untested solution from the preferred candidate set. Repeat the process of removing and inserting workpieces. When the solutions obtained three consecutive times are all greater than the solution with the smallest objective value in the initial population, re-select an unselected solution from the preferred candidate set to start exploration. If there is no solution meeting the requirements in the preferred candidate set at this time, end the backtracking process and update the solution with the smallest objective value.

[0054] Step 3: Use the ternary tournament method to select a solution from the initial population and sequentially execute 6 local search operators, with each local search operator executed 5 times. Among them, after each execution of the local search operator, execute the Q-learning learning mechanism. The ternary tournament method means randomly selecting 3 solutions from the initial population, comparing the objective values of the 3 solutions, and determining the one with the smallest objective value among the 3 solutions. If there are multiple solutions with the same and smallest objective value, select the first selected solution with the smallest objective value to execute the local search operator. The local search operators include the key factory optimization operator, the large impact workpiece optimization operator, the disruption and reconstruction operator, the two-stage optimization operator, the special workpiece optimization operator, and the inter-factory exchange operator. The key factory refers to the factory with the largest objective value of the solution among all factories. If there are multiple factories with the same objective value of the solution, select the factory with the smallest factory number. The objective value of a factory means the sum of the products of the weights of each workpiece assigned to a factory and the corresponding completion time of each workpiece. Among them, the operation process of the key factory optimization operator is to remove all the workpieces in the key factory and randomly insert the removed workpieces into the positions in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the solution is improved through the removal and insertion operations, retain the obtained new solution; otherwise, restore the original solution. Perform the removal and insertion operations at most five times, and finally output the best solution among the five removal and insertion operations.

[0055] The operation process of the large impact workpiece optimization operator is to remove the first 50% of the workpieces with the greatest impact on the objective value of the solution from the current solution and randomly insert them into the positions in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the solution is improved through the removal and insertion operations, retain the obtained new solution; otherwise, restore the original solution. Perform the removal and insertion operations at most five times, and finally output the best solution among the five removal and insertion operations.

[0056] The operation process of the destruction and reconstruction operator is as follows: randomly remove a part of the workpieces, and reinsert the removed workpieces into the position in all factory sequences that can minimize the objective value of the obtained solution. If the quality of the obtained solution is improved through the removal and insertion operation, the obtained new solution is retained; otherwise, the original solution is restored, and the removal and insertion operation is performed at most five times. Finally, the best solution among the five removal and insertion operations is output.

[0057] The operation process of the two-stage optimization operator is divided into two stages. The first stage is the same as the destruction and reconstruction operator. In the second stage, the workpieces in all factories are exchanged in turn. If the exchange operation improves the quality of the solution, the obtained new solution is retained; otherwise, the solution before the exchange is restored, and the exchange operation is performed at most five times. Finally, the best solution among the five exchange operations is output.

[0058] The operation process of the special workpiece optimization operator is as follows: randomly select a factory, and exchange the positions of two special workpieces and other workpieces in turn. If the obtained solution is improved, it is updated; otherwise, the original solution is restored.

[0059] The operation process of the inter-factory exchange operator is as follows: select the top two factories with the largest objective values of the solutions of the factories, exchange the latter half of the workpieces in the processing sequences of the two factories, respectively, so that the exchanged workpieces are transferred to the new factories, and reinsert them into the position in the new factory sequences that can minimize the objective value of the obtained solution. If the obtained solution is improved, it is updated; otherwise, the original solution is restored.

[0060] The execution process of the Q-learning learning mechanism includes: when executing the 6 local search operators 5 times in step 3, record the results of each local search operator each time, and update the Q value corresponding to the local search operator according to the comparison result between the obtained new solution and the original solution. Specifically:

[0061] If the obtained new solution is better than the original solution, the Q value is rewarded ;

[0062] If the obtained new solution is worse than the original solution, the Q value is punished ;

[0063] If the obtained new solution is equal to the original solution, the Q value remains unchanged;

[0064] After performing five local searches, sort the Q values corresponding to each local search operator, and select the local search operator with the highest corresponding Q value to execute once. If the objective value of the new solution is better, update the best solution.

[0065] Step 4: Replace the solution with the largest objective value in the optimized population with the new solution to obtain a new population. If there is no improvement for 5 consecutive times, trigger the perturbation mechanism to update the new population, and combine the perturbed new population with the new population before perturbation to obtain a size of 2 ×PSize Combined population ， Sort each solution in the combined population in ascending order according to the objective value of the solution, and select the first PSize solutions and continue the iteration. Among them, the perturbation mechanism includes two perturbation operators, the shift perturbation operator and the swap perturbation operator. Each time, a perturbation operator is randomly selected for execution. The shift perturbation operator means randomly selecting a workpiece in the current solution and moving the selected workpiece to a position different from the selected workpiece in the current solution. The swap perturbation operator means randomly selecting two workpieces and swapping the positions of the two selected workpieces in the solution.

[0066] Step 5: Iteratively execute Step 3 and Step 4, continue the next round of search until the limited maximum time t × n × m is reached, and output the solution with the smallest objective value of the solution and terminate the execution. Among them, n is the total number of workpieces, m is the total number of machines in each factory.

[0067] To better prove the effectiveness of the present invention, the following will further describe and explain the present invention through experimental analysis of a series of examples of the present invention.

[0068] The test data includes 225 large-scale instances, and these 225 large-scale instances are based on the total number of factories f , the total number of machines in each factory m , and the total number of workpieces n created. Specifically, f ∈ {2, 3, 4}, n ∈ {20, 40, 60, 80, 100}, m ∈ {3, 5, 7}, and there are 5 different test cases for each parameter combination { f , n , m}. In the first factory, the processing time of each workpiece is randomly generated within the range of [10, 40]. In subsequent factories, the processing time of each workpiece on each machine either remains unchanged or randomly increases by 0.05, 0.1, or 0.2 on the basis of the previous factory. The release time of the workpiece is randomly generated within the range of [0, 5 n , and at least f workpieces have a release time of 0. When allocating factories, two special workpieces have been fixedly allocated to the corresponding specific factories and can only perform operations within the specific factories. The CPU time is used as the termination criterion for comparing algorithms, and the termination criterion is set to t × n × m milliseconds. Among them,t is a multiple, set to 60. To better solve and optimize the distributed heterogeneous permutation flow shop scheduling problem based on printed circuit board production, in terms of parameter settings, set PSize = 5. In the local search operator, the number of randomly removed workpieces by the destruction and reconstruction operator is 6.

[0069] To verify the effectiveness of the proposed theoretical results, an instance in the simulation data was selected. The manufacturer consists of two factories, each with two machines. There are 10 workpieces in the current order that need to be processed. The specific information on their processing times, weights, and release times is shown in Table 1:

[0070] Table 1 Specific Information of the Manufacturer

[0071]

[0072] In Table 1, represents the processing time of workpiece j on machine k in factory i . j is the workpiece number, j = 1, 2,..., n , k is the factory number, k = 1, 2,..., f , i is the machine number, i = 1, 2,..., m , is the release time of workpiece j . is the weight of workpiece j . Among them, workpiece 4, workpiece 6, and workpiece 10 are special workpieces. Workpiece 4 and workpiece 10 can only be processed in factory 1, and workpiece 6 can only be processed in factory 2.

[0073] Figure 3 This is the Gantt chart of the embodiment of the present invention, used to show the workpiece arrangement on different machines in two factories. The vertical axis of the chart represents different factories and machines, and the horizontal axis represents the processing time. Each workpiece task is represented in the form of a bar chart. The left and right endpoints of the bar represent the start and completion times of the workpiece respectively. represents workpiece j on machine k in factory iThe completion time on it, with the unit of unit time. The completion times of workpiece 1 to workpiece 10 are 172, 118, 49, 132, 111, 80, 125, 82, 39, 158 respectively. The processing sequence of workpieces in Factory 1 is 3, 8, 2, 4, 10, and the processing sequence of workpieces in Factory 2 is 9, 6, 5, 7, 1.

[0074] To calculate the objective value of the solution, we need to multiply the weight of each workpiece by the corresponding completion time of each workpiece and sum up all the products. The following is the specific calculation process, which can be obtained from Figure 3 the completion times of workpieces in

[0075] The completion time of workpiece 1 is 172 unit times, the weight is 4, and the product is 4 × 172 = 688;

[0076] The completion time of workpiece 2 is 118 unit times, the weight is 5, and the product is 5 × 118 = 590;

[0077] The completion time of workpiece 3 is 49 unit times, the weight is 7, and the product is 7 × 49 = 343;

[0078] The completion time of workpiece 4 is 132 unit times, the weight is 4, and the product is 4 × 132 = 528;

[0079] The completion time of workpiece 5 is 111 unit times, the weight is 5, and the product is 5 × 111 = 555;

[0080] The completion time of workpiece 6 is 80 unit times, the weight is 7, and the product is 7 × 80 = 560;

[0081] The completion time of workpiece 7 is 125 unit times, the weight is 4, and the product is 4 × 125 = 500;

[0082] The completion time of workpiece 8 is 82 unit times, the weight is 5, and the product is 5 × 82 = 410;

[0083] The completion time of workpiece 9 is 39 unit times, the weight is 9, and the product is 9 × 39 = 351;

[0084] The completion time of workpiece 10 is 158 unit times, the weight is 1, and the product is 1 × 158 = 158;

[0085] Summing up these products, we get the objective value of the solution: 688 + 590 + 343 + 528 + 555 + 560 + 500 + 410 + 351 + 158 = 4683.

[0086] The experimental results and analysis of this example are as follows. After setting the parameters for the algorithm (QMA) that solves and optimizes the distributed heterogeneous permutation flow shop scheduling problem in the present invention, it is experimentally compared with an improved fruit fly algorithm (DFFO), three improved IG algorithms (IIG, CMSIG, IGP), and an improved evolutionary algorithm (NEA). To enable the existing five comparison algorithms to adapt to the problems to be solved, necessary modifications are required, including using unified instances, adopting the same objective value, handling special workpieces, etc., and following the details of their respective original algorithms. Select the algorithm type, f , n and m as analysis factors, and compare the instance results. To evaluate the performance of the algorithms, each instance is independently run 5 times, and the relative percentage increase (RPI) is calculated as the evaluation criterion. The calculation formula for the RPI value is , T is the objective value of the solution obtained by a certain algorithm, is the objective value of the smallest solution obtained by the six comparison algorithms. Obviously, the smaller the RPI value, the better the performance of the algorithm. At the same time, the average RPI (ARPI) is also used as the evaluation criterion. The comparison results of the ARPI values of the six algorithms are shown in Table 2:

[0087] Table 2 ARPI values of six algorithms

[0088] Type CMSIG IIG IGP DFFO NEA QMA =2 4.649 10.025 4.352 2.589 9.226 1.942 =3 4.030 9.236 3.899 3.313 9.228 2.312 =4 3.912 8.213 2.869 3.568 8.895 2.397 =20 1.119 1.547 1.538 1.057 6.370 1.177 =40 2.843 7.010 2.261 2.617 9.472 2.131 =60 3.965 9.896 3.529 3.432 9.961 2.499 =80 5.843 12.981 4.631 4.064 10.021 2.485 =100 7.216 14.357 6.575 4.613 9.759 2.795 =3 2.336 10.946 4.721 4.252 10.381 2.624 =5 5.466 8.368 3.443 2.797 8.949 2.092 =7 4.790 8.161 2.957 2.421 8.020 1.936 Average value 4.197 9.158 3.707 3.156 9.116 2.217

[0089] It can be seen from the data in Table 2 that for all scales of data, the QMA algorithm performs better than the existing five comparison algorithms in most problems, showing good performance. Moreover, for different total numbers of factories, the QMA algorithm of the present invention shows better performance. This indicates that the QMA algorithm can effectively handle the scheduling problems of distributed factories.

[0090] Figure 4 is the mean graph of the present invention and the existing algorithms. From Figure 4 it can be seen that the QMA algorithm of the present invention is significantly better than the existing five comparison algorithms statistically, showing good adaptability and optimization ability. Generally speaking, the QMA algorithm of the present invention shows good performance in data analysis.

[0091] In summary, the QMA algorithm of the present invention shows excellent performance, successfully solves a distributed heterogeneous permutation flow shop scheduling problem considering release time and special workpieces, provides an innovative solution, provides strong support for optimized scheduling in actual production scenarios, and provides a feasible method for improving production efficiency and reducing costs.

Claims

1. A method for solving the distributed heterogeneous permutation flow shop scheduling problem, characterized in that: The following steps are included: Step 1: Analyze the characteristics of the distributed heterogeneous permutation flow shop scheduling problem in printed circuit board manufacturing, determine the solution goal to minimize the total weighted completion time, and initialize the parameters, including the population size. PSize , time parameter t ; Step 2: Initialize the population, use the shortest processing time and release time rule, the maximum weight rule, and the minimum release time rule, combined with the greedy insertion method to generate the first three solutions of the initial population, use the composite method to generate the fourth solution of the initial population, and use the random method to generate the remaining solutions of the initial population. PSize -4 solutions, and apply the backtracking optimization method to the initial population to obtain the optimized population; Step 3: Use the ternary tournament method to select a solution from the initial population, and execute 6 local search operators in sequence, each of which is executed 5 times. After each execution of the local search operator, the Q-learning mechanism is executed. If the new solution is better than the original solution, the Q value is increased; if the new solution is worse than the original solution, the Q value is reduced; if the new solution is equal to the original solution, the Q value remains unchanged. After the 5 local search operators are executed, the Q values ​​corresponding to each local search operator are sorted, and the local search operator with the highest corresponding Q value is selected to execute once. If the target value of the new solution obtained after the selected local search operator is executed is smaller, the new solution is retained. Step 4: Replace the solution with the largest target value in the optimized population with the new solution to obtain a new population. If there is no improvement for 5 consecutive times, the perturbation mechanism is triggered to update the new population, and the new population after the perturbation is combined with the new population before the perturbation to obtain a population of size 2 × PSize The combined population ， Sort each solution in the combined population from small to large according to the target value of the solution, and select the first PSize solution, and continue to iterate; Step 5, iteratively execute steps 3 and 4, and continue the next round of search until the maximum time is reached, output the solution with the smallest target value, and terminate the execution.

2. The method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 1 is characterized in that: The shortest sum of processing time and release time rule is to determine the priority according to the sum of the total processing time and release time of the workpiece, and sort the workpieces from small to large according to the sum of the total processing time and release time of the workpiece; The maximum weight rule is to determine the priority according to the weight of the workpiece, and sort the workpieces from the largest to the smallest weight; The minimum release time rule is to determine the priority according to the release time of the workpiece, and sort the workpieces from the smallest to the largest release time; The greedy insertion method means that for each workpiece sequence sorted by the sorting rule, one workpiece is selected in turn and inserted into the position in all factory sequences where the target value of the solution is minimized. The process of selecting and inserting workpieces is repeated until all the workpieces in the workpiece sequence sorted by the shortest processing time and release time rule, the maximum weight rule, and the minimum release time rule are inserted, and the first three solutions are obtained.

3. The method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 2 is characterized in that: The implementation process of the composite method includes the following steps: (1) sorting all artifacts according to the maximum weight rule to obtain an initial artifact sequence; (2) extracting artifacts one by one from the initial artifact sequence, and when extracting each artifact, checking whether there are other artifacts with the same weight as the extracted artifact; (3) if there are no other artifacts with the same weight, directly insert the extracted artifact into the position in all factory sequences that minimizes the target value of the solution, and continue to extract the next artifact; (4) if there are other artifacts with the same weight, put the artifacts with the same weight into a new artifact sequence, and re-sort them according to the rule of the sum of the shortest processing time and the release time, and insert the newly sorted artifacts into the positions in all factory sequences that minimize the target value of the solution, until all artifacts in the new artifact sequence complete the insertion process; (5) according to the order of artifacts in the initial artifact sequence, select a artifact that has not been extracted by the initial artifact sequence and the new artifact sequence, and repeat steps (3) and (4) until all artifacts complete the insertion process, generating a fourth solution.

4. The method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 3 is characterized in that: In the backtracking optimization method, a solution with the smallest target value in the initial population is selected as the initial candidate set. If there are multiple solutions with the smallest and identical target values, they are all added to the initial candidate set as the new candidate set. A solution is randomly selected from the initial population, and the workpieces therein are removed one by one. The removed workpieces are reinserted into the position in all factory sequences where the target value of the obtained solution can be minimized. During the insertion process, if a better solution is generated, the original solution is replaced by the better solution. If the better solution is not greater than the solution with the smallest target value in the initial population, it is added to the new candidate set to obtain the preferred candidate set, and the first untested solution is selected from the preferred candidate set. The process of removing and inserting workpieces is repeated. When the solutions obtained for three consecutive times are all greater than the solution with the smallest target value in the initial population, a solution that has not been selected is reselected from the preferred candidate set to start exploration. If there is no solution that meets the requirements in the preferred candidate set at this time, the backtracking process is terminated and the solution with the smallest target value is updated.

5. A method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 4, characterized in that: The ternary tournament method randomly selects three solutions from the initial population, compares the target values ​​of the three solutions, and determines the one with the smallest target value among the three solutions. If there are multiple solutions with the same target value and they are all the smallest, the first selected solution with the smallest target value is selected to execute the local search operator, where: The local search operators include the key factory optimization operator, the large-impact workpiece optimization operator, the destruction and reconstruction operator, the two-stage optimization operator, the special workpiece optimization operator, and the inter-factory exchange operator. The key factory refers to the factory with the largest target value of the factory solution among all factories. If there are multiple factories with the same target value of the solution, the factory with the smallest factory number is selected. The target value of the factory solution refers to the sum of the weight of each workpiece assigned to a factory and the product of the completion time corresponding to each workpiece, where The operation process of the key factory optimization operator is to remove all the workpieces in the key factory and randomly insert the removed workpieces into the position in all factory sequences that can minimize the target value of the obtained solution. If the quality of the solution is improved by the removal and insertion operation, the new solution is retained; otherwise, the original solution is restored, and the removal and insertion operations are performed at most five times, and finally the best solution among the five removal and insertion operations is output; The operation process of the large-impact workpiece optimization operator is to remove the top 50% of the workpieces that have the greatest impact on the target value of the solution from the current solution, and randomly insert them into the position in all factory sequences that can minimize the target value of the solution. If the quality of the solution is improved by the removal and insertion operation, the new solution is retained; otherwise, the original solution is restored, and a maximum of five removal and insertion operations are performed, and finally the best solution among the five removal and insertion operations is output; The operation process of the destructive reconstruction operator is to randomly remove a part of the workpieces and reinsert the removed workpieces into the position in all factory sequences that can minimize the target value of the obtained solution. If the quality of the obtained solution is improved by the removal and insertion operation, the new solution is retained; otherwise, the original solution is restored, and a maximum of five removal and insertion operations are performed, and finally the best solution among the five removal and insertion operations is output; The operation process of the two-stage optimization operator is divided into two stages. The first stage is the same as the destruction and reconstruction operator. In the second stage, all the workpieces in the factory are exchanged in turn. If the exchange operation improves the quality of the solution, the new solution is retained; otherwise, the solution before the exchange is restored. A maximum of five exchange operations are performed, and the best solution among the five exchange operations is finally output. The operation process of the special workpiece optimization operator is to randomly select a factory, exchange the positions of the two special workpieces and other workpieces in turn, and update if the solution obtained is improved, otherwise restore the original solution; The operation process of the inter-factory exchange operator is to select the first two factories whose solution target values ​​are the largest, exchange the second half of the workpieces in the processing sequences of the two factories, transfer the exchanged workpieces to the new factories, and reinsert them into the new factory sequence at a position where the target value of the solution can be minimized. If the solution is improved, it is updated, otherwise the original solution is restored.

6. A method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 5, characterized in that: The Q-learning learning mechanism execution process includes, when step 3 executes 6 local search operators 5 times, recording the results of each local search operator each time, and if the new solution is better than the original solution, the Q value is rewarded , if the new solution is worse than the original solution, the Q value is penalized If the new solution is equal to the original solution, the Q value remains unchanged. After executing five local searches, sort the Q values ​​corresponding to each local search operator, select the local search operator with the highest Q value and execute it once. If the target value of the new solution is better, update the best solution.

7. A method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 6, characterized in that: The perturbation mechanism includes two types of perturbation operators, the shift perturbation operator and the exchange perturbation operator. One perturbation operator is randomly selected to execute each time. The shift perturbation operator refers to randomly selecting a workpiece in the current solution and moving the selected workpiece to a position different from the selected workpiece in the current solution. The exchange perturbation operator refers to randomly selecting two workpieces and exchanging the positions of the two selected workpieces in the solution.

8. The method for solving the distributed heterogeneous permutation flow shop scheduling problem according to claim 1 is characterized in that: The maximum time limit is t × n × m,n is the total number of workpieces, m is the total number of machines in each factory.

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