Distributed workshop scheduling optimization method based on mathematical heuristic and self-learning driving

Abstract

The invention discloses a distributed workshop scheduling optimization method based on mathematical heuristic and self-learning driving, belongs to the technical field of distributed workshop scheduling, and provides an order allocation and plan scheduling scheme for automobile and electronic assembly enterprises oriented to distributed factory layout. The method comprises the following steps of: decomposing a scheduling decision problem of a distributed heterogeneous assembly flow shop into a first sub-problem related to a workpiece and a second sub-problem related to a product according to an affiliation relationship among the workpiece, the product and a customer, and obtaining an initial solution according to a delivery deadline, a distributed heterogeneous attribute and an SPT heuristic algorithm while solving the first sub-problem and the second sub-problem; the product is inserted into the position with the lowest delay cost to optimize the initial solution; and based on the optimized initial solution, by setting a nested greedy stage, a self-learning local search stage and an acceptance mechanism, completing the scheduling decision of the distributed heterogeneous assembly flow shop. According to the invention, the scheduling optimization scheme can be quickly and efficiently obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed workshop scheduling, and in particular to a distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive. Background Art

[0002] At present, mass customization has become the main production model of contemporary manufacturing companies. This approach requires companies to provide a range of diversified and customized products and services designed to meet the unique needs of individual consumers while maintaining cost-effectiveness. In this model, companies strategically disperse production capacity to different locations and equip multiple workshops for mass production of different product components. This strategy aims to improve production efficiency and reduce manufacturing costs. Subsequently, the final assembly of the product is customized according to the specific provisions of the customer order. This multi-stage and multi-workshop collaborative operation is optimized as the distributed assembly shop scheduling problem (DAFSP). Under this problem, an effective scheduling mechanism is to comprehensively utilize the production capacity and resource allocation of multiple factories to improve the overall efficiency within the distributed manufacturing system. This complex scheduling scheme is essential to optimize the production process, ensure rapid response to market demand, and maintain competitive advantage in the globalized economy.

[0003] Although DAFSP has been studied quite a lot so far, there are still some limitations in the existing research work. There is a common assumption in current research that all participating manufacturing or assembly plants are homogeneous, which is inconsistent with the real world. At the same time, around the above assumption, many scholars have focused on the scheduling optimization mechanism under different constraints and different target requirements, and designed customized optimization algorithms to obtain suitable scheduling solutions. .

[0004] There are two main technical shortcomings in existing research work:

[0005] (1) Existing work usually assumes that manufacturing plants are identical, which oversimplifies the geographical dispersion and inherent variability of plants in the real world. The heterogeneous properties of these plants, such as differences in the number of machines or processing capabilities, should be an integral consideration in distributed scheduling. Considering these properties is crucial to reflecting a more realistic manufacturing environment and developing more practical and applicable scheduling solutions.

[0006] (2) In today’s competitive market, fulfilling make-to-order delivery commitments is critical to maintaining customer satisfaction and enhancing market competitiveness. This necessity emphasizes the importance of meeting the diverse product specifications required by different customers and the need to complete and ship all items in customer orders within the specified delivery time. In this context, efficient scheduling must prioritize minimizing the overall delay costs associated with each customer order. However, current research work ignores this point and fails to truly respond to the actual needs of the industry.

[0007] In summary, in today's competitive market, fulfilling the delivery commitment of make-to-order production is essential to maintaining customer satisfaction and enhancing market competitiveness. This necessity emphasizes the importance of meeting the diverse product specifications required by different customers, and the necessity to complete and ship all items in customer orders within the specified delivery time. In addition, the geographical dispersion and inherent variability of factories in the real world cause these factories to have heterogeneous properties, such as differences in the number of machines or processing capabilities. Existing technologies design mathematical models and intelligent algorithms under the assumption of efficiency goals and homogeneous properties of factories, ignoring the order-oriented production, distribution and delivery, as well as the order importance and production synergy brought about by the heterogeneous properties of factories. Summary of the invention

[0008] In order to solve the above problems, the purpose of the present invention is to provide a distributed shop scheduling optimization technology based on mathematical heuristics and self-learning drive, aiming to provide order allocation and planning scheduling solutions for automobile and electronic assembly companies when facing distributed factory layout.

[0009] In order to achieve the above technical objectives, the present application provides a distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive, comprising the following steps:

[0010] Taking minimizing the total delay penalty cost as the objective function, a mixed integer programming model for scheduling distributed heterogeneous assembly flow shops under large-scale personalized customization is constructed by setting workpiece allocation sequence constraints, workpiece completion time constraints, product allocation and sorting constraints, product completion time constraints and customer overdue time constraints.

[0011] Based on the mixed integer programming model, according to the relationship between workpieces, products and customers, the scheduling decision problem of distributed heterogeneous assembly flow shops is decomposed into multiple workpiece-related first sub-problems and multiple product-related second sub-problems, and different sub-problems are solved;

[0012] Based on the solution process of the first and second subproblems, the initial solution is obtained according to the delivery deadline, distributed heterogeneous properties and SPT heuristic algorithm, and the insertion operation is used to insert the product to the position with the lowest delay cost to optimize the initial solution;

[0013] Based on the optimized initial solution, the scheduling decision of the distributed heterogeneous assembly flow shop is completed by setting the nested greedy stage, the self-learning local search stage and the acceptance mechanism.

[0014] Preferably, in the process of constructing the mixed integer programming model, the completion time of the workpiece on different machines in the processing plant is determined by the completion time constraint of the workpiece;

[0015] Through product allocation and sorting constraints, ensure that each product must be assigned to an assembly plant and control the product sequence of each assembly plant;

[0016] Through customer overdue time constraints, we ensure that the actual delivery time for any customer is not earlier than the completion time of the product they require, while emphasizing that early delivery is not allowed.

[0017] Preferably, in the process of solving the first subproblem, based on the first subproblem, according to the candidate work set given any product, by releasing the task allocation and sequence of all other workpieces in the manufacturing plant, and the sequence of all products in the assembly plant, the completion time of the allocated workpiece on each machine is regarded as the release time, and the candidate work set completion time is regarded as the target of the first subproblem, and the mixed integer linear programming of the first subproblem solved by the CPLEX / MIP solver is used to find the optimal allocation and sequence of partial workpieces.

[0018] Preferably, in the process of solving the first subproblem, when the first subproblem contains many workpieces, the optional interval object of the jth workpiece on the kth machine of the uth processing plant is used as an interval variable, and several interval variables are combined into sequence variables and solved by CPLEX / CP.

[0019] Preferably, in the process of solving the second sub-problem, based on the second sub-problem, according to the product sequence and the completion time of all given workpieces, by releasing the allocation and sequence of all other products in the assembly plant, and the allocation and sequence of all workpieces in the processing plant, the second sub-problem is solved according to the planning and solving method of the first sub-problem.

[0020] Preferably, in the process of obtaining the initial solution, the customer sequence is determined according to the ascending order of the delivery deadline, and for each customer, the product sequence is determined according to the ascending order of the total processing time of the customer's products to obtain the initial solution.

[0021] Preferably, in the process of optimizing the initial solution, the first product is placed in an empty two-dimensional sequence, and the remaining products are inserted into all possible positions in turn. In each insertion, the position with the smallest delay cost is selected to complete the optimization of the initial solution, wherein all products under the same customer are located in the same dimension and all products under the same customer are regarded as a whole.

[0022] Preferably, in the process of setting the nested greedy stage, some customers and products are extracted, and a partial two-dimensional sequence is constructed of the extracted products;

[0023] According to the remaining customers and products, the construction operation follows the product order of the partial two-dimensional sequence, and sequentially iteratively inserts the products of the partial two-dimensional sequence into the optimal position that results in the minimum late delivery cost.

[0024] Preferably, in the process of setting the self-learning local search phase, setting the local search operation includes:

[0025] Internal exchange for non-critical customers LS1: Select a product from the pre-selected products of non-critical customers, exchange it with all other products of the same customer, and output the newly generated solution with the minimum late delivery cost;

[0026] Non-critical customer internal insertion LS2: extract the pre-selected products of non-critical customers from the current solution, reinsert the products into all possible positions of the customer, and output the newly generated solution with the minimum late delivery cost;

[0027] LS3: Select a product from the pre-selected products of the key customer, exchange it with all other products of the same customer, and output the newly generated solution with the minimum late delivery cost;

[0028] Key customer internal insertion LS4: extract the pre-selected products of the key customer from the current solution, reinsert the product into all possible positions of the customer, and output the newly generated solution with the minimum late delivery cost;

[0029] Key customer forward insertion LS5: Extract a pre-selected key customer from the current solution and forward insert it into all possible positions, outputting a newly generated solution with the minimum late delivery cost;

[0030] Based on the local search operation, according to the characteristics of the customer sequence, four rules are set to determine the candidate operations, including:

[0031] Rule 1: If there is no key customer after the non-key customer, or all non-key customers contain only one product, LS1 and LS2 are not executed;

[0032] Rule 2: If all key customers contain only one product, LS3 and LS4 are not executed;

[0033] Rule 3: If there is only one key customer and this customer is ranked first, LS5 will not be executed;

[0034] Rule 4: If there are no critical customers, this indicates that the optimal solution is found and all operators are not executed;

[0035] According to the four rules set, a self-learning selection strategy is set to select superior operators, determine appropriate customers or products, perform local search phases and update the information matrix; among them,

[0036] The process of selecting a superior operator includes:

[0037] Three dynamic two-dimensional matrices are used to store the historical success rate information of operations, customers and products, namely sr ope 、sr cus and sr pro , from sr ope Extract the historical success rate information of all candidate operations and put it into a new two-dimensional matrix sr can In, through The weighted cumulative success rate in |sr is used to evaluate all candidate operations. can i| is the row width of the i-th selection; is the jth historical success rate of the ith choice;

[0038] According to the weighted cumulative success rate, Calculate the probabilities and then select a superior action via roulette wheel selection;

[0039] The process of executing the local search phase and updating the information matrix includes: taking the appropriate customer or product as input, the selected operation performs a local search on the current solution to generate a new solution, and Get a new success rate, TTC best and TTC new are the delay costs of the best solution and the new solution respectively, and the new success rate will be added to sr ope and sr cus (or sr pro ) at the end of the corresponding row in , if the row width exceeds RL, delete its first element.

[0040] Preferably, in the process of setting the acceptance mechanism, whether to replace the current solution with the new solution is decided by a temperature-based acceptance criterion.

[0041] The present invention also discloses a distributed workshop scheduling optimization system based on mathematical heuristics and self-learning drive, which is used to implement the above-mentioned distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive, and the system includes:

[0042] The model building module is used to build a mixed integer programming model for scheduling distributed heterogeneous assembly flow shops under large-scale personalized customization by setting workpiece allocation sequence constraints, workpiece completion time constraints, product allocation and sorting constraints, product completion time constraints, and customer overdue time constraints, with the objective function of minimizing the total delay penalty cost;

[0043] The sub-problem decomposition module is used to decompose the scheduling decision problem of the distributed heterogeneous assembly flow shop into multiple first sub-problems related to workpieces and multiple second sub-problems related to products based on the mixed integer programming model and the relationship between workpieces, products and customers, and solve different sub-problems;

[0044] The initial solution generation module is used to obtain the initial solution based on the solution process of the first subproblem and the second subproblem according to the delivery deadline, distributed heterogeneous attributes and SPT heuristic algorithm, and insert the product to the position with the lowest delay cost by using the insertion operation to optimize the initial solution;

[0045] The scheduling decision module is used to complete the scheduling decision of the distributed heterogeneous assembly flow shop based on the optimized initial solution by setting the nested greedy stage, the self-learning local search stage and the acceptance mechanism.

[0046] The present invention discloses the following technical effects:

[0047] (1) In dealing with order-oriented production, distribution and delivery, the present invention designs a mathematical heuristic decoding based on mixed integer programming and constraint programming to decompose the complex and multifaceted decisions inherent in the original problem into smaller sub-decisions. These sub-decisions are accurately solved by various sub-MILPs (or sub-CPs) derived from the main MILP.

[0048] (2) When optimizing scheduling problems with distributed heterogeneous attributes, the present invention designs a NEH heuristic based on mathematical heuristics to integrate the requirements of specific problems to produce high-quality initial solutions; implements a nested greedy stage, including extracting customers and products, to improve the overall performance of the algorithm; and proposes a self-learning local search stage, which organically integrates knowledge-based operations, rule-based operation candidate sets, and self-learning strategies, thereby enhancing the algorithm's deep exploration capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0050] Figure 1 is the number of wins of the algorithm in the pairwise comparison in the heat map described in the present invention;

[0051] Figure 2 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0052] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0053] like Figure 1-2 As shown, the present invention provides a distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive, which specifically includes the following contents:

[0054] 1. Establish a mixed integer optimization model for large-scale personalized customization:

[0055] 1.1. Description of main parameters and variables, as shown in Table 1:

[0056] Table 1

[0057] parameter illustrate parameter illustrate j,j Workpieces; f Number of processing plants; u Processing plants; g Number of assembly plants; k machine; <![CDATA[t j，k，u ]]> The processing time of workpiece j on machine k in processing plant u; i,i′ product <![CDATA[p i，v ]]> The assembly time of product i at assembly plant v; v Assembly plants; <![CDATA[I i ]]> The set of artifacts required by product i; h client; H， The product set that customers demand; n Number of workpieces; <![CDATA[d h ]]> The delivery date of customer h; <![CDATA[m u ]]> The number of machines in the processing plant u; <![CDATA[β h ]]> The delay penalty coefficient of client h; s Quantity of products; M A maximum value. b Number of customers;

[0058] Table 2

[0059] variable illustrate <![CDATA[Z j，u ]]> (Binary variable) If workpiece j is assigned to processing plant u, it is 1; otherwise, it is 0; <![CDATA[X j，j’，u ]]> (Binary variable) If workpiece j is the direct predecessor of workpiece j' in processing plant u, it is 1; otherwise, it is 0; <![CDATA[L iv ]]> (Binary variable) 1 if product i is assigned to assembly plant v; 0 otherwise; <![CDATA[Y i，i’，v ]]> (Binary variable) 1 if product i is the immediate predecessor of product i' at assembly plant v; 0 otherwise; <![CDATA[CM j，k，u ]]> (Continuous variable) The completion time of job j on machine k in processing plant u; <![CDATA[FCM j ]]> (Continuous variable) The final completion time of job j in the processing stage; <![CDATA[CA i，v ]]> (Continuous variable) The completion time of product i at assembly plant v; <![CDATA[DT h ]]> (Continuous variable) Actual delivery time for customer h; <![CDATA[OT h ]]> (Continuous variable) The overdue time of customer h; TTC Total delay penalty cost.

[0060] 1.2. The mixed integer programming model for the distributed heterogeneous assembly flow shop scheduling problem under large-scale personalized customization is shown in Table 3:

[0061] Table 3

[0062]

[0063]

[0064] Among them, formula (1) indicates that the objective function is to minimize the total delay penalty cost. Formula (2-7) is the workpiece allocation sequence constraint, which aims to constrain the binary variable Z j，u and X j，j’，uFormula (8-12) is the workpiece completion time constraint, which aims to determine the completion time of the workpiece on different machines in the processing plant. Formula (13-18) is the product allocation and sorting constraint, which aims to constrain the binary variable L i，v and Y i，i’，v , to ensure that each product must be assigned to an assembly plant and control the product sequence of each assembly plant. Formula (19-22) is the product completion time constraint, which aims to determine the completion time of the product in the assembly plant. Formula (23-26) is the customer overdue time constraint, which ensures that the actual delivery time of any customer is not earlier than the completion time of the product required by the customer, and emphasizes that early delivery is not allowed.

[0065] 2. Self-learning iterative greedy algorithm based on mathematical heuristics for large-scale personalized customization:

[0066] The mixed integer programming model for the distributed heterogeneous assembly flow shop scheduling problem under large-scale personalized customization mentioned above has the characteristics of strong coupling, multiple constraints, multiple variables and multiple objectives, and is a typical NP-hard problem. If the conventional model solving method is adopted, it is difficult to meet the requirements of large-scale cases, and it is urgent to adopt an intelligent optimization algorithm for fast and efficient solution. The iterative greedy algorithm is an efficient local search algorithm with a simple structure and few parameters. This algorithm was first applied to the flow shop scheduling problem and showed excellent performance, so it stood out from many well-known algorithms. Based on the basic framework of the iterative greedy algorithm, the present invention proposes an extended version with mathematical heuristics, specific knowledge and self-learning ability, and named it as a self-learning iterative greedy algorithm based on mathematical heuristics (MSIG). The main difference between this algorithm and the traditional iterative greedy algorithm is:

[0067] (1) The MSIG algorithm designs a mathematical heuristic decoding method based on mixed integer programming and constraint programming;

[0068] (2) The MSIG algorithm proposes a NEH heuristic method based on mathematical heuristics and problem characteristics to obtain a high-quality initial solution;

[0069] (3) The MSIG algorithm uses a nested greedy stage to explore the neighborhood structure of the workpiece sequence and the product sequence respectively;

[0070] (4) The MSIG algorithm designs knowledge-based operators, rule-based operator candidate sets, and a self-learning local search phase for self-learning selection to improve the algorithm's deep exploration capabilities.

[0071] The detailed steps of the algorithm are as follows:

[0072] Step 1: Mathematical heuristic decoding based on mixed integer programming and constraint programming:

[0073] The distributed heterogeneous assembly flow shop scheduling problem under large-scale personalized customization includes four decision-making processes: workpiece allocation, workpiece sorting, product allocation, and product sorting. Since the solution space of large-scale problems is large, if metaheuristics are used directly, the efficiency is low. In order to improve this, this work decomposes the original problem into multiple workpiece-related sub-problems and multiple product-related sub-problems based on the relationship between workpieces, products, and customers. And for different sub-problems, different integer programming models or constraint programming models are used for accurate solutions. The specific process is as follows:

[0074] (1) For each subproblem related to an artifact, given a set of candidate jobs for any product, denoted by I i , mathematical heuristic algorithm 1 schedules them in the manufacturing plant. This is achieved by releasing the task assignment and order of all other workpieces in the manufacturing plant, and the order of all products in the assembly plant. Since the assigned workpiece directly affects the start time of the candidate workpiece on different machines, the completion time of the assigned workpiece on each machine is regarded as the release time, denoted as rt k,u . Collection I i The completion time of is taken as the objective of this subproblem. Hence, a mixed integer linear programming of the subproblem solved by CPLEX / MIP solver is used to find the optimal allocation and sequence of the partial workpieces in a very short time.

[0075] (2) Each artifact-related subproblem may contain many artifacts, which means that the mathematical heuristic algorithm 1 may not be able to find the optimal solution in a short time, which in turn affects the quality of solving subsequent subproblems. In order to improve this situation, a novel constraint programming model, namely mathematical heuristic 2, is designed to find high-quality solutions for subproblems containing many artifacts. In this model, there are two decision variables: interval variables and sequence variables. The former is op j,k,u , refers to the optional interval object of the jth workpiece on the kth machine in the uth processing plant. The latter is mch k,u , is a set of ops on the kth machine in the uth processing plant j,k,u The constructed model is solved by CPLEX / CP.

[0076] (3) For each product-related subproblem, given the completion time of all workpieces, mathematical heuristic algorithm 3 arranges the candidate products for any customer (set H h ) in the assembly plant. This is achieved by releasing the allocation and order of all other products in the assembly plant, and the allocation and order of all workpieces in the processing plant. The completion time of all workpieces in the set Hh is a fixed value derived from the mathematical heuristic algorithm 1-2. Similar to the mathematical heuristic algorithm 1, the completion time of the allocated product on each machine is regarded as the release time, denoted by rav The mathematical model is constructed and solved using the CPLEX / MIP solver to find the set H in a very short time. h The optimal allocation and order of all products in .

[0077] (4) In product order, the proposed decoding first uses mathematical heuristics 1-2 to determine each set I i The selection of mathematical heuristics 1-2 depends on the I i If I i If the value is greater than a given parameter qt, then mathematical heuristic algorithm 1 is selected to ensure the optimality of the solution. Instead, mathematical heuristic algorithm 2 is selected to balance operational efficiency and optimality. After a large number of initial experiments, the parameter qt is set to 9. Mathematical heuristic algorithm 3 then iterates over the customers in this solution to schedule all products. After mathematical heuristic algorithms 1-3 are run, the resulting completion time is used to update the release time rt k,u or v .

[0078] Step 2: NEH heuristic method based on mathematical heuristics and problem characteristics:

[0079] In order to obtain a high-quality initial solution, the algorithm combines the specific requirements of the problem, such as delivery deadline, delay cost minimization, and distributed heterogeneous properties, with the NEH heuristic algorithm and the SPT heuristic algorithm. The resulting new hybrid heuristic is the NEH heuristic method based on mathematical heuristics and problem characteristics. The method mainly consists of four steps: Step 1-2 obtains the initial solution based on the delivery deadline, distributed heterogeneous properties, and the SPT heuristic algorithm; Step 3-4 uses an insertion operation to insert the product to the position with the lowest delay cost to optimize the initial solution. The specific details are as follows:

[0080] (1) Step 1: Determine the customer sequence [σ 1 , ..., σ a , ..., σ b ].

[0081] (2) Step 2: For each customer σ a ,according to The product sequence is determined in ascending order of the total processing time of the products Right now to obtain a complete initial solution.

[0082] (3) Step 3: Place the first product into an empty two-dimensional sequence and insert the remaining products into all possible positions in turn. In each insertion, choose the position with the lowest delay cost. Note that all products under the same customer are located in the same dimension.

[0083] (4) Step 4: Treat all products under the same customer as a whole and adjust the customer sequence using a method similar to that in step 3.

[0084] Step 3: Nested Greedy Phase:

[0085] The greedy phase is an important process in the traditional iterative greedy algorithm. It expands the search space and develops better and more promising regions of the solution space. Considering the unique characteristics of the research problem, such as the relationship between customers and products, the present invention designs a nested greedy phase, which aims to extract some customers and products and reinsert them into the best position to build a better solution.

[0086] In short, the destruction operation first randomly selects d customers, namely Where d is the algorithm parameter that needs to be calibrated. Further extraction from the solution products. Belongs to the customer The number of products. All extracted products construct a partial two-dimensional sequence. Subsequently, the construction operation follows the product order of the partial two-dimensional sequence and iteratively inserts the products into the best position that results in the minimum late delivery cost.

[0087] Step 4: Self-learning local search phase of knowledge-based operators, rule-based operator candidate sets, and self-learning selection:

[0088] Local search is a very effective technique that can improve the algorithm's deep exploration ability. This paper proposes five local search operations based on the relationship between customers and products. In each iteration, some operations that can effectively improve the current solution are first screened as candidates. Then, a self-learning strategy combined with historical success rate is designed to select a superior operator to generate a new solution.

[0089] (1) Local search operations. The knowledge of a specific problem can guide the operation to explore a better solution space. Therefore, considering the minimization of the delay cost associated with the delivery date, the present invention first defines key customers. For any customer, if there is a product that is completed after the deadline, then this customer is a key customer. Then, 5 local search operations are designed based on key customers and are described in detail as follows.

[0090] Non-key customer internal exchange (LS1): Select a product from the pre-selected products of a non-key customer and exchange it with all other products of the same customer. Output the newly generated solution with the minimum late delivery cost.

[0091] Non-critical customer internal insertion (LS2): Extract the pre-selected product for a non-critical customer from the current solution. Re-insert the product into all possible positions for this customer. Output the newly generated solution with the minimum late delivery cost.

[0092] Intra-key customer exchange (LS3): Select a product from the pre-selected products of the key customer and exchange it with all other products of the same customer. Output the newly generated solution with the minimum late delivery cost.

[0093] Key Customer Intra-Insertion (LS4): Extract the pre-selected products of the key customer from the current solution. Re-insert the product into all possible positions of this customer. Output the newly generated solution with the minimum late delivery cost.

[0094] Key Customer Forward Insertion (LS5): Extract a pre-selected key customer from the current solution and forward insert it into all possible positions. Output the newly generated solution with the minimum late delivery cost.

[0095] (2) Rule-based method for determining the candidate set of operators. The above operations perform neighborhood searches within or between customers for different types of customers. Sometimes, a small amount of product or customer adjustments obviously cannot improve the current solution, resulting in invalid evolution. To avoid this, this section considers the characteristics of the customer sequence in the current solution and designs four rules to determine the candidate operations.

[0096] Rule 1: If no key customer follows the non-key customer, or all non-key customers contain only one product, LS1 and LS2 are not executed.

[0097] Rule 2: If all key accounts contain only one product, LS3 and LS4 are not executed.

[0098] Rule 3: If there is only one key customer and that customer is ranked first, LS5 is not executed.

[0099] Rule 4: If there are no critical customers, this indicates that the optimal solution is found and all operators are not executed.

[0100] (3) Self-learning selection strategy. In order to fully utilize the exploration ability of the above operations, the self-learning strategy not only needs to select superior operations from the operation candidate set, but also needs to determine the appropriate customers or products for adjustment. This strategy refers to the historical success rate and adaptively makes selection decisions to maximize the probability of improving the current solution. Since three selection decisions are involved, the self-learning strategy displays three dynamic two-dimensional matrices to store the historical success rate information of operations, customers, and products, namely, sr ope 、sr cus and sr pro . These matrices have different fixed lengths 5, b, and s, respectively. Given the lower reference value of the success rate in early iterations, these matrices have a maximum width RL, which is an algorithm parameter that needs to be calibrated. Regardless of how the information is updated, the number of rows in these matrices cannot exceed RL. Initially, all rows of these matrices have the same width 1, and all elements have the same ratio. That is, sr oPe =[0.2, 0.2, 0.2, 0.2, 0.2] T , sr cus =[1 / b,1 / b,...] T and sr pro =[1 / s, 1 / s, ...] T .

[0101] In each iteration, the following steps are performed:

[0102] Step 1: Choose a superior operator. This strategy is derived from sr ope Extract the historical success rate information of all candidate operations and put them into a new two-dimensional matrix sr can It evaluates all candidate operations by the weighted cumulative success rate in equation (27). In this equation, |sr can i| is the row width of the i-th selection; is the jth historical success rate of the ith choice. Based on the weighted cumulative success rate, this strategy calculates the probability through equation (28) and then selects a superior operation through the roulette wheel selection method.

[0103] Step 2: Identify the appropriate customer or product. If LS1 or LS2 is selected, pro Extract information about products belonging to all non-key customers from Sr. pro If LS5 is selected, then information about products belonging to all key customers is extracted from Sr cus The extracted information is put into a new two-dimensional matrix sr can and use the method in step one to identify appropriate customers or products.

[0104] Step 3: Perform the local search phase and update the information matrix. With the appropriate customer or product as input, the selected operation performs a local search on the current solution to generate a new solution. Subsequently, the new success rate is obtained through equation (29), where TTC best and TTC new are the delay costs of the best solution and the new solution respectively. The new success rate will be added to sr ope and sr cus (or sr pro ) at the end of the corresponding row in . If the row width exceeds RL, its first element is deleted:

[0105]

[0106] Step 5: Acceptance Mechanism:

[0107] The present invention adopts a temperature-based acceptance criterion to decide whether to replace the current solution with a new solution. Considering the distributed heterogeneous nature of the research problem, the present invention designs a new temperature calculation formula, as shown in formula (30). In this formula, rm and ra are the randomly selected processing and assembly plants, respectively; T 0 is the initial temperature parameter that needs to be calibrated. If the new solution is better than the current solution, it is accepted. Otherwise, the probability of accepting the new solution is

[0108] Based on the above, in order to minimize the delay cost, the present invention proposes a mixed integer linear programming model and a self-learning iterative greedy (MSIG) algorithm based on mathematical heuristics. Considering that the problem involves multi-faceted and complex decision-making processes, the proposed algorithm strategically disassembles these decisions. In the decoding stage, the optimization problem of a part of small-scale decision variables is accurately solved through mathematical heuristics. At the same time, large-scale decisions are optimized through improved algorithmic mechanisms. It is worth noting that in order to obtain a high-quality initial solution, a NEH heuristic based on mathematical heuristics is designed to meet the specific requirements of the problem. And a nested greedy stage is introduced to intelligently extract customers and products in the algorithm encoding to enhance the effectiveness of the algorithm. In addition, the knowledge-based operator set, the rule-based operator candidate set and the self-learning selection strategy are integrated into the local search stage, thereby enhancing the algorithm's deep exploration ability. Finally, the superiority of the MSIG algorithm is verified by comparing nine existing heuristic algorithms and five state-of-the-art meta-heuristic algorithms.

[0109] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0110] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0111] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive, characterized in that: The following steps are involved: Taking minimizing the total delay penalty cost as the objective function, a mixed integer programming model for scheduling distributed heterogeneous assembly flow shops under large-scale personalized customization is constructed by setting workpiece allocation sequence constraints, workpiece completion time constraints, product allocation and sorting constraints, product completion time constraints and customer overdue time constraints. Based on the mixed integer programming model, according to the relationship between workpieces, products and customers, the scheduling decision problem of the distributed heterogeneous assembly flow shop is decomposed into a first sub-problem related to multiple workpieces and a second sub-problem related to multiple products, and different sub-problems are solved; Based on the solution process of the first sub-problem and the second sub-problem, an initial solution is obtained according to the delivery deadline, distributed heterogeneous properties and SPT heuristic algorithm, and an insertion operation is used to insert the product to the position with the lowest delay cost to optimize the initial solution; Based on the optimized initial solution, the scheduling decision of the distributed heterogeneous assembly flow shop is completed by setting a nested greedy stage, a self-learning local search stage and an acceptance mechanism.

2. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 1 is characterized in that: In the process of constructing the mixed integer programming model, the completion time of the workpiece on different machines in the processing plant is determined by the completion time constraint of the workpiece; Through the product allocation and sorting constraints, it is ensured that each product must be allocated to an assembly plant, and the product sequence of each assembly plant is controlled; Through the customer overdue time constraint, it is ensured that the actual delivery time of any customer is not earlier than the completion time of the product required by the customer, while emphasizing that early delivery is not allowed.

3. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 2 is characterized in that: In the process of solving the first subproblem, based on the first subproblem, according to the candidate work set given for any product, by releasing the task allocation and sequence of all other workpieces in the manufacturing plant, and the sequence of all products in the assembly plant, the completion time of the allocated workpiece on each machine is regarded as the release time, and the candidate work set completion time is regarded as the objective of the first subproblem. The mixed integer linear programming of the first subproblem solved by the CPLEX / MIP solver is used to find the optimal allocation and sequence of some workpieces.

4. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 3 is characterized by: In the process of solving the first subproblem, when the first subproblem contains many workpieces, the optional interval object of the jth workpiece on the kth machine of the uth processing plant is used as an interval variable, and several of the interval variables are combined into sequence variables and solved by CPLEX / CP.

5. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 4 is characterized in that: In the process of solving the second sub-problem, based on the second sub-problem, according to the product sequence and the completion time of all given workpieces, by releasing the allocation and sequence of all other products in the assembly plant, and the allocation and sequence of all workpieces in the processing plant, the second sub-problem is solved according to the planning and solving method of the first sub-problem.

6. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 5 is characterized by: In the process of obtaining the initial solution, the customer sequence is determined according to the ascending order of the delivery period, and for each customer, the product sequence is determined according to the ascending order of the customer's total product processing time to obtain the initial solution.

7. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 6 is characterized by: In the process of optimizing the initial solution, the first product is placed in an empty two-dimensional sequence, and the remaining products are inserted into all possible positions in turn. In each insertion, the position with the smallest delay cost is selected to complete the optimization of the initial solution, in which all products under the same customer are located in the same dimension and all products under the same customer are regarded as a whole.

8. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 7 is characterized in that: In the process of setting up the nested greedy stage, some customers and products are extracted, and a partial two-dimensional sequence is constructed of the extracted products; According to the remaining customers and products, the construction operation follows the product order of the partial two-dimensional sequence, and sequentially iteratively inserts the products of the partial two-dimensional sequence into the optimal position that results in the minimum late delivery cost.

9. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 8 is characterized in that: In the process of setting the self-learning local search phase, the local search operation is set, including: Internal exchange for non-critical customers LS1: Select a product from the pre-selected products of non-critical customers, exchange it with all other products of the same customer, and output the newly generated solution with the minimum late delivery cost; Non-critical customer internal insertion LS2: extract the pre-selected products of non-critical customers from the current solution, reinsert the products into all possible positions of the customer, and output the newly generated solution with the minimum late delivery cost; LS3: Select a product from the pre-selected products of the key customer, exchange it with all other products of the same customer, and output the newly generated solution with the minimum late delivery cost; Key customer internal insertion LS4: extract the pre-selected products of the key customer from the current solution, reinsert the product into all possible positions of the customer, and output the newly generated solution with the minimum late delivery cost; Key customer forward insertion LS5: Extract a pre-selected key customer from the current solution and forward insert it into all possible positions, outputting a newly generated solution with the minimum late delivery cost; Based on the local search operation, according to the characteristics of the customer sequence, four rules are set to determine the candidate operations, including: Rule 1: If there is no key customer after the non-key customer, or all non-key customers contain only one product, LS1 and LS2 are not executed; Rule 2: If all key customers contain only one product, LS3 and LS4 are not executed; Rule 3: If there is only one key customer and this customer is ranked first, LS5 will not be executed; Rule 4: If there are no critical customers, this indicates that the optimal solution is found and all operators are not executed; According to the four rules set, a self-learning selection strategy is set to select superior operators, determine appropriate customers or products, perform local search phases and update the information matrix; among them, The process of selecting a superior operator includes: Three dynamic two-dimensional matrices are used to store the historical success rate information of operations, customers and products, namely sr ope 、sr cus and sr pro , from sr ope Extract the historical success rate information of all candidate operations and put it into a new two-dimensional matrix sr can In, through The weighted cumulative success rate in |sr is used to evaluate all candidate operations. can i| is the row width of the i-th selection; is the jth historical success rate of the ith choice; According to the weighted cumulative success rate, Calculate the probabilities and then select a superior action via roulette wheel selection; The process of executing the local search phase and updating the information matrix includes: taking the appropriate customer or product as input, the selected operation performs a local search on the current solution to generate a new solution, and Get a new success rate, TTC best and TTC new are the delay costs of the best solution and the new solution respectively, and the new success rate will be added to sr ope and sr cus (or sr pro ) at the end of the corresponding row in , if the row width exceeds RL, delete its first element.

10. The distributed workshop scheduling optimization method based on mathematical heuristics and self-learning drive according to claim 9 is characterized in that: In the process of setting up the acceptance mechanism, a temperature-based acceptance criterion is used to decide whether to replace the current solution with a new solution.

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