Dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening

Abstract

The present invention provides a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line opening, which relates to the technical field of production scheduling. The scheduling method sets input parameters and operating parameters, constructs an initial solution set on the premise of giving priority to agent 2, selects the optimal solution as the initial solution x0; performs a shaking operation on the initial solution x0 to obtain a new solution x1, performs a local search on x1 to obtain a new solution x2, and determines whether the fitness value of x2 is better than the fitness value of x1. If so, x2 is used as the initial solution and iterates continuously until the global optimal solution x0 is found. best , according to x best The provided solution assigns production tasks to suppliers to maximize the resource utilization and operational efficiency of high-end equipment manufacturing companies and reduce the total cost of the supply chain.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and in particular to a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation. Background Art

[0002] In recent years, the high-end equipment market has demonstrated rapid growth. With the continued expansion of the market and intensified competition, the efficiency and quality requirements for batch production and maintenance within the high-end equipment supply chain are becoming increasingly stringent. Minimizing the total cost of batch production while ensuring the regular delivery of maintenance spare parts is of great value to the company's supply chain. Driven by the development of next-generation information technology, high-end equipment manufacturers are increasingly valuing the convenience and versatility of dual-agent scheduling. Dual-agent scheduling can be categorized into single-stage dual-agent scheduling and multi-stage dual-agent scheduling, depending on the processing stage. In the field of high-end equipment manufacturing, production is a crucial link.

[0003] Taking the aviation industry as an example, large aviation companies rely on suppliers to produce batches of parts, such as batch parts A and B, which are indispensable for aircraft manufacturing. At the same time, maintenance spare parts, such as C, are crucial to ensuring the continued safe operation of aircraft. When two agents are involved, each agent has a specific role and task. Agent 1 is primarily responsible for producing batch parts A and B, ensuring the smooth progress of the aircraft manufacturing process. Agent 2, on the other hand, focuses on the production of maintenance spare part C, providing support for the subsequent maintenance and operation of the aircraft. This dual-agent scheduling problem is of great significance in high-end equipment manufacturing. It requires companies to be able to effectively coordinate and manage the production activities of different agents to ensure a smooth and efficient manufacturing process.

[0004] Against this backdrop, high-end equipment manufacturers impose strict deadlines on suppliers for the delivery of batch parts. Exceeding these deadlines triggers delay penalty costs, creating an economic constraint on suppliers' ability to deliver on time. For maintenance parts, the urgency is even greater; they must be delivered unconditionally within the specified timeframe to ensure operational continuity and safety. Therefore, when formulating production plans, companies must strive to minimize overall delay penalty costs while meeting the urgent need for maintenance parts and effectively controlling production line startup costs to achieve optimal cost-effectiveness. In practice, batch parts from Agent 1 and maintenance parts from Agent 2 share the supplier's flexible production line resources. This flexible production model requires highly precise scheduling and coordination. Based on the dynamic fluctuations in the number of workpieces, suppliers must flexibly adjust the number of production lines activated to ensure optimal resource allocation. However, this adjustment is not unlimited; it is subject to the physical limitations of the supplier's total production line capacity. This requires scheduling strategies to maintain efficiency while also considering realistic production capacity limits.

[0005] In summary, when faced with dual-agent scheduling, high-end equipment manufacturers must comprehensively consider multiple dimensions, including time, cost, and resources, to develop an optimal production plan that both meets production needs and is economically efficient. This not only tests supplier management capabilities but also holds the key to enhancing a company's overall competitiveness.

[0006] Currently, most solutions to the dual-agent collaborative scheduling problem for high-end equipment, including mass production parts and maintenance spare parts, use precise algorithms, heuristic methods, or artificial intelligence algorithms. However, when considering the requirement that one agent can represent two or more workpieces, the problem becomes significantly more complex, making it difficult to find an optimal solution quickly. This, in turn, impacts the dual-agent collaborative scheduling of high-end equipment, including mass production parts and maintenance spare parts. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention provides a dual-agent collaborative scheduling method for the high-end equipment supply chain based on the opening of flexible production lines, which solves the problem that the existing collaborative scheduling technology for batch production parts and operation and maintenance accessories of high-end equipment in the production stage cannot quickly and accurately obtain the optimal solution while considering multiple workpiece agents.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] A dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation includes the following steps:

[0010] S1. Setting input parameters of a variable neighborhood search algorithm based on data generated during the production process of high-end equipment;

[0011] S2. Set the operating parameters of the variable neighborhood search algorithm, which include: the maximum number of iterations k of the variable neighborhood search algorithm max ;Number of neighborhood structures N s ; Initialize the number of iterations k = 0; Initialize the neighborhood structure s = 1; Variable neighborhood search algorithm local search neighborhood structure initial weight

[0012] S3, encode the high-end equipment production task based on the variable neighborhood search algorithm, and randomly generate the initial solution x0 based on the priority of satisfying the maintenance spare parts product C of agent 2;

[0013] S4, based on the variable neighborhood search algorithm, the initial solution x0 is shaken, and an individual population is obtained within the neighborhood structure. The optimal individual in the individual population is obtained by the greedy algorithm, and the initial solution is updated through the optimal individual to obtain the new solution x1;

[0014] S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood N sPerform local search to obtain the local optimal solution x2;

[0015] S6. Compare the fitness value f(x1) of the new solution x1 with the fitness value f(x2) of the local optimal solution x2. If f(x2)≤f(x1), assign the value of x2 to x1 and continue to perform local search based on the current neighborhood structure to obtain the local optimal solution. If not, set s=s+1 and execute S7.

[0016] S7. Determine s≤N s Is it true? If so, return to S5; if not, set k = k + 1 and go to S8;

[0017] S8. Determine k≤k max Is it established? If yes, go to S4; if not, go to S9;

[0018] S9, the algorithm terminates and outputs the global optimal solution x best , for x best Decode and output set PN l , PN l The set of workpiece sequences representing the workpiece numbers of all workpieces of agent 1 and agent 2 on production line l.

[0019] Preferably, in S1, the input parameters include:

[0020] The number of workpieces n of product A of agent 1 in the production phase A , the number of workpieces of product B n B , the number of workpieces n of product C of agent 2 C ;Total number of workpieces N=n A +n B +n C ; Maximum number of production lines L in the production phase; Production line startup cost sc; Product X workpiece processing time The artifact set of product X is

[0021] Preferably, the S3 specifically includes the following steps:

[0022] S3.1. Based on the constraints of the high-end equipment production stage, prioritize the processing of workpiece C for agent 2. On this basis, randomly generate codes for the production stages and add all initial solutions x to the initial solution set X.

[0023] S3.2. Determine whether the number of initial solutions in the initial solution set X is greater than the number of initial solutions N0 in the initial solution set. If not, return to S3.1 and continue generating initial solutions. Otherwise, output the initial solution set X.

[0024] S3.3. Calculate the fitness value of each solution in the initial solution set X, and select the solution with the smallest fitness value as the initial solution x0.

[0025] Preferably, the fitness value calculation formula in S3.3 is expressed as follows:

[0026]

[0027] in,

[0028] Among them, F min It means the total cost is minimized;

[0029] D A Indicates the deadline time for product A in agent 1;

[0030] D B Indicates the deadline time for product B in agent 1;

[0031] α and β are the delay penalty cost coefficients of product A and product B respectively;

[0032] sc represents the setup cost of starting a production line;

[0033] represents the maximum completion time of job X, X∈{A, B, C};

[0034] Q C represents the latest completion time of agent 2;

[0035] represents the production time of the process of high-end equipment product X at the i-th position on the production line l, X∈{A, B, C};

[0036] It represents the production time of the process of high-end equipment product X at the last process position j on the production line l, X∈{A, B, C}.

[0037] Preferably, the S4 specifically includes the following steps:

[0038] S4.1. Define variables i, j, g = 1, obtain input x0, and the current iteration number is k;

[0039] S4.2. Randomly generate two integers in the interval [1, N] and assign them to variables i and j.

[0040] S4.3. Select the i-th and j-th elements in x0 and swap them to obtain the new solution x1.

[0041] S4.4. Let \(g = g + 1\), and determine whether \(g\leq k\) holds. If it holds, return to S4.2; otherwise, execute step S4.5.

[0042] S4.5. Calculate the fitness value, and determine whether the solution \(x1\) is better than \(x0\). If so, output \(x1\); otherwise, let \(x1 = x0\).

[0043] Preferably, the S5 specifically includes the following steps:

[0044] S5.1. When initially setting the algorithm parameters, due to the unknown structural effectiveness of the local search neighborhood, the initial neighborhood structure weights are default set to be equal; the local search neighborhood structure set of the variable neighborhood search algorithm is \(N\) s , \(s = 1, 2, 3,\cdots s\) max , where the initial weights corresponding to each neighborhood structure are

[0045] S5.2. Combine the probability formula of the roulette wheel to calculate the probabilities of each neighborhood structure

[0046] S5.3. Calculate the cumulative probability of each neighborhood structure That is, the sum of the selection probabilities of all neighborhood structures before each neighborhood structure;

[0047] S5.4. Define a variable \(r\), randomly generate a number between \((0, 1)\) and assign it to the variable \(r\). If \(Q\) s-1 \(< r < Q\) s , then select the neighborhood structure \(N\) s for local search.

[0048] Preferably, the neighborhood structure includes:

[0049] Neighborhood Structure 1: Define variables \(x1\), \(x2\), \(y1\), \(y2\). For the production line sequence coding, randomly select two integers in the interval \([1, L]\) and assign them to \(x1\) and \(x2\) and \(x1 < x2\), and take the average of the numbers at the \(x1\)-th position and the \(x2\)-th position in the current solution's coding; for the workpiece sequence coding, randomly select two integers in the interval \([1, N]\) and assign them to \(y1\) and \(y2\) and \(y1 < y2\), and swap the numbers before the \(y1\)-th position and after the \(y2\)-th position in the current solution's coding;

[0050] Neighborhood Structure 2: Define variables x1, x2, y1, y2. For the encoding of the production line sequence, randomly select two integers within the interval [1, L], assign them to x1 and x2 where x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the encoding of the workpiece sequence, randomly select two integers within the interval [1, N], assign them to y1 and y2 where y1 < y2, and reverse the production line position numbers corresponding to the positions between the y1-th and y2-th positions in the encoding of the current solution.

[0051] Neighborhood Structure 3: Define variables x1, x2, x3, y1, y2. For the encoding of the production line sequence, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3 where x1 < x2 < x3, and take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the encoding of the workpiece sequence, randomly select two integers within the interval [1, N], assign them to y1 and y2 where y1 < y2, exchange the production line position numbers corresponding to the y1-th and y2-th positions in the encoding of the current solution, and exchange the production line position numbers before the y1-th position with the production line position numbers between the y1-th and y2-th positions.

[0052] Neighborhood Structure 4: Define variables x1, x2, y1, y2, y3. For the encoding of the production line sequence, randomly select two integers within the interval [1, L], assign them to x1 and x2 where x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the encoding of the workpiece sequence, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3 where y1 < y2 < y3, and exchange the production line position numbers between the y1-th and y2-th positions with the production line position numbers between the y2-th and y3-th positions in the encoding of the current solution.

[0053] Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the encoding of the production line sequence, randomly select two integers within the interval [1, L], assign them to x1 and x2 where x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the encoding of the workpiece sequence, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3 where y1 < y2 < y3, exchange the left side of the y1-th position with the production line position numbers between the y1-th and y2-th positions in the encoding of the current solution, and then exchange the production line position numbers corresponding to the y2-th and y3-th positions.

[0054] Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the production line sequence encoding, randomly select two integers within the interval [1, L], and assign them to x1 and x2 with x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select three integers within the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3. Swap the production line position numbers on the left side of the y1-th position and on the right side of the y3-th position in the encoding of the current solution, assign the production line position number at the y1-th position to z, then assign the production line position number at the y3-th position to the y1-th position, assign the production line position number at the y2-th position to the y3-th position, and assign z to the y2-th position;

[0055] Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the production line sequence encoding, randomly select three integers within the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3, and take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the interval [1, N], and assign them to y1 and y2. Assign the encoding of the current solution to form 2 solutions. Swap the two sides of the y1-th position in the encoding of one solution, and then swap the two sides of the y2-th position in the encoding of the other solution. Randomly select an integer within the interval [1, N], and assign it to z. Combine the production line position encodings on the left side of the z-th position and including the z-th position in the encoding of the first solution and on the right side of the z-th position in the encoding of the second solution to form a new solution;

[0056] Neighborhood Structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the production line sequence encoding, randomly select three integers within the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3, and take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select four integers within the interval [1, N], and assign them to y1, y2, y3, and y4 with y1 < y2 < y3 < y4. Swap the y1-th and y2-th positions in the encoding of the current solution, swap the y3-th and y4-th positions in the encoding of the current solution, and then swap the production line position numbers between the y1-th and y2-th positions and the production line position numbers between the y3-th and y4-th positions.

[0057] Preferably, S9 specifically includes the following steps:

[0058] S9.1. From the solution x bestGenerate the workpiece set PN assigned to production line l l ;

[0059] S9.2、h l The number of the set of workpieces processed on the lth production line is

[0060] S9.3, for the workpiece number on the first production line Sort by

[0061] S9.4, according to the formula Calculate the manufacturing span CmaxX,X∈{A,B} of product A and product B;

[0062] S9.5, according to the formula Output F min .

[0063] Preferably, the heuristic rules set in S9.3 are as follows:

[0064] S9.3.1. If the workpiece number y i >n A +n B When the workpiece number {n A +n B +1,…,N}, number this part of the workpiece {n A +n B +1,…,N} are sorted in non-increasing order by processing time;

[0065] S9.3.2. Find the critical point Q of the processing time of product C on production line l, and assign the workpiece number {n A +n B +1,…,N} are placed before the critical point Q;

[0066] S9.3.3, number the remaining workpieces {1,2,…,n A +n B}Sort in non-increasing order by processing time.

[0067] This invention provides a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation. Compared with existing technologies, it has the following advantages:

[0068] In the present invention, input parameters based on the variable neighborhood search algorithm are set according to the data of the high-end equipment production process, and the operating parameters of the variable neighborhood search algorithm are set. Under the premise of giving priority to satisfying agent 2, an initial solution set is constructed, and the optimal solution is selected as the initial solution x0 according to the fitness value of the solution; a shaking operation is performed on the initial solution x0 to obtain a new solution x1, and a local search neighborhood structure is selected based on the roulette probability strategy. A local search is performed on x1 in the neighborhood structure to obtain a new solution x2, and it is judged whether the fitness value of x2 is better than the fitness value of x1. If so, x2 is used as the initial solution and it is continued to iterate until the global optimal solution x1 is searched. best , according to x best The proposed solution assigns production tasks to suppliers to minimize the target total delay penalty cost of agent 1 and ensure that agent 2 completes production within the specified time limit; it maximizes the resource utilization and operational efficiency of high-end equipment manufacturing enterprises and reduces the total cost of the supply chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0070] Figure 1 is a flowchart of a scheduling method according to an embodiment of the present invention;

[0071] Figure 2 Schematic diagram of coding in an embodiment of the present invention. DETAILED DESCRIPTION

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0073] The embodiment of the present application solves the problem that the existing collaborative scheduling technology of high-end equipment batch production parts and operation and maintenance accessories in the production stage cannot quickly and accurately find the optimal solution while considering multiple workpiece agents by providing a dual-agent collaborative scheduling method for the high-end equipment supply chain based on the opening of flexible production lines.

[0074] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0075] Example:

[0076] like Figure 1 As shown, the present invention provides a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation, and the scheduling method includes the following steps:

[0077] S1. Setting input parameters of a variable neighborhood search algorithm based on data generated during the production process of high-end equipment;

[0078] S2. Set the operating parameters of the variable neighborhood search algorithm, including: the maximum number of iterations k of the variable neighborhood search algorithm max ;Number of neighborhood structures N s ; Initialize the number of iterations k = 0; Initialize the neighborhood structure s = 1; Variable neighborhood search algorithm local search neighborhood structure initial weight

[0079] S3, encode the high-end equipment production task based on the variable neighborhood search algorithm, and randomly generate the initial solution x0 based on the priority of satisfying the maintenance spare parts product C of agent 2;

[0080] S4, based on the variable neighborhood search algorithm, the initial solution x0 is shaken, and an individual population is obtained within the neighborhood structure. The optimal individual in the individual population is obtained by the greedy algorithm, and the initial solution is updated through the optimal individual to obtain the new solution x1;

[0081] S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood N s Perform local search to obtain the local optimal solution x2;

[0082] S6. Compare the fitness value f(x1) of the new solution x1 with the fitness value f(x2) of the local optimal solution x2. If f(x2)≤f(x1), assign the value of x2 to x1 and continue to perform local search based on the current neighborhood structure to obtain the local optimal solution. If not, set s=s+1 and execute S7.

[0083] S7. Determine s≤N s Is it true? If so, return to S5; if not, set k = k + 1 and go to S8;

[0084] S8. Determine k≤k max Is it established? If yes, go to S4; if not, go to S9;

[0085] S9, the algorithm terminates and outputs the global optimal solution x best , for x best Decode and output set PNl , PN l The set of workpiece sequences representing the workpiece numbers of all workpieces of agent 1 and agent 2 on production line l.

[0086] This embodiment of the present invention considers dual-agent scheduling for flexible production lines: one agent handles two batch production parts, while the other handles one maintenance spare part. This allows for flexibility in the production line during the supplier's production phase. In this scenario, collaborative scheduling of the production process for high-end equipment is performed to achieve a near-optimal solution, effectively assigning workpieces to production lines. This minimizes overall supply chain costs and improves resource utilization and collaboration efficiency for high-end equipment manufacturers.

[0087] The following will describe each step in detail based on the specific content:

[0088] In S1, input parameters of the variable neighborhood search algorithm are set based on data from the high-end equipment production process, wherein the input parameters include:

[0089] The number of workpieces n of product A of agent 1 in the production phase A , the number of workpieces of product B n B , the number of workpieces n of product C of agent 2 C ;Total number of workpieces N=n A +n B +n C ; Maximum number of production lines L in the production phase; Production line startup cost sc; Product X workpiece processing time The artifact set of product X is

[0090] In S3, the high-end equipment production task is encoded based on the variable neighborhood search algorithm, and the initial solution x0 is randomly generated based on the priority of satisfying the maintenance spare parts product C of agent 2, specifically including:

[0091] Based on the variable neighborhood search algorithm, the production line problem and product workpieces of the high-end equipment manufacturing process are encoded to obtain the initial solution x0. x0 is composed of two sequences: the production line sequence PL and the workpiece sequence PN. The PL code indicates whether the production line is active and the number of workpieces processed on the active production line, and the PN code indicates the production line assigned to all workpiece numbers. The specific implementation process is as follows:

[0092] The encoding process is as follows:

[0093] Based on the characteristics of the flexible production line, the solution x0 consists of two parts: the production line sequence PL and the workpiece sequence PN, which can be expressed as x0 = {h1,h2,…,h L ; 1,2,…,n A ,n A+1 …,nA +n B ,…,N}. The code of the production line sequence PL is {h1,h2,h3,…,h L}, the length of the production line sequence PL is the total number of production lines L, h l Indicates the code of the production line sequence PL, if h l =0, indicating that the lth production line is not started; if h l =m, which means that m workpieces are processed on the lth production line; a total of N workpieces are processed on L production lines, that is, The encoding of the workpiece sequence PN is {1,2,…,n A ,n A+1 ,…,n A +n B ,…,N}, the length of the workpiece sequence PN is the total number of workpieces of products A, B, and C, that is, N = n A +n B +n C ,y i Represents the encoding of the workpiece sequence PN, {1,2,…,n A} represents the workpiece number of product A, {n A+1 ,…,n A +n B} represents the workpiece number of product B, {n A +n B +1,…,N} represents the workpiece number of product C.

[0094] Therefore, the initial solution can be expressed as x0 = {h1,h2,h3,…,h L ; 1,2,…,n A ,n A+1 ,…,n A +n B ,…,N},

[0095] like Figure 2 As shown, the solution is encoded using a one-dimensional array, and the length of the first part is the number of production lines L, h l Represents the number of workpieces processed by the lth production line; the length of the second part is the set of all workpieces of the product N, y i Represents the artifact number of the i-th product artifact.

[0096] The S3 specifically includes the following steps:

[0097] S3.1. Based on the constraints of the high-end equipment production stage, prioritize the processing of workpiece C for agent 2. On this basis, randomly generate codes for the production stages and add all initial solutions x to the initial solution set X.

[0098] S3.2. Determine whether the number of initial solutions in the initial solution set X is greater than the number of initial solutions N0 in the initial solution set. If not, return to S3.1 and continue generating initial solutions. Otherwise, output the initial solution set X.

[0099] S3.3. Calculate the fitness value of each solution in the initial solution set X, and select the solution with the smallest fitness value as the initial solution x0.

[0100] The fitness value calculation formula in S3.3 is as follows:

[0101]

[0102] in,

[0103] Among them, F min It means the total cost is minimized;

[0104] D A Indicates the deadline time for product A in agent 1;

[0105] D B Indicates the deadline time for product B in agent 1;

[0106] α and β are the delay penalty cost coefficients of product A and product B respectively;

[0107] sc represents the setup cost of starting a production line;

[0108] represents the maximum completion time of job X, X∈{A, B, C};

[0109] Q C represents the latest completion time of agent 2;

[0110] represents the production time of the process of high-end equipment product X at the i-th position on the production line l, X∈{A, B, C};

[0111] It represents the production time of the process of high-end equipment product X at the last process position j on the production line l, X∈{A, B, C}.

[0112] In S4, the initial solution x0 is shaken based on the variable neighborhood search algorithm to obtain an individual population within the neighborhood structure, and the optimal individual in the individual population is obtained by the greedy algorithm. The initial solution is updated by the optimal individual to obtain a new solution x1, which specifically includes:

[0113] Select the kth neighborhood structure (initial k = 1), perform a shaking operation on the initial solution x0 obtained in step S3, obtain a population of q individuals, calculate the fitness values ​​of q individuals in the population, and use the greedy algorithm to obtain the optimal individual x in the population. min , and update the new solution x1=x min Before obtaining the individual population through the neighborhood structure, it is necessary to set the neighborhood structure of the algorithm Shaking operation. The set Shaking operation perturbation neighborhood set is N k ,k=1,2,…,k max

[0114] S4.1. Define variables i, j, g = 1, obtain input x0, and the current iteration number is k;

[0115] S4.2. Randomly generate two integers in the interval [1, N] and assign them to variables i and j.

[0116] S4.3. Select the i-th and j-th elements in x0 and swap them to obtain the new solution x1.

[0117] S4.4. Set g = g + 1 and determine whether g ≤ k. If so, return to S4.2; otherwise, proceed to step S4.5.

[0118] S4.5. Calculate the fitness value and determine whether the solution x1 is better than x0. If so, output x1; otherwise, set x1 = x0.

[0119] The corresponding shaking operation here is to transform the initial solution to another point in the feasible domain according to certain rules. This can prevent the same initial solution from falling into the local optimum under continuous iteration, thereby improving the global search capability of the algorithm.

[0120] In said S5, based on the roulette probability selection, a local search neighborhood structure is obtained. In the selected neighborhood N s Perform local search to obtain the local optimal solution x2, including:

[0121] It should be noted that the local search in the variable neighborhood search algorithm is to recycle the neighborhood structure only when the neighborhood structure finds a solution that is better than the current solution. In order to search for a more effective neighborhood structure in advance and reduce unnecessary iterations and cycle time, a weighted selection strategy, namely roulette wheel probability selection, is added when selecting the neighborhood structure. The specific process is as follows:

[0122] S5.1. When setting the algorithm parameters initially, due to the unknown structural validity of the local search neighborhood, the default setting of the initial neighborhood structure weights is equal; the local search neighborhood structure set of the variable neighborhood search algorithm is N s, s = 1, 2, 3, … s max , where the initial weight corresponding to each neighborhood structure is

[0123] S5.2. Calculate the probabilities of each neighborhood structure in combination with the probability formula of roulette

[0124] S5.3. Calculate the cumulative probability of each neighborhood structure That is, the sum of the selection probabilities of all previous neighborhood structures corresponding to each neighborhood structure;

[0125] S5.4. Define a variable r, randomly generate a number between (0, 1) and assign it to the variable r. If Q s-1 < r < Q s , then select the neighborhood structure N s for local search.

[0126] According to the roulette probability weight strategy, select the neighborhood structure. Due to the characteristics of high-end equipment manufacturing enterprises such as numerous tasks and complex constraint relationships, 8 different neighborhood structures are set in the local search algorithm. The specific situations are as follows:

[0127] Neighborhood structure 1: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers in the interval [1, L] and assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers in the interval [, N] and assign them to y1 and y2, and y1 < y2. Swap the numbers before the y1-th position and after the y2-th position in the encoding of the current solution.

[0128] Neighborhood structure 2: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers in the interval [1, L] and assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers in the interval [1, N] and assign them to y1 and y2, and y1 < y2. Reverse the production line position numbers corresponding between the y1-th and y2-th positions in the encoding of the current solution.

[0129] Neighborhood Structure 3: Define variables x1, x2, x3, y1, y2. For the production line sequence encoding, randomly select three integers within the interval [1, L], and assign them to x1, x2, and x3, where x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select two integers within the interval [1, N], and assign them to y1 and y2, where y1 < y2. Swap the production line position numbers corresponding to the y1-th and y2-th positions in the encoding of the current solution, and also swap the production line position numbers before the y1-th position with those between the y1-th and y2-th positions.

[0130] Neighborhood Structure 4: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers within the interval [1, L], and assign them to x1 and x2, where x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select three integers within the interval [1, N], and assign them to y1, y2, and y3, where y1 < y2 < y3. Swap the production line position numbers between the y1-th and y2-th positions with those between the y2-th and y3-th positions in the encoding of the current solution.

[0131] Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers within the interval [1, L], and assign them to x1 and x2, where x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select three integers within the interval [1, N], and assign them to y1, y2, and y3, where y1 < y2 < y3. Swap the left side of the y1-th position with the production line position numbers between the y1-th and y2-th positions in the encoding of the current solution, and then swap the y2-th position with the production line position number corresponding to the y3-th position.

[0132] Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the production line sequence coding, randomly select two integers within the interval [1, L], assign them to x1 and x2 and x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the coding of the current solution; for the workpiece sequence coding, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3 and y1 < y2 < y3, swap the production line position numbers on the left side of the y1-th position and on the right side of the y3-th position in the coding of the current solution, assign the production line position number at the y1 position to z, then assign the production line position number at the y3 position to the y1 position, assign the production line position number at the y2 position to the y3 position, and assign z to the y2 position.

[0133] Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the production line sequence coding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3 and x1 < x2 < x3, and take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the coding of the current solution; for the workpiece sequence coding, randomly select two integers within the interval [1, N], assign them to y1 and y2, assign the coding of the current solution to form 2 solutions, swap the two sides of the y1-th position in the coding of one solution, and then swap the two sides of the y2-th position in the coding of the other solution. Randomly select an integer within the interval [1, N], assign it to z, and combine the production line position coding on the left side of the z-th position and including the z-th position in the coding of the first solution and the production line position coding on the right side of the z-th position in the coding of the second solution to form a new solution.

[0134] Neighborhood Structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the production line sequence coding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3 and x1 < x2 < x3, and take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the coding of the current solution; for the workpiece sequence coding, randomly select four integers within the interval [1, N], assign them to y1, y2, y3, and y4 and y1 < y2 < y3 < y4, swap the y1-th position and the y2-th position in the coding of the current solution, swap the y3-th position and the y4-th position in the coding of the current solution, and then swap the production line position numbers between the y1-th position and the y2-th position and the production line position numbers between the y3-th position and the y4-th position.

[0135] In the embodiments of the present invention, eight neighborhood structures are designed according to the actual problem background, which improves the ability of the algorithm to globally search for the optimal solution.

[0136] In the above S9, x best The decoding process is to assign all workpieces to the corresponding production lines for processing, then arrange the workpieces in the processing order based on the heuristic algorithm, calculate the manufacturing span of each product, and finally calculate the total cost of agent 1. The specific operations include the following:

[0137] S9.1, by solving x best Generate the workpiece set PN assigned to production line l l ;

[0138] S9.2、h l The number of the set of workpieces processed on the lth production line is

[0139] S9.3, for the workpiece number on the first production line To sort, set the following heuristic rules:

[0140] S9.3.1. If the workpiece number y i >n A +n B When the workpiece number {n A +n B +1,…,N}, number this part of the workpiece {n A +n B +1,…,N} are sorted in non-increasing order by processing time;

[0141] S9.3.2. Find the critical point Q of the processing time of product C on production line l, and assign the workpiece number {n A +n B +1,…,N} are placed before the critical point Q;

[0142] S9.3.3, number the remaining workpieces {1,2,…,n A +n B} Sort in non-increasing order by processing time;

[0143] S9.4, according to the formula Calculate the manufacturing span CmaxX,X∈{A,B} of product A and product B;

[0144] S9.5, according to the formula Output F min .

[0145] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0146] 1. In the embodiment of the present invention, the input parameters of the variable neighborhood search algorithm are set according to the data of the high-end equipment production process, the operating parameters of the variable neighborhood search algorithm are set, and the initial solution set is constructed under the premise of giving priority to satisfying agent 2. According to the fitness value of the solution, the optimal solution is selected as the initial solution x0; the initial solution x0 is shaken to obtain a new solution x1, and a local search neighborhood structure is selected based on the roulette probability strategy. A local search is performed on x1 in the neighborhood structure to obtain a new solution x2. It is determined whether the fitness value of x2 is better than the fitness value of x1. If so, x2 is used as the initial solution and it is iterated continuously until the global optimal solution x1 is searched. best , according to x best The proposed solution assigns production tasks to suppliers to minimize the target total delay penalty cost of agent 1 and ensure that agent 2 completes production within the specified time limit; it maximizes the resource utilization and operational efficiency of high-end equipment manufacturing enterprises and reduces the total cost of the supply chain.

[0147] 2. In an embodiment of the present invention, dual-agent scheduling with flexible production lines is considered, that is, one agent is responsible for two types of batch production parts, and the other agent is responsible for one type of operation and maintenance spare parts, and the production line is flexible during the supplier's production stage; in this case, the production process of high-end equipment is collaboratively scheduled to obtain an approximate optimal solution, which can effectively assign production lines, thereby minimizing the total cost of the supply chain and improving the resource utilization efficiency and collaboration efficiency of high-end equipment manufacturing enterprises.

[0148] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0149] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation, characterized in that: The scheduling method includes the following steps: S1. Set the input parameters based on the variable neighborhood search algorithm according to the data generated in the high-end equipment production process; S2. Set the operating parameters of the variable neighborhood search algorithm. The operating parameters include: the maximum number of iterations of the variable neighborhood search algorithm ; Number of neighborhood structures ; Initialize the number of iterations ; Initialize the neighborhood structure ; Initial weight of local search neighborhood structure of variable neighborhood search algorithm ; S3, based on the variable neighborhood search algorithm, encode the high-end equipment production tasks, and randomly generate the initial solution based on the priority of satisfying the maintenance spare parts product C of agent 2. ; S4, based on the variable neighborhood search algorithm for the initial solution Perform shaking operations to obtain individual populations within the neighborhood structure, and use the greedy algorithm to obtain the optimal individual in the individual population. Update the initial solution through the optimal individual to obtain a new solution. ; S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood Perform local search to obtain the local optimal solution ; S6, relatively new solution The fitness value of and local optimal solution The fitness value of The size of , then Assign the value of , continue to search locally based on the current neighborhood structure to obtain the local optimal solution; if not, let , and execute S7; S7. Judgment Is it true? If so, return to S5; if not, , and transfer to S8; S8. Judgment Is it established? If yes, go to S4; if not, go to S9; S9, the algorithm terminates and outputs the global optimal solution ,right Decode and output the set , Indicates that all artifacts from agent 1 and agent 2 are in A set of workpiece sequences with workpiece numbers on each production line; Specifically, S3 includes the following steps: S3.

1. Based on the constraints of the high-end equipment production stage, give priority to satisfying the processing of workpiece C of agent 2; on this basis, randomly generate the code of the production stage and convert all the initial solutions into Add to the initial solution set X; S3.

2. Determine whether the number of initial solutions in the initial solution set X is greater than the number of initial solutions in the initial solution set If it is not greater than, return to S3.1 to continue generating the initial solution, otherwise output the initial solution set X; S3.

3. Calculate the fitness value of each solution in the initial solution set X and select the solution with the smallest fitness value as the initial solution ; In S3.3, the fitness value calculation formula is expressed as follows: in, in, It means the total cost is minimized; Indicates the deadline time for product A in agent 1; Indicates the deadline time for product B in agent 1; are the delay penalty cost coefficients of product A and product B respectively; represents the setup cost of starting a production line; express The maximum completion time of the workpiece, ; represents the latest completion time of agent 2; Indicates high-end equipment products Process in the production line Previous Production time at each location, ; Indicates high-end equipment products Process in the production line The last process location Production time, .

2. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 1 is characterized in that: In S1, the input parameters include: The number of workpieces of product A for agent 1 during the production phase , the number of workpieces of product B , the number of workpieces of product C of agent 2 ;Total number of workpieces ; Maximum number of production lines in a production phase Production line startup costs ; Product X workpiece processing time ; The set of artifacts for product X is .

3. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 1 is characterized in that: Specifically, S4 includes the following steps: S4.

1. Define variables , get input , the current iteration number is ; S4.2, randomly generate two Integer in the range, assigned to the variable ; S4.

3. Selection The and elements, swap these two elements and get a new solution ; S4.4, Order ,judge Is it true? If so, return to S4.2; Otherwise, execute step S4.5; S4.

5. Calculate the fitness value and determine the solution Is it better than If so, then output Otherwise, let .

4. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 1 is characterized in that: Specifically, S5 includes the following steps: S5.

1. When setting the algorithm parameters initially, due to the unknown structural validity of the local search neighborhood, the default setting of the initial neighborhood structure weights is equal; the local search neighborhood structure set of the variable neighborhood search algorithm is , where the initial weights corresponding to each neighborhood structure are ; S5.

2. Calculate the probability of each neighborhood structure using the roulette probability formula ; S5.

3. Calculate the cumulative probability of each neighborhood structure , that is, the sum of the selection probabilities of all neighborhood structures before each neighborhood structure; S5.

4. Define a variable , randomly generate a number between (0, 1) and assign it to the variable ,like , then select the neighborhood structure Perform a local search.

5. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 1 is characterized in that: The neighborhood structures include: Neighborhood structure 1: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers in the interval [1, L], and assign them to x1 and x2, where x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the encoding of the current solution. For the workpiece sequence encoding, randomly select two integers in the interval [1, N], and assign them to y1 and y, where y1 < y2. Swap the numbers before the y1-th position and after the y2-th position in the encoding of the current solution. Neighborhood structure 2: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers in the interval [1, L], and assign them to x1 and x2, where x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the encoding of the current solution. For the workpiece sequence encoding, randomly select two integers in the interval [1, N], and assign them to y1 and y2, where y1 < y2. Reverse the production line position numbers corresponding to the positions between the y1-th position and the y2-th position in the encoding of the current solution. Neighborhood structure 3: Define variables x1, x2, x3, y1, y2. For the production line sequence encoding, randomly select three integers in the interval [1, L], and assign them to x1, x2, and x3, where x1 < x2 < x3. Take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the encoding of the current solution. For the workpiece sequence encoding, randomly select two integers in the interval [1, N], and assign them to y1 and y2, where y1 < y2. Swap the production line position numbers corresponding to the y1-th position and the y2-th position in the encoding of the current solution, and swap the production line position numbers before the y1-th position and between the y1-th position and the y2-th position. Neighborhood structure 4: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers in the interval [1, L], and assign them to x1 and x2, where x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the encoding of the current solution. For the workpiece sequence encoding, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3, where y1 < y2 < y3. Swap the production line position numbers between the y1-th position and the y2-th position and between the y2-th position and the y3-th position in the encoding of the current solution. Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the encoding of the production line sequence, randomly select two integers in the interval [1, L], and assign them to x1 and x2 with x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the encoding of the workpiece sequence, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3. Swap the production line position numbers to the left of the y1-th position and between the y1-th and y2-th positions in the encoding of the current solution, and then swap the production line position numbers corresponding to the y2-th and y3-th positions. Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the encoding of the production line sequence, randomly select two integers in the interval [1, L], and assign them to x1 and x2 with x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the encoding of the workpiece sequence, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3. Swap the production line position numbers to the left of the y1-th position and to the right of the y3-th position in the encoding of the current solution, assign the production line position number at the y1-th position to z, then assign the production line position number at the y3-th position to the y1-th position, assign the production line position number at the y2-th position to the y3-th position, and assign z to the y2-th position. Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the encoding of the production line sequence, randomly select three integers in the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution. For the encoding of the workpiece sequence, randomly select two integers in the interval [1, N], and assign them to y1 and y2. Assign the encoding of the current solution to form 2 solutions. Swap the two sides of the y1-th position in the encoding of one solution, and then swap the two sides of the y2-th position in the encoding of the other solution. Randomly select an integer in the interval [1, N], and assign it to z. Combine the production line position encodings to the left of the z-th position (including the z-th position) in the encoding of the first solution and to the right of the z-th position in the encoding of the second solution to form a new solution. Neighborhood structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the encoding of the production line sequence, randomly select three integers within the interval [1, L], and assign them to x1, x2, and x3, where x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution. For the encoding of the workpiece sequence, randomly select four integers within the interval [1, N], and assign them to y1, y2, y3, and y4, where y1 < y2 < y3 < y4. Swap the numbers at the y1-th and y2-th positions in the encoding of the current solution, swap the numbers at the y3-th and y4-th positions in the encoding of the current solution, and then swap the production line position numbers between the y1-th and y2-th positions and the production line position numbers between the y3-th and y4-th positions.

6. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 1 is characterized in that: The specific steps of S9 are as follows: S9.1, by solution Generate and distribute to production lines Artifact collection on ; S9.2, Indicates the The number of the set of workpieces processed on the production line is ; S9.3, for Workpiece number on the production line Sort by S9.4, according to the formula 、 , calculate the manufacturing span of product A and product B ; S9.5, according to the formula , output .

7. The dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation according to claim 6 is characterized in that: Set the heuristic rules in S9.3 as follows: S9.3.

1. If the workpiece number When the workpiece number is processed first , number this part of the workpiece Sort by processing time in non-increasing order; S9.3.

2. Find the processing time of product C on the production line The critical point , number the workpiece At the critical point in front of; S9.3.

3. Number the remaining workpieces Sort in non-increasing order by processing time.

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