Production planning and scheduling cooperation method based on improved particle swarm optimization algorithm

Abstract

The invention provides a production planning and scheduling collaboration method and system based on an improved particle swarm optimization algorithm, a storage medium and electronic equipment, and relates to the field of production planning and scheduling collaboration. According to production characteristics of new energy battery product processing, an integration problem of a multi-cycle production plan and distributed belt assembly flow shop scheduling is proposed, an improved particle swarm optimization algorithm based on a differential disturbance strategy is adopted to solve an upper-layer plan model, an optimal production plan in each production scheduling cycle is obtained, and a new energy battery product is obtained. Complementary advantages of the two strategies are fully exerted, a distributed belt assembly flow shop scheduling problem is considered in lower-layer scheduling, a heuristic algorithm is adopted for solving, and an optimal scheduling scheme in a single production scheduling period is obtained so as to meet a corresponding optimal production plan. The method is suitable for the actual production process of new energy battery products, reasonable production plans and scheduling schemes can be formulated for enterprises within limited time, and scientific decision support is provided for the enterprises.

Description

Technical Field

[0001] The present invention relates to the field of production planning and scheduling collaboration, and in particular to a production planning and scheduling collaboration method, system, storage medium and electronic equipment based on an improved particle swarm optimization algorithm. Background Art

[0002] In recent years, the development of new energy vehicle power batteries has made significant progress. In this context, in order to improve the competitiveness of enterprises, it is necessary to make full use of existing production resources and design reasonable production plans and scheduling plans for new energy power batteries.

[0003] In the related art, the paper (Vieira M, Moniz S, BS, et al. A two-level optimization-simulation method for production planning and scheduling: the industrial case of a human-robot collaborative assembly line [J]. International Journal of Production Research, 2022, 60(9): 2942-2962.) studied the integrated problem of production planning and task scheduling for multi-stage assembly lines. With the goal of minimizing operating costs and completion time, a two-level MILP model was established, and a recursive optimization-based simulation method (ROSA) was developed to solve the optimal solution for collaborative planning and scheduling of multi-stage assembly lines.

[0004] However, the above scheme only considers the scheduling problem of multi-stage assembly lines. The production process of new energy power batteries involves multiple complex links, and battery packs are usually divided into three levels: battery cells, modules, and battery packs. Based on this production characteristic, it is necessary to add an assembly stage on the basis of a distributed assembly workshop to make the research problem more in line with actual production conditions. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the shortcomings of the prior art, the present invention provides a production planning and scheduling collaborative method, system, storage medium and electronic device based on an improved particle swarm optimization algorithm, which solves the technical problem of scheduling distributed assembly flow workshops of new energy vehicle power batteries.

[0007] (II) Technical solution

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

[0009] A production planning and scheduling collaborative method based on an improved particle swarm optimization algorithm, comprising:

[0010] Obtain production resources and product demand;

[0011] Based on the production resources and product demand, the production planning cycle is evenly divided into several production scheduling cycles, and an upper-level planning model applied to all production planning cycles is constructed with the goal of minimizing the total cost, and a lower-level scheduling model applied to a single production scheduling cycle is constructed with the goal of minimizing the maximum completion time;

[0012] Using an improved particle swarm optimization algorithm based on a differential perturbation strategy to solve the upper-level planning model, and obtaining the optimal production plan within each production scheduling cycle;

[0013] A heuristic algorithm is used to solve the lower-level scheduling model to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

[0014] Preferably, the upper planning model includes:

[0015]

[0016]

[0017] Wherein, formula (1) represents the minimization of total cost, including inventory holding cost and penalty cost of delayed delivery; Min represents the minimization function, TC represents the total cost; t represents the production scheduling cycle index, T represents the number of production scheduling cycles; p represents the product index, P represents the number of products; U represents the product index, P represents the number of products; p I represents the unit inventory holding cost of product p; pt represents the inventory holding of product p at the end of period t; C p represents the penalty cost per cycle for delayed delivery of product type p; R pt represents the number of out-of-stock items due to delayed delivery of product p at the end of period t;

[0018] Constraint (2) represents the inventory level I at the end of period t pt Equal to the inventory level I of the previous period p(t-1) Add the production / assembly quantity Q of the current product pt Subtract the current product demand D pt ;

[0019] Constraint (3) gives the upper limit of production capacity within the cycle; B pt is a binary variable, which is 1 if product p is produced in period t, otherwise it is 0; W pt represents the production / assembly volume Q of product type p in period t ptThe upper limit of

[0020] Constraints (4) and (5) give the domains of variables Qpt and Bpt respectively.

[0021] Preferably, the lower layer scheduling model includes:

[0022] Min C max (6)

[0023]

[0024]

[0025] Among them, formula (6) represents minimizing the maximum completion time; C max Indicates the processing completion time of the entire scheduling sequence;

[0026] Constraint (7) indicates that a workpiece can only be assigned to one factory; i represents the workpiece index, J represents the number of workpieces; h represents the processing sequence index, H represents the number of processing sequences; f represents the factory index, F represents the number of factories; X ihf is a binary variable, which is 1 if job i is assigned to the hth processing sequence of factory f, otherwise it is 0;

[0027] Constraint (8) indicates that a job can only be assigned to one processing sequence in one factory;

[0028] Constraints (9) and (10) indicate that a workpiece can only be processed on the current machine after it has been processed on the previous machine; j represents the machine index, M represents the number of machines in a single factory; C (j-1)hf , C jhf denote the hth processing sequence of the workpiece on machine j-1 and machine j in factory f, respectively; p ij represents the processing time of workpiece i on machine j;

[0029] Constraint (11) represents the time relationship between adjacent workpieces to be processed; C j(h-1)f represents the h-1th processing sequence of the workpiece on machine j in factory f; p ij represents the processing time of workpiece i on machine j;

[0030] Constraints (12) and (13) indicate that in the assembly phase, a product has one and only one immediate predecessor and no more than one successor; Y pq Represented as a binary variable, it is 1 if product q follows product p, otherwise it is 0;

[0031] Constraint (14) indicates that the assembly of a product will not begin until all workpieces of the product have been produced; Cap represents the completion time of product p in the assembly stage; C iM G represents the time when workpiece i is processed on the last machine M in the factory; ip is a binary variable, which is 1 if workpiece i belongs to product p, otherwise it is 0; pa p represents the assembly time of product p in the assembly stage;

[0032] Constraint (15) specifies the assembly completion time of the product; C h represents the assembly completion time of the hth processing sequence in the factory; Y ph represents a binary variable, which is 1 if the processing sequence h in the factory is immediately followed by the product p, otherwise it is 0; W represents a sufficiently large positive number;

[0033] Constraint (16) specifies the order relationship between products; C h-1 represents the assembly completion time of the h-1th processing sequence in the factory;

[0034] Constraint (17) indicates that the maximum completion time is equal to the assembly completion time of the last product;

[0035] Constraints (18) to (22) give the variables C jhf , Ca p , X ihf , Y pq , G ip The domain of definition.

[0036] Preferably, the improved particle swarm optimization algorithm based on differential perturbation strategy is used to solve the upper-level planning model to obtain the optimal production plan in each production scheduling cycle; including:

[0037] S31, set the number of iterations k = 0, initialize the population size, particle speed and position, fitness, individual historical optimal solution P best and the global optimal solution G best , initialize the particle swarm optimization algorithm parameters; the position of each particle is encoded by a possible production plan;

[0038] S32. Based on formula (1), calculate the fitness of each particle in the population and update the individual historical optimal solution P best and the global optimal solution G best , and calculate the average fitness value of the current particle swarm

[0039] S33. Use the difference strategy and perturbation strategy to update the position and velocity of particles:

[0040] From better than average fitness value Randomly select a particle from the particle set and denote its position as x u from the particle set that is inferior to the average fitness value Randomly select a particle from the particle set and denote its position as x l Using x u - x l as the difference term, use the differential strategy to update the position and velocity of the current particle, and denote the position and velocity of the updated current particle as s1 and v1 respectively;

[0041] And use the perturbation strategy to perturb the global optimal solution G best to update the position and velocity of the current particle, and denote the position and velocity of the updated current particle as s2 and v2 respectively;

[0042] S34. Calculate the fitness value. If f(s1) < f(s2), then use s1 and v1 as the position and velocity of the current particle, otherwise use s2 and v2 as the position and velocity of the current particle; Compare the new position of the current particle with its historical optimal position. If the new position of the current particle is better than its historical optimal position, then update the individual historical optimal solution P best ; Check the current individual historical optimal solution P best whether it is better than the global optimal solution G best , if so, then update the global optimal solution G best ;

[0043] S35. k = k + 1;

[0044] S36. Repeat S32 - S35 until the maximum number of iterations is reached or the global optimal solution G best no longer improves significantly, terminate the algorithm process, output the global optimal solution G best , and decode to obtain the optimal production plan for each production scheduling period.

[0045] Preferably, the position of each particle is encoded by a possible production plan, and the specific encoding rule adopted is:

[0046] In a population of size N, the position of the particle with index i and belonging to the k-th iteration is represented as K represents the maximum number of iterations, k = 1, 2,..., K;

[0047]

[0048] where the position of each particle corresponds to a possible production plan; Q represents the production plan matrix, and the dimension of the matrix is P × T.

[0049] Preferably, the difference strategy and the perturbation strategy are used to update the position and velocity of the particle, and the update formula used specifically includes:

[0050] (1) Particle position update formula:

[0051] x i (k+1)=x i (k)+v i (k+1) (23)

[0052] (2) Introduce the particle velocity update formula of the differential strategy:

[0053]

[0054] (3) Particle velocity update formula with perturbation strategy introduced:

[0055] v i (k+1)=ωv i (k)+c1r1(P best -x i (k))+c2r2(G′ best -x i (k)) (25)

[0056] G′ best =N(G best ,σ) (26)

[0057]

[0058] Among them, x i (k+1), x i (k) represents the position of particle i in the k+1th and kth iterations respectively;

[0059] v i (k+1), v i (k) represents the velocity of particle i in the k+1th and kth iterations respectively;

[0060] ω is the inertia weight, which indicates the weight of the current particle affected by the previous iteration;

[0061] r1, r2, and r3 are random numbers between (0, 1);

[0062] c1 and c2 are both learning factors, representing the degree of dependence of the particle on its own historical best position and the global best position respectively;

[0063] c3 is the control factor, which represents the weight of adjusting the particle to fly in the beneficial direction and is used to control the difference term (x u -x l ) on particle velocity updates;

[0064] G′ best represents the position after the current global optimal solution is disturbed;

[0065] N(G best ,σ) represents a global optimal solution G best A normal distribution with a mean of σ and a standard deviation of σ;

[0066] σ max Represents the initial value of the maximum disturbance amplitude, which is set to a constant value to control the initial intensity of the disturbance. Represents the ratio between the current number of iterations k and the maximum number of iterations K;

[0067] c is the control factor, which controls the nonlinear decreasing speed of σ with the number of iterations, and the value of c is a constant.

[0068] Preferably, the method of using a heuristic algorithm to solve the lower-level scheduling model to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding production plan includes:

[0069] S41. Generate product artifact sequence:

[0070] The NEH heuristic algorithm based on the shortest processing time rule is used to generate product p l The workpiece sequence π l =[π l (1), π l (2), ..., π l (h l )],n l Is the product l The number of artifacts included;

[0071] S42, generate product sequence:

[0072] Using the NR2 rule, product p l The workpiece sequence π l =[π l (1), π l (2), ..., π l (n l )] is assigned to the factory and the product p is calculated l The earliest possible assembly start time E l , l = 1, 2, ..., P;

[0073] Based on E l The non-descending sorting results generate a product sequence σ = [σ(1), σ(2), ..., σ(P)]; among which, for products with the same earliest possible assembly start time, products with a smaller number of workpieces are processed first;

[0074] S43, generate the final scheduling sequence of the workpiece:

[0075] Based on product l The workpiece sequence π l =[π l (1), π l (2), ..., π l (n l )] and the product sequence σ = [σ(1), σ(2), ..., σ(P)], generating the final scheduling sequence δ = [δ(1), δ(2), ..., δ(N)];

[0076] S44. Allocate workpieces to factories:

[0077] Using the NR2 rule, the workpieces of the final scheduling sequence δ = [δ(1), δ(2), ..., δ(N)] are allocated to each factory, and the processing order of the workpieces in each factory is determined;

[0078] S45. Generate the final assembly sequence of the product:

[0079] Calculate the earliest assembly time E for each product l , l = 1, 2, ..., P, based on E l The non-descending arrangement results are used to generate the final assembly sequence of products σ′=[σ′(1), σ′(2), ..., σ′(P)]; among which for products with the same earliest possible assembly start time, products with a smaller number of workpieces are processed first.

[0080] A production planning and scheduling collaborative system based on an improved particle swarm optimization algorithm, comprising:

[0081] The acquisition module is used to obtain production resources and product demand;

[0082] A construction module is used to evenly divide the production planning cycle into several production scheduling cycles based on the production resources and product demand, to construct an upper-level planning model applied to all production planning cycles with the goal of minimizing the total cost, and to construct a lower-level scheduling model applied to a single production scheduling cycle with the goal of minimizing the maximum completion time;

[0083] A solution module, used for solving the upper-level planning model by using an improved particle swarm optimization algorithm based on a differential perturbation strategy to obtain an optimal production plan within each production scheduling cycle;

[0084] And it is used to solve the lower scheduling model by using a heuristic algorithm to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

[0085] A storage medium stores a computer program for production planning and scheduling coordination based on an improved particle swarm optimization algorithm, wherein the computer program enables a computer to execute the production planning and scheduling coordination method as described above.

[0086] An electronic device, comprising:

[0087] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including a method for executing the production planning and scheduling collaborative method as described above.

[0088] (III) Beneficial effects

[0089] The present invention provides a production planning and scheduling coordination method, system, storage medium and electronic device based on an improved particle swarm optimization algorithm. Compared with the prior art, it has the following beneficial effects:

[0090] In view of the production characteristics of new energy battery product processing, the present invention proposes the integration problem of multi-cycle production planning and distributed assembly flow shop scheduling, and adopts the improved particle swarm optimization algorithm based on differential perturbation strategy to solve the upper-level planning model, obtain the optimal production plan in each production scheduling cycle, give full play to the complementary advantages of the two strategies, and consider the distributed assembly flow shop scheduling problem in the lower-level scheduling, and adopt the heuristic algorithm to solve, obtain the optimal scheduling plan in a single production scheduling cycle, so as to meet the corresponding optimal production plan. The present invention is applicable to the actual production process of new energy battery products, and can formulate reasonable production plans and scheduling plans for enterprises within a limited time, and provide scientific decision-making support for enterprises. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] 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 or the description of the prior art 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.

[0092] Figure 1 A block diagram of a production planning and scheduling collaborative method based on an improved particle swarm optimization algorithm provided by an embodiment of the present invention;

[0093] Figure 2 A schematic diagram of an integrated optimization problem of production planning and scheduling for a distributed assembly flow shop provided by an embodiment of the present invention;

[0094] Figure 3A flowchart of an improved particle swarm optimization algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0095] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0096] The embodiments of the present application solve the technical problem of distributed assembly line scheduling of new energy vehicle power batteries by providing a production planning and scheduling collaboration method, system, storage medium and electronic device based on an improved particle swarm optimization algorithm.

[0097] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows:

[0098] Since the single-cycle distributed assembly flow shop scheduling problem is an NP-hard problem, and the embodiment of the present invention studies the integration problem of multi-cycle production planning and distributed assembly flow shop scheduling, the problem studied by the embodiment of the present invention is also an NP-hard problem.

[0099] For NP-hard problems, it is extremely difficult to generate an optimal solution in a short time. Since heuristics and meta-heuristics can obtain approximate optimal solutions within a reasonable computing time, the embodiments of the present invention carry out research on heuristic and meta-heuristic algorithms for the integration problem of multi-period production planning and distributed assembly flow shop scheduling.

[0100] The purpose of the embodiment of the present invention is to solve the corresponding production planning and scheduling integration problem according to the characteristics of the production mode of new energy battery product processing. The modeling is divided into two stages. In the first stage, the production cycle is divided into multiple small cycles. With the goal of minimizing the total cost, the types of products and the corresponding quantities to be produced in each cycle are decided; in the second stage, with the goal of minimizing the maximum completion time, the workpieces are assigned to multiple factories for processing to meet the production plan. The embodiment of the present invention designs corresponding heuristic algorithms and improved particle swarm (PSO) algorithms to formulate reasonable production plans and scheduling decisions for enterprises within a limited time, and provide scientific decision-making support for enterprises.

[0101] In particular, the "distributed assembly flow shop" in the embodiment of the present invention specifically refers to: in multiple distributed factories, each of which has a flow shop, and these flow shops have added assembly processes on the basis of traditional flow shops, that is, at certain nodes, multiple parts need to be assembled on an assembly line. The assembly process usually requires the coordination of multiple inputs and is more complicated than a simple processing process.

[0102] In addition, distributed manufacturing systems are divided into homogeneous factories and heterogeneous factories. In the distributed workshop scheduling problem of homogeneous factories, the factory attributes of all factories are consistent, such as the wear time of each machine, the processing model of the workpiece, the processing sequence of the machine, etc. In a distributed heterogeneous factory system, the factory attributes or the processing models in different factories may be different.

[0103] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0104] Embodiment 1:

[0105] like Figure 1 As shown, an embodiment of the present invention provides a production planning and scheduling collaborative method based on an improved particle swarm optimization algorithm, comprising:

[0106] S1. Obtain production resources and product demand;

[0107] S2. Based on the production resources and product demand, the production planning cycle is evenly divided into several production scheduling cycles, and an upper-level planning model applied to all production planning cycles is constructed with the goal of minimizing the total cost, and a lower-level scheduling model applied to a single production scheduling cycle is constructed with the goal of minimizing the maximum completion time;

[0108] S3, using an improved particle swarm optimization algorithm based on a differential perturbation strategy to solve the upper-level planning model and obtain the optimal production plan within each production scheduling cycle;

[0109] S4. Use a heuristic algorithm to solve the lower-level scheduling model and obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

[0110] The embodiments of the present invention are applicable to the actual production process of new energy battery products, and can formulate reasonable production plans and scheduling plans for enterprises within a limited time, thereby providing scientific decision-making support for enterprises.

[0111] First of all, if Figure 2 As shown, the embodiment of the present invention is aimed at the integrated optimization problem of production planning and scheduling of distributed assembly flow workshops. Figure 2It can be seen that the embodiment of the present invention divides the production planning and scheduling integration problem into two stages:

[0112] In the first stage, that is, the production planning stage, a production planning cycle is evenly divided into T production scheduling cycles. Assume that the customer demand for product p in cycle t is D pt The upper-level production plan needs to minimize the total cost and decide the production (assembly) quantity Q of type p products in period t. pt , the production volume will be passed into the lower model as the output of the upper model.

[0113] In the second stage, that is, the production scheduling stage, the scheduling within a single cycle, the present invention considers the distributed assembly flow shop scheduling problem. Assume that there are F isomorphic factories, each of which has an assembly line consisting of m machines responsible for the processing of the job. J workpieces with the same process route are first assigned to F factories for processing, and then assembled into P products in the assembly stage. Each product p l , l = 1, 2, ..., P, by n l Assembled from workpieces, To simplify the model, the assembly stage is abstracted as an assembly machine. The assembly of a product can only begin after all workpieces belonging to the product have been processed.

[0114] Next, we will combine Figure 2 The following are the steps of the above solution:

[0115] In step S1, production resources and product demand are obtained.

[0116] In this step, the production resources and product demand data used for mathematical modeling in the subsequent steps are obtained, and the symbols shown in Table 1 are defined:

[0117] Table 1

[0118]

[0119]

[0120] In step S2, based on the production resources and product demand, the production planning cycle is evenly divided into several production scheduling cycles. With the goal of minimizing the total cost, an upper-level planning model applied to all production planning cycles is constructed, and with the goal of minimizing the maximum completion time, a lower-level scheduling model applied to a single production scheduling cycle is constructed.

[0121] It is necessary to clarify the following assumptions related to model construction in advance:

[0122] ①Each machine can only process one workpiece at a time.

[0123] ② Each workpiece can only be processed on one machine at a time.

[0124] ③ Regardless of equipment failure, all machines are available.

[0125] ④ Preemption is not allowed. Once a workpiece starts to be processed, it cannot be interrupted or terminated until the workpiece processing is completed.

[0126] ⑤ Assembly of a product can only begin after all workpieces belonging to the product have been processed.

[0127] On this basis, the embodiment of the present invention divides the production planning and scheduling integration problem of new energy battery products into two stages:

[0128] In the first stage, that is, the production planning stage, the production planning cycle is evenly divided into several production scheduling cycles. With the goal of minimizing the total cost, an upper-level planning model applied to all production planning cycles is constructed.

[0129] Specifically, the upper-level planning model includes:

[0130]

[0131] Among them, formula (1) represents minimizing the total cost, including inventory holding cost and penalty cost of delayed delivery;

[0132] Constraint (2) represents the inventory level I at the end of period t pt Equal to the inventory level I of the previous period p(t-1) Add the production / assembly quantity Q of the current product pt Subtract the current product demand D pt ;

[0133] Constraint (3) gives the upper limit of production capacity within the cycle;

[0134] Constraints (4) and (5) give the variable Q pt , B pt The domain of definition.

[0135] In the second stage, that is, the production scheduling stage, with the goal of minimizing the maximum completion time, a lower-level scheduling model applied to a single production scheduling cycle is constructed (that is, scheduling within a single cycle, the embodiment of the present invention considers the distributed assembly line scheduling problem).

[0136] Specifically, the lower layer scheduling model includes:

[0137] Min C max (6)

[0138]

[0139]

[0140] Among them, formula (6) represents minimizing the maximum completion time;

[0141] Constraint (7) indicates that a workpiece can only be assigned to one factory;

[0142] Constraint (8) indicates that a job can only be assigned to one processing sequence in one factory;

[0143] Constraints (9) and (10) indicate that a workpiece can only be processed on the current machine after it has been processed on the previous machine;

[0144] Constraint (11) represents the time relationship between adjacent workpieces to complete the processing

[0145] Constraints (12) and (13) indicate that in the assembly phase, a product has one and only one immediate predecessor product and no more than one successor product;

[0146] Constraint (14) indicates that the assembly of a product will not begin until all workpieces of the product have been produced; Ca p represents the completion time of product p in the assembly stage;

[0147] Constraint (15) specifies the assembly completion time of the product;

[0148] Constraint (16) specifies the order relationship between products;

[0149] Constraint (17) indicates that the maximum completion time is equal to the assembly completion time of the last product;

[0150] Constraints (18) to (22) give the variables C jhf , Ca p , X ihf , Y pq , G ip The domain of definition.

[0151] In step S3, an improved particle swarm optimization algorithm based on a differential perturbation strategy is used to solve the upper-level planning model to obtain the optimal production plan in each production scheduling cycle.

[0152] The embodiment of the present invention designs an improved particle swarm optimization algorithm based on a differential perturbation strategy suitable for upper-level planning. The differential strategy enhances the diversity of the particle swarm by adding a differential term to the particle velocity update formula, which helps to escape from the local optimum. The perturbation strategy enhances the global search capability of the algorithm. This improvement improves the convergence speed of the algorithm and the quality of the solution.

[0153] like Figure 3 As shown, Figure 3 The complete flow chart of the improved particle swarm optimization algorithm based on differential perturbation strategy is given. Figure 3 , the specific steps are as follows:

[0154] S31, set the number of iterations k = 0, initialize the population size, particle speed and position, fitness, individual historical optimal solution P best and the global optimal solution G best , initialize the particle swarm optimization algorithm parameters.

[0155] The position of each particle is obtained by encoding a possible production plan. The encoding rules used are as follows:

[0156] In a population of size N, the position of the particle with index i belonging to the kth iteration is represented as K represents the maximum number of iterations, k = 1, 2, ..., K;

[0157]

[0158] Among them, the position of each particle corresponds to a possible production plan; Q represents the production plan matrix, and the dimension of the matrix is ​​P×T.

[0159] S32. Based on formula (1), calculate the fitness of each particle in the population and update the individual historical optimal solution P best and the global optimal solution G best , and calculate the average fitness value of the current particle swarm

[0160] S33. Use the difference strategy and perturbation strategy to update the position and velocity of particles:

[0161] The differential strategy draws on the mutation operation in the differential evolution (DE) algorithm. Its main idea is to generate new candidate solutions through differential mutation operations to increase the diversity and exploration ability of the particle swarm. The relevant operations are:

[0162] From better than average fitness value A particle is randomly selected from the particle set, and its position is recorded as x u , which is inferior to the average fitness value A particle is randomly selected from the particle set, and its position is recorded as x l , with x u -x l As a differential term, the position and velocity of the current particle are updated using a differential strategy, and the updated position and velocity of the current particle are recorded as s1 and v1 respectively.

[0163] The difference term (x u -x l ) encourages particles to move from areas with poor fitness to areas with better fitness, which helps particles find better solutions. In addition, by utilizing the differences between different solutions in the population, the differential term helps particles explore new areas in the search space, helps particles jump out of the current local optimal area, and further discovers a better global solution, thereby enhancing the global search capability of the algorithm.

[0164] The perturbation strategy is to add some random changes to the current position or velocity of the particle to enhance the global search ability of the particle swarm. The relevant operations are:

[0165] Use the perturbation strategy to perturb the global optimal solution G best , to update the position and velocity of the current particle, and record the updated position and velocity of the current particle as s2 and v2 respectively.

[0166] By calculating the current global optimal solution G best Apply a small range of normal perturbations to generate G′ best , which can prevent the particle swarm from falling into the local optimum too early in the search process. The perturbation slightly "pushes" the particles away from the current global optimal solution, allowing them to explore a wider area and increase the possibility of finding a better solution. In addition, as the number of iterations increases, σ decreases nonlinearly, and the amplitude of the perturbation gradually decreases. By dynamically adjusting the perturbation amplitude σ, the algorithm balances global search and local development at different stages. In the early stage, larger perturbations promote global exploration; in the later stage, smaller perturbations contribute to fine search.

[0167] Specifically, the difference strategy and perturbation strategy are used to update the position and velocity of the particle, and the update formula used specifically includes:

[0168] (1) Particle position update formula:

[0169] x i (k+1)=x i (k)+v i (k+1) (23)

[0170] (2) Introduce the particle velocity update formula of the differential strategy:

[0171]

[0172] (3) Particle velocity update formula with perturbation strategy introduced:

[0173] v i (k+1)=ωv i (k)+c1r1(P best -xi (k))+c2r2(G′ best -x i (k)) (25)

[0174] G′ best =N(G best ,σ) (26)

[0175]

[0176] Among them, x i (k+1), x i (k) represents the position of particle i in the k+1th and kth iterations respectively;

[0177] v i (k+1), v i (k) represents the velocity of particle i in the k+1th and kth iterations respectively;

[0178] ω is the inertia weight, which indicates the weight of the current particle affected by the previous iteration;

[0179] r1, r2, and r3 are random numbers between (0, 1);

[0180] c1 and c2 are both learning factors, representing the degree of dependence of the particle on its own historical best position and the global best position respectively;

[0181] c3 is the control factor, which represents the weight of adjusting the particle to fly in the beneficial direction and is used to control the difference term (x u -x l ) on particle velocity updates;

[0182] G′ best represents the position after the current global optimal solution is disturbed;

[0183] N(G best ,σ) represents a global optimal solution G best A normal distribution with a mean of σ and a standard deviation of σ;

[0184] σ max Represents the initial value of the maximum disturbance amplitude, which is set to a constant value to control the initial intensity of the disturbance. Represents the ratio between the current number of iterations k and the maximum number of iterations K;

[0185] c is the control factor, which controls the nonlinear decreasing speed of σ with the number of iterations, and the value of c is a constant.

[0186] S34. Calculate the fitness value. If f(s1) < f(s2), then use s1 and v1 as the position and velocity of the current particle; otherwise, use s2 and v2 as the position and velocity of the current particle. Compare the new position of the current particle with its historical best position. If the new position of the current particle is better than its historical best position, then update the individual historical best solution P best ; Check the current individual historical best solution P best to see if it is better than the global best solution G best . If so, then update the global best solution G best ;

[0187] S35. k = k + 1;

[0188] S36. Repeat S32 - S35 until the maximum number of iterations is reached or the global best solution G best no longer improves significantly, then terminate the algorithm process and output the global best solution G best , and decode to obtain the optimal production plan for each of the production scheduling cycles.

[0189] In step S4, use a heuristic algorithm to solve the lower - layer scheduling model and obtain the optimal scheduling plan for a single production scheduling cycle to meet the corresponding optimal production plan.

[0190] The embodiments of the present invention design a heuristic algorithm applicable to lower - layer scheduling to solve the distributed assembly - line flow - shop scheduling problem for application in the actual production of new - energy vehicle power batteries. The specific steps are as follows:

[0191] S41. Generate the product workpiece sequence:

[0192] Use the NEH heuristic algorithm based on the shortest processing time rule to generate the workpiece sequence π l of product p l = [π l (1), π l (2),..., π l (h l )], where n l is the number of workpieces included in product p l .

[0193] S42. Generate the product sequence:

[0194] Use the NR2 rule to assign the workpiece sequence π l of product p l = [π l (1), π l (2),..., π l (n l )] to the factory and calculate product p lThe earliest possible assembly start time E l , l=1,2,...,P; that is, the processing completion time of all workpieces of the product.

[0195] Based on E l The non-descending arrangement results generate a product sequence σ = [σ(1), σ(2), ..., σ(P)]; among which for products with the same earliest possible assembly start time, products with a smaller number of workpieces are given priority because the assembly of these products is relatively simple and fast.

[0196] It can be understood that the NR2 rule is a heuristic allocation rule. Its basic idea is to assign tasks to the factory or machine that can complete the task earliest, so as to minimize the waiting time and total completion time of the task. That is, the workpiece is assigned to the last position of the current processing sequence of each factory for processing, and the factory with the shortest maximum completion time is selected.

[0197] S43, generate the final scheduling sequence of the workpiece:

[0198] Based on product l The workpiece sequence π l =[π l (1), π l (2), ..., π l (n l )] and the product sequence σ = [σ(1), σ(2), ..., σ(P)] to generate the final scheduling sequence δ = [δ(1), δ(2), ..., δ(N)].

[0199] For example, there are 4 products and 10 workpieces. The product sequence is {3, 4, 1, 2}, and the workpiece sequence of products 1, 2, 3, 4 is {3, 5}, {6, 9, 10}, {7, 2, 1}, {4, 8}, then the final scheduling sequence is {7, 2, 1, 4, 8, 3, 5, 6, 9, 10}.

[0200] S44. Allocate workpieces to factories:

[0201] Using the NR2 rule, the workpieces in the final scheduling sequence δ = [δ(1), δ(2), ..., δ(N)] are allocated to each factory, and the processing order of the workpieces in each factory is determined.

[0202] Continuing with the above example, the final scheduling sequence is δ = {7, 2, 1, 4, 8, 3, 5, 6, 9, 10}, where {7, 2, 1} is assigned to factory F1, {4, 8, 3} is assigned to factory F2, and {5, 6, 9, 10} is assigned to factory F3. The final scheduling sequence with the corresponding relationship between workpieces and factories is expressed as δ F=[(7,F1),(2,F1),(1,F1),(4,F2),(8,F2),(3,F2),(5,F3),(6,F3),(9,F3),(10,F3)].

[0203] S45. Generate the final assembly sequence of the product:

[0204] Calculate the earliest assembly time E for each product l , l=1, 2, ..., P, based on the non-descending arrangement results of El, generate the final assembly sequence of products σ′=[σ′(1), σ′(2), ..., σ′(P)]; among which for products with the same earliest possible assembly start time, products with a smaller number of workpieces are processed first.

[0205] So far, the embodiment of the present invention has completed the entire process of the production planning and scheduling collaborative method based on the improved particle swarm optimization algorithm.

[0206] Embodiment 2:

[0207] The embodiment of the present invention provides a production planning and scheduling collaborative system based on an improved particle swarm optimization algorithm, including:

[0208] The acquisition module is used to obtain production resources and product demand;

[0209] A construction module is used to evenly divide the production planning cycle into several production scheduling cycles based on the production resources and product demand, to construct an upper-level planning model applied to all production planning cycles with the goal of minimizing the total cost, and to construct a lower-level scheduling model applied to a single production scheduling cycle with the goal of minimizing the maximum completion time;

[0210] A solution module, used for solving the upper-level planning model by using an improved particle swarm optimization algorithm based on a differential perturbation strategy to obtain an optimal production plan within each production scheduling cycle;

[0211] And it is used to solve the lower scheduling model by using a heuristic algorithm to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

[0212] Embodiment 3:

[0213] An embodiment of the present invention provides a storage medium storing a computer program for production planning and scheduling collaboration based on an improved particle swarm optimization algorithm, wherein the computer program enables a computer to execute the production planning and scheduling collaboration method as described in Example 1.

[0214] Embodiment 4:

[0215] An embodiment of the present invention provides an electronic device, including:

[0216] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include a method for executing the production planning and scheduling collaborative method as described in Example 1.

[0217] It can be understood that the production planning and scheduling collaborative system, storage medium and electronic device based on the improved particle swarm optimization algorithm provided in the embodiments of the present invention correspond to the production planning and scheduling collaborative method based on the improved particle swarm optimization algorithm provided in the embodiments of the present invention, and the explanations, examples and beneficial effects of the relevant contents can refer to the corresponding parts in the production planning and scheduling collaborative method, which will not be repeated here.

[0218] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0219] 1. In the embodiment of the present invention, the integrated problem of multi-cycle production planning and distributed assembly flow shop scheduling is proposed for the production characteristics of new energy battery product processing, and the improved particle swarm optimization algorithm based on differential perturbation strategy is used to solve the upper-level planning model to obtain the optimal production plan in each production scheduling cycle, give full play to the complementary advantages of the two strategies, and consider the distributed assembly flow shop scheduling problem in the lower-level scheduling, and use the heuristic algorithm to solve it, and obtain the optimal scheduling plan in a single production scheduling cycle to meet the corresponding optimal production plan. The present invention is applicable to the actual production process of new energy battery products, and can formulate reasonable production plans and scheduling plans for enterprises within a limited time, providing scientific decision-making support for enterprises.

[0220] 2. The embodiment of the present invention aims at the production mode characteristics of new energy battery product processing, proposes the integration problem of multi-cycle production planning and distributed assembly flow shop scheduling, and designs an improved particle swarm optimization algorithm based on differential perturbation strategy. The differential strategy enhances the diversity of the particle swarm by adding differential terms to the particle speed update formula, which helps to jump out of the local optimum. The perturbation strategy enhances the global search ability of the algorithm. This improvement improves the convergence speed of the algorithm and the quality of the solution.

[0221] 3. The embodiment of the present invention considers the distributed assembly flow shop scheduling problem in the lower-level scheduling based on the actual production situation, and provides a corresponding heuristic algorithm to solve the corresponding problem, which can finally be applied in the actual production process of new energy vehicle power batteries.

[0222] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0223] 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 the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. 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 embodiments of the present invention.

Claims

1. A production planning and scheduling collaborative method based on an improved particle swarm optimization algorithm, characterized in that: include: Obtain production resources and product demand; Based on the production resources and product demand, the production planning cycle is evenly divided into several production scheduling cycles, and an upper-level planning model applied to all production planning cycles is constructed with the goal of minimizing the total cost, and a lower-level scheduling model applied to a single production scheduling cycle is constructed with the goal of minimizing the maximum completion time; Using an improved particle swarm optimization algorithm based on a differential perturbation strategy to solve the upper-level planning model, and obtaining the optimal production plan within each production scheduling cycle; A heuristic algorithm is used to solve the lower-level scheduling model to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

2. The production planning and scheduling collaborative method according to claim 1, characterized in that: The upper planning model includes: Wherein, formula (1) represents the minimization of total cost, including inventory holding cost and penalty cost of delayed delivery; Min represents the minimization function, TC represents the total cost; t represents the production scheduling cycle index, T represents the number of production scheduling cycles; p represents the product index, P represents the number of products; U represents the product index, P represents the number of products; p I represents the unit inventory holding cost of product p; pt represents the inventory holding of product p at the end of period t; C p represents the penalty cost per cycle for delayed delivery of product type p; R pt represents the number of out-of-stock items due to delayed delivery of product p at the end of period t; Constraint (2) represents the inventory level i at the end of period t pt Equal to the inventory level i in the previous period p(t-1) Add the production / assembly quantity Q of the current product pt Subtract the current product demand D pt ; Constraint (3) gives the upper limit of production capacity within the cycle; B pt is a binary variable, which is 1 if product p is produced in period t, otherwise it is 0; W pt represents the production / assembly volume Q of product type p in period t pt The upper limit of Constraints (4) and (5) give the variable Q pt , B pt The domain of definition.

3. The production planning and scheduling collaborative method according to claim 2, characterized in that: The lower layer scheduling model includes: My C max (6) Among them, formula (6) represents minimizing the maximum completion time; C max Indicates the processing completion time of the entire scheduling sequence; Constraint (7) indicates that a workpiece can only be assigned to one factory; i represents the workpiece index, J represents the number of workpieces; h represents the processing sequence index, H represents the number of processing sequences; f represents the factory index, F represents the number of factories; X ihf is a binary variable, which is 1 if job i is assigned to the hth processing sequence of factory f, otherwise it is 0; Constraint (8) indicates that a job can only be assigned to one processing sequence in one factory; Constraints (9) and (10) indicate that a workpiece can only be processed on the current machine after it has been processed on the previous machine; j represents the machine index, M represents the number of machines in a single factory; C (j-1)hf , C jhf denote the hth processing sequence of the workpiece on machine j-1 and machine j in factory f, respectively; p ij represents the processing time of workpiece i on machine j; Constraint (11) represents the time relationship between adjacent workpieces to be processed; C j(h-1)f represents the h-1th processing sequence of the workpiece on machine j in factory f; p ij represents the processing time of workpiece i on machine j; Constraints (12) and (13) indicate that in the assembly phase, a product has one and only one immediate predecessor and no more than one successor; Y pq Represented as a binary variable, it is 1 if product q follows product p, otherwise it is 0; Constraint (14) indicates that the assembly of a product will not begin until all workpieces of the product have been produced; Ca p represents the completion time of product p in the assembly stage; C iM G represents the time when workpiece i is processed on the last machine M in the factory; ip is a binary variable, which is 1 if workpiece i belongs to product p, otherwise it is 0; pa p represents the assembly time of product p in the assembly stage; Constraint (15) specifies the assembly completion time of the product; C h represents the assembly completion time of the hth processing sequence in the factory; Y ph represents a binary variable, which is 1 if the processing sequence h in the factory is immediately followed by the product p, otherwise it is 0; W represents a sufficiently large positive number; Constraint (16) specifies the order relationship between products; C h-1 represents the assembly completion time of the h-1th processing sequence in the factory; Constraint (17) indicates that the maximum completion time is equal to the assembly completion time of the last product; Constraints (18) to (22) give the variables C jhf , Ca p , X ihf , Y pq , G ip The domain of definition.

4. The production planning and scheduling collaborative method according to claim 2, characterized in that: The improved particle swarm optimization algorithm based on differential perturbation strategy is used to solve the upper-level planning model to obtain the optimal production plan in each production scheduling cycle; including: S31, set the number of iterations k = 0, initialize the population size, particle speed and position, fitness, individual historical optimal solution P best and the global optimal solution G best , initialize the particle swarm optimization algorithm parameters; the position of each particle is encoded by a possible production plan; S32. Based on formula (1), calculate the fitness of each particle in the population and update the individual historical optimal solution P best and the global optimal solution G best , and calculate the average fitness value of the current particle swarm S33. Use the difference strategy and perturbation strategy to update the position and velocity of particles: From better than average fitness value A particle is randomly selected from the particle set, and its position is recorded as x u , which is inferior to the average fitness value A particle is randomly selected from the particle set, and its position is recorded as x l , with x u -x l As a differential term, the position and velocity of the current particle are updated using the differential strategy, and the updated position and velocity of the current particle are recorded as s1 and v1 respectively; And use the perturbation strategy to perturb the global optimal solution G best , to update the position and velocity of the current particle, and record the updated position and velocity of the current particle as s2 and v2 respectively; S34. Calculate the fitness value. If f(s1) < f(s2), then use s1 and v1 as the position and velocity of the current particle; otherwise, use s2 and v2 as the position and velocity of the current particle. Compare the new position of the current particle with its historical best position. If the new position of the current particle is better than its historical best position, then update the individual historical best solution P best ; Check the current individual historical best solution P best to see if it is better than the global best solution G best . If so, then update the global best solution G best ; S35, k=k+1; S36, repeat S32 to S35 until the maximum number of iterations or the global optimal solution G is reached best When there is no significant improvement, the algorithm process is terminated and the global optimal solution G is output best , and decode to obtain the optimal production plan within each production scheduling cycle.

5. The production planning and scheduling collaborative method according to claim 4, characterized in that: The position of each particle is obtained by encoding a possible production plan, and the encoding rule used specifically refers to: In a population of size N, the position of a particle with index i belonging to the kth iteration is represented as K represents the maximum number of iterations, k = 1, 2, ..., K; Among them, the position of each particle corresponds to a possible production plan; Q represents the production plan matrix, and the dimension of the matrix is ​​P×T.

6. The production planning and scheduling collaborative method according to claim 4, characterized in that: The difference strategy and perturbation strategy are used to update the position and velocity of the particle, and the update formula used specifically includes: (1) Particle position update formula: x i (k+1)=x i (k)+v i (k+1) (23) (2) Introduce the particle velocity update formula of the differential strategy: (3) Particle velocity update formula with perturbation strategy introduced: v i (k+1)=ωv i (k)+c1r1(P best -x i (k))+c2r2(G′ best -x i (k)) (25) G′ best =N(G best ,s) (26) Among them, x i (k+1), x i (k) represents the position of particle i in the k+1th and kth iterations respectively; v i (k+1), v i (k) represents the velocity of particle i in the k+1th and kth iterations respectively; ω is the inertia weight, which indicates the weight of the current particle affected by the previous iteration; r1, r2, and r3 are random numbers between (0, 1); c1 and c2 are both learning factors, representing the degree of dependence of the particle on its own historical best position and the global best position respectively; c3 is the control factor, which represents the weight of adjusting the particle to fly in the beneficial direction and is used to control the difference term (x u -x l ) on particle velocity updates; G b ′ est represents the position after the current global optimal solution is disturbed; N(G best ,σ) represents a global optimal solution G best A normal distribution with a mean of σ and a standard deviation of σ; σ max Represents the initial value of the maximum disturbance amplitude, which is set to a constant value to control the initial intensity of the disturbance. Represents the ratio between the current number of iterations k and the maximum number of iterations K; c is the control factor, which controls the nonlinear decreasing speed of σ with the number of iterations, and the value of c is a constant.

7. The production planning and scheduling collaborative method according to claim 3, characterized in that: The method of using a heuristic algorithm to solve the lower-level scheduling model and obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding production plan includes: S41. Generate product artifact sequence: The NEH heuristic algorithm based on the shortest processing time rule is used to generate product p l The workpiece sequence π l =[π l (1),π l (2),…,π l (n l )],n l Is the product l The number of artifacts included; S42, generate product sequence: Using the NR2 rule, product p l The workpiece sequence π l =[π l (1),π l (2),…,π l (n l )] is assigned to the factory and the product p is calculated l The earliest possible assembly start time E l ,l=1,2,…,P; Based on E l The non-descending sorting results generate a product sequence σ = [σ(1), σ(2), …, σ(P)]; among which, for products with the same earliest possible assembly start time, products with a smaller number of workpieces are processed first; S43, generate the final scheduling sequence of the workpiece: Based on product l The workpiece sequence π l =[π l (1),π l (2),…,π l (n l )] and the product sequence σ=[σ(1),σ(2),…,σ(P)], generate the final scheduling sequence δ=[δ(1),δ(2),…,δ(N)]; S44. Allocate workpieces to factories: Using the NR2 rule, the workpieces of the final scheduling sequence δ = [δ(1), δ(2), …, δ(N)] are assigned to each factory, and the processing order of the workpieces in each factory is determined; S45. Generate the final assembly sequence of the product: Calculate the earliest assembly time E for each product l ,l=1,2,…,P,based on E l The non-descending sorting results generate the final assembly sequence σ of the product ′ =[σ ′ (1),σ ′ (2),…,σ ′ (P)]; among which, for products with the same earliest possible assembly start time, products with a smaller number of workpieces are processed first.

8. A production planning and scheduling collaborative system based on an improved particle swarm optimization algorithm, characterized in that: include: The acquisition module is used to obtain production resources and product demand; A construction module is used to evenly divide the production planning cycle into several production scheduling cycles based on the production resources and product demand, to construct an upper-level planning model applied to all production planning cycles with the goal of minimizing the total cost, and to construct a lower-level scheduling model applied to a single production scheduling cycle with the goal of minimizing the maximum completion time; A solution module, used for solving the upper-level planning model by using an improved particle swarm optimization algorithm based on a differential perturbation strategy to obtain an optimal production plan within each production scheduling cycle; And it is used to solve the lower scheduling model by using a heuristic algorithm to obtain the optimal scheduling solution within a single production scheduling cycle to meet the corresponding optimal production plan.

9. A storage medium, characterized in that: The computer program for production planning and scheduling coordination based on an improved particle swarm optimization algorithm is stored therein, wherein the computer program enables a computer to execute the production planning and scheduling coordination method as claimed in any one of claims 1 to 7.

10. An electronic device, characterized in that: include: one or more processors; Memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including programs for executing the production planning and scheduling collaborative method as described in any one of claims 1 to 7.

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