A Production Planning and Scheduling Coordination Method Based on an Improved Particle Swarm Optimization Algorithm

Abstract

This invention provides a production planning and scheduling coordination method, system, storage medium, and electronic device based on an improved particle swarm optimization algorithm, relating to the field of production planning and scheduling coordination. Specifically, this invention addresses the production characteristics of new energy battery product processing by proposing an integration problem of multi-cycle production planning and distributed assembly line scheduling. An improved particle swarm optimization algorithm based on a differential perturbation strategy is used to solve the upper-level planning model, obtaining the optimal production plan for each production scheduling cycle. This fully leverages the complementary advantages of the two strategies. Furthermore, the lower-level scheduling considers the distributed assembly line scheduling problem and employs a heuristic algorithm to obtain the optimal scheduling scheme within a single production scheduling cycle, thus satisfying the corresponding optimal production plan. This invention is applicable to the actual production process of new energy battery products, enabling enterprises to formulate reasonable production plans and scheduling schemes within a limited time, providing scientific decision support.

Description

Technical Field

[0001] This invention relates to the field of production planning and scheduling coordination, and more specifically to a production planning and scheduling coordination method, system, storage medium, and electronic device based on an improved particle swarm optimization algorithm. Background Technology

[0002] In recent years, significant progress has been made in the development of power batteries for new energy vehicles. Against this backdrop, in order to enhance corporate competitiveness, it is essential to fully utilize existing production resources and design reasonable production and scheduling plans for new energy power batteries.

[0003] In related technologies, 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.) This study investigates the integrated problem of production planning and task scheduling in multi-stage assembly lines. With the goal of minimizing operating costs and completion time, a two-level MILP model was established, and a simulation method based on recursive optimization (ROSA) was developed to solve the optimal solution for the coordination of planning and scheduling in 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 stages, and battery packs are typically divided into three levels: cells, modules, and the battery pack itself. Based on this production characteristic, an assembly stage must be added to the existing distributed assembly line to make the research problem more aligned with actual production conditions. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a collaborative method, system, storage medium, and electronic device for production planning and scheduling based on an improved particle swarm optimization algorithm, which solves the technical problem of distributed assembly line scheduling for power batteries in new energy vehicles.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A production planning and scheduling coordination method based on an improved particle swarm optimization algorithm includes:

[0010] Acquire 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. With the goal of minimizing the total cost, an upper-level planning model is constructed that applies to all production planning cycles. With the goal of minimizing the maximum completion time, a lower-level scheduling model is constructed that applies to a single production scheduling cycle.

[0012] An 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 for each production scheduling cycle.

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

[0014] Preferably, the upper-level planning model includes:

[0015]

[0016]

[0017] Wherein, equation (1) represents minimizing the total cost, including inventory holding costs and penalty costs for 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 product quantity; U p Indicates the unit inventory holding cost of product class p; I pt C represents the inventory holdings of product class p at the end of period t; p R represents the unit late delivery penalty cost per cycle for product class p; pt This represents the number of product category p that is out of stock due to delayed delivery 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 period pt Subtract the current product demand D pt ;

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

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

[0021] Preferably, the lower-level scheduling model includes:

[0022] Min C max (6)

[0023]

[0024]

[0025] Equation (6) represents minimizing the maximum completion time; C max This 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 This is a binary variable. If workpiece i is assigned to the h-th processing sequence of factory f, it is 1; otherwise, it is 0.

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

[0028] Constraints (9) and (10) indicate that a workpiece can only begin processing 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 p represents the h-th processing sequence of the workpiece on machine j-1 and machine j in factory f, respectively; ij This represents the processing time of workpiece i on machine j;

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

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

[0031] Constraint (14) indicates that the assembly work of the product will only begin after all parts of the product have been manufactured; Cap C represents the completion time of product p during the assembly stage; iM G represents the time when workpiece i is completed on the last machine M in the factory; ip This is a binary variable; if workpiece i belongs to product p, it is 1; otherwise, it is 0. p This indicates the assembly time of product p during the assembly stage;

[0032] Constraint (15) specifies the assembly completion time of the product; C h Y represents the assembly completion time of the h-th processing sequence in the factory; ph The variable represents a binary number. If the processing order h in the factory immediately follows the product p, the value is 1; otherwise, it is 0. W represents a sufficiently large positive number.

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

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

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

[0036] Preferably, the step of 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 for each production scheduling cycle includes:

[0037] S31. Set the iteration count k = 0, and initialize the population size, particle velocity and position, fitness, and individual historical best solution P. best and the global optimal solution G best Initialize the particle swarm optimization algorithm parameters; where the position of each particle is obtained by encoding a possible production plan.

[0038] S32. Based on equation (1), calculate the fitness of each particle in the population and update the individual's 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. Update the position and velocity of the particles using a difference strategy and a perturbation strategy:

[0040] From better than the 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 update formula used to update the position and velocity of the particles using the difference strategy and perturbation strategy specifically includes:

[0050] (1) Particle position update formula:

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

[0052] (2) Introducing the particle velocity update formula for the differential strategy:

[0053]

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

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

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

[0060] ω is the inertia weight, representing the weight of the current particle's influence from the previous iteration;

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

[0062] c1 and c2 are both learning factors, representing the degree to which a particle depends on its own historical best position and global best position, respectively.

[0063] c3 is a control factor, representing the weight that adjusts the particle's flight direction, and is used to control the difference term (x). u -x l The effect on particle velocity updates;

[0064] G′ best This indicates the position after perturbing the current global optimal solution;

[0065] N(G best σ) represents a solution with global optimality G best It follows a normal distribution with mean σ and standard deviation σ.

[0066] σ max This represents the initial value of the maximum disturbance amplitude, set to a constant value to control the initial strength of the disturbance. This represents the ratio between the current iteration number k and the maximum iteration number K;

[0067] c is a control factor that controls the nonlinear decreasing rate of σ with the number of iterations; the value of c is a constant.

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

[0069] S41. Generate product workpiece sequence:

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

[0071] S42. Generate product sequence:

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

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

[0074] S43. Generate the final scheduling sequence of the workpieces:

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

[0076] S44. Assign the workpiece to the factory:

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

[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 order of the results generates the final assembly sequence σ′=[σ′(1), σ′(2), ..., σ′(P)]; where for products with the same earliest possible start time for assembly, products with fewer workpieces are processed first.

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

[0081] The acquisition module is used to acquire production resources and product demand.

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

[0083] The solution module is used to solve the upper-level planning model using an improved particle swarm optimization algorithm based on differential perturbation strategy, and to obtain the optimal production plan in each production scheduling cycle.

[0084] And it is used to solve the lower-level scheduling model using heuristic algorithms to obtain the optimal scheduling scheme within a single production scheduling cycle, so as to meet the corresponding optimal production plan.

[0085] A storage medium storing a computer program for production planning and scheduling coordination based on an improved particle swarm optimization algorithm, wherein the computer program causes 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 configured to be executed by the one or more processors, the programs including methods for performing production planning and scheduling coordination as described above.

[0088] (III) Beneficial Effects

[0089] This 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 existing technologies, it has the following advantages:

[0090] This invention addresses the production characteristics of new energy battery product processing by proposing an integrated problem of multi-cycle production planning and distributed assembly line scheduling. An improved particle swarm optimization algorithm based on a differential perturbation strategy is employed to solve the upper-level planning model, obtaining the optimal production plan for each production scheduling cycle. This fully leverages the complementary advantages of the two strategies. Furthermore, the lower-level scheduling considers the distributed assembly line scheduling problem and uses a heuristic algorithm to obtain the optimal scheduling scheme within a single production scheduling cycle, thus satisfying the corresponding optimal production plan. This invention is applicable to the actual production process of new energy battery products, enabling enterprises to formulate reasonable production plans and scheduling schemes within a limited time, providing scientific decision support. Attached Figure Description

[0091] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0092] Figure 1 A block diagram illustrating a production planning and scheduling coordination method based on an improved particle swarm optimization algorithm, provided in an embodiment of the present invention.

[0093] Figure 2 This is a schematic diagram illustrating the integrated optimization problem of production planning and scheduling in a distributed assembly line workshop, as provided in an embodiment of the present invention.

[0094] Figure 3This is a flowchart of an improved particle swarm optimization algorithm provided in an embodiment of the present invention. Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0096] This application provides a production planning and scheduling coordination method, system, storage medium, and electronic device based on an improved particle swarm optimization algorithm, which solves the technical problem of distributed assembly line scheduling for power batteries of new energy vehicles.

[0097] The technical solution in this application is to solve the above-mentioned technical problems, and the general idea is as follows:

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

[0099] For NP-hard problems, it is extremely difficult to generate the optimal solution in a short time. Since heuristics and metaheuristics can obtain near-optimal solutions within a reasonable computation time, this invention conducts research on heuristic and metaheuristic algorithms for the integrated problem of multi-cycle production planning and distributed assembly line scheduling.

[0100] The purpose of this invention is to solve the corresponding production planning and scheduling integration problem based on 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 smaller cycles, and the types and quantities of products to be produced in each cycle are determined with the goal of minimizing total cost. In the second stage, with the goal of minimizing the maximum completion time, workpieces are allocated to multiple factories for processing to meet the production plan. This invention designs corresponding heuristic algorithms and improved particle swarm optimization (PSO) algorithms to formulate reasonable production plans and scheduling decisions for enterprises within a limited time, providing scientific decision support for enterprises.

[0101] Specifically, the "distributed assembly line workshop" in this embodiment of the invention refers to multiple distributed factories, each with its own assembly line workshop. These workshops add assembly processes to the traditional assembly line workshop, meaning that at certain nodes, multiple components need to be assembled on an assembly line. The assembly process typically requires coordinating multiple inputs and is more complex than a simple processing process.

[0102] Furthermore, distributed manufacturing systems are categorized into homogeneous factories and heterogeneous factories. In the distributed shop floor scheduling problem of homogeneous factories, all factories share the same factory attributes, such as the wear time of each machine, the processing model of the workpiece, and the processing sequence of the machines. However, in distributed heterogeneous factory systems, the factory attributes or the processing models in different factories may differ.

[0103] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0104] Example 1:

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

[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. With the goal of minimizing the total cost, an upper-level planning model is constructed that applies to all production planning cycles. With the goal of minimizing the maximum completion time, a lower-level scheduling model is constructed that applies to a single production scheduling cycle.

[0108] S3. 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.

[0109] S4. Use a heuristic algorithm to solve the lower-level scheduling model to obtain the optimal scheduling scheme within a single production scheduling cycle, so as 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 help enterprises formulate reasonable production plans and scheduling schemes within a limited time, providing scientific decision support for enterprises.

[0111] First of all, it should be noted that, Figure 2 As shown, this embodiment of the invention addresses the integrated optimization problem of production planning and scheduling in a distributed assembly line workshop. Furthermore, it is... Figure 2As can be seen, the embodiments of the present invention divide the production planning and scheduling integration problem into two stages:

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

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

[0114] Next, we will combine Figure 2 The steps of the above scheme are described in detail:

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

[0116] In this step, we obtain production resource and product demand data for mathematical modeling in subsequent steps, and define the symbols as shown in Table 1:

[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 is constructed that applies to all production planning cycles, and with the goal of minimizing the maximum completion time, a lower-level scheduling model is constructed that applies to a single production scheduling cycle.

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

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

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

[0124] ③Ignoring equipment failures, all machines are usable.

[0125] ④ No preemption is allowed. Once a workpiece is started, it cannot be interrupted or stopped until the workpiece is completed.

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

[0127] Based on this, the embodiments of the present invention divide the production planning and scheduling integration problem of new energy battery products into two stages:

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

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

[0130]

[0131] Equation (1) represents minimizing the total cost, including inventory holding costs and penalty costs for 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 period 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) respectively give the variable Q pt B pt The domain of definition.

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

[0136] Specifically, the lower-level scheduling model includes:

[0137] Min C max (6)

[0138]

[0139]

[0140] Equation (6) represents minimizing the maximum completion time;

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

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

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

[0144] Constraint (11) represents the time relationship between the completion of machining of adjacent workpieces.

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

[0146] Constraint (14) indicates that the assembly work of the product will only begin after all parts of the product have been manufactured; Ca p This indicates the completion time of product p during 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) means that the maximum completion time is equal to the assembly completion time of the last product;

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

[0151] In step S3, 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 for each production scheduling cycle.

[0152] This invention presents 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 local optima. The perturbation strategy enhances the algorithm's global search capability. This improvement improves the algorithm's convergence speed and solution quality.

[0153] like Figure 3 As shown, Figure 3 A complete flowchart of the improved particle swarm optimization algorithm based on the differential perturbation strategy is presented. Combined with... Figure 3 The specific steps are as follows:

[0154] S31. Set the iteration count k = 0, and initialize the population size, particle velocity and position, fitness, and individual historical best 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, and the encoding rule used specifically refers to:

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

[0157]

[0158] In this context, the position of each particle corresponds to a possible production plan; Q represents the production plan matrix, and the matrix has a dimension of P×T.

[0159] S32. Based on equation (1), calculate the fitness of each particle in the population and update the individual's 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. Update the position and velocity of the particles using a difference strategy and a perturbation strategy:

[0161] The differential strategy borrows the mutation operation from 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 as follows:

[0162] From better than the average fitness value Let x be the position of a randomly selected particle from the set of particles. u From inferior to the average fitness value Let x be the position of a randomly selected particle from the set of particles. l , with x u -x l As a difference term, the position and velocity of the current particle are updated using a difference strategy, and the updated position and velocity of the current particle are denoted as s1 and v1, respectively.

[0163] Difference term (x) u -x l The introduction of the difference term encourages particles to move from regions with poor fitness to regions with better fitness, thus helping them find better solutions. Furthermore, by utilizing the differences between solutions in the population, the difference term helps particles explore new regions in the search space, enabling them to escape their current local optima and discover even better global solutions, thereby enhancing the algorithm's global search capability.

[0164] The perturbation strategy adds random variations to the current position or velocity of particles to enhance the global search capability of the particle swarm. The relevant operations are as follows:

[0165] The global optimal solution G is perturbed using a perturbation strategy. best This is used to update the position and velocity of the current particle, and the updated position and velocity of the current particle are denoted as s2 and v2, respectively.

[0166] By analyzing the current globally optimal solution G best Apply a small-scale normal perturbation to generate G′. best This approach prevents the particle swarm from getting trapped in local optima too early during the search process. The perturbation slightly "pushes" the particles away from the vicinity of the current global optimum, allowing them to explore a wider area and increasing the likelihood of finding a better solution. Furthermore, as the number of iterations increases, the nonlinearity of σ decreases, and the magnitude of the perturbation gradually decreases. By dynamically adjusting the perturbation magnitude σ, the algorithm balances global search and local exploration at different stages. In the early stages, larger perturbations promote global exploration; in the later stages, smaller perturbations facilitate finer-grained searching.

[0167] Specifically, the update formulas used to update the position and velocity of particles using the difference strategy and perturbation strategy include:

[0168] (1) Particle position update formula:

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

[0170] (2) Introducing the particle velocity update formula for the differential strategy:

[0171]

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

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

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

[0178] ω is the inertia weight, representing the weight of the current particle's influence from the previous iteration;

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

[0180] c1 and c2 are both learning factors, representing the degree to which a particle depends on its own historical best position and global best position, respectively.

[0181] c3 is a control factor, representing the weight that adjusts the particle's flight direction, and is used to control the difference term (x). u -x l The effect on particle velocity updates;

[0182] G′ best This indicates the position after perturbing the current global optimal solution;

[0183] N(G best σ) represents a solution with global optimality G best It follows a normal distribution with mean σ and standard deviation σ.

[0184] σ max This represents the initial value of the maximum disturbance amplitude, set to a constant value to control the initial strength of the disturbance. This represents the ratio between the current iteration number k and the maximum iteration number K;

[0185] c is a control factor that controls the nonlinear decreasing rate of σ with the number of iterations; 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 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 ;

[0187] S35. k = k + 1;

[0188] S36. Repeat S32 - S35 until the maximum number of iterations is reached or the global optimal solution G best no longer improves significantly, then terminate the algorithm process and output the global optimal solution G best , and decode to obtain the optimal production plan for each of the said 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 start time of assembly E l l = 1, 2, ..., P; that is, the time required to complete the processing of all workpieces of the product.

[0195] Based on E l The non-descending order of the results generates a product sequence σ = [σ(1), σ(2), ..., σ(P)]; where for products with the same earliest possible start time for assembly, products with fewer workpieces are processed first, because the assembly of these products is relatively simple and fast.

[0196] As you can understand, the NR2 rule is a heuristic allocation rule. Its basic idea is to assign tasks to the factory or machine that can complete them earliest, in order to minimize task waiting time and total completion time. In other words, it assigns workpieces to the last position in the current processing sequence of each factory, selecting the factory with the shortest maximum completion time.

[0197] S43. Generate the final scheduling sequence of the workpieces:

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

[0199] For example, if there are 4 products and 10 workpieces, and the product sequence is {3, 4, 1, 2}, and the workpiece sequence for 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. Assign the workpiece to the factory:

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

[0202] Continuing with the example above, 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 correspondence between workpieces and factories is then represented 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 order of El, the final assembly sequence of the product is generated as σ′ = [σ′(1), σ′(2), ..., σ′(P)]; where for products with the same earliest possible start time for assembly, products with fewer workpieces are processed first.

[0205] Thus, this embodiment of the invention completes the entire process of the production planning and scheduling coordination method based on the improved particle swarm optimization algorithm.

[0206] Example 2:

[0207] This invention provides a production planning and scheduling coordination system based on an improved particle swarm optimization algorithm, comprising:

[0208] The acquisition module is used to acquire production resources and product demand.

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

[0210] The solution module is used to solve the upper-level planning model using an improved particle swarm optimization algorithm based on differential perturbation strategy, and to obtain the optimal production plan in each production scheduling cycle.

[0211] And it is used to solve the lower-level scheduling model using heuristic algorithms to obtain the optimal scheduling scheme within a single production scheduling cycle, so as to meet the corresponding optimal production plan.

[0212] Example 3:

[0213] This invention provides a storage medium storing a computer program for production planning and scheduling coordination based on an improved particle swarm optimization algorithm, wherein the computer program causes a computer to execute the production planning and scheduling coordination method as described in Embodiment 1.

[0214] Example 4:

[0215] This invention provides an electronic device, comprising:

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

[0217] It is understood that the production planning and scheduling coordination 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 coordination method based on the improved particle swarm optimization algorithm provided in the embodiments of the present invention. The explanation, examples and beneficial effects of the relevant contents can be referred to the corresponding parts of the production planning and scheduling coordination method, and will not be repeated here.

[0218] In summary, compared with existing technologies, it has the following beneficial effects:

[0219] 1. This invention addresses the production characteristics of new energy battery product processing by proposing an integration problem of multi-cycle production planning and distributed assembly line scheduling. An improved particle swarm optimization algorithm based on a differential perturbation strategy is used to solve the upper-level planning model, obtaining the optimal production plan for each production scheduling cycle. This fully leverages the complementary advantages of the two strategies. Furthermore, the distributed assembly line scheduling problem is considered in the lower-level scheduling, and a heuristic algorithm is used to solve it, obtaining the optimal scheduling scheme within a single production scheduling cycle to meet the corresponding optimal production plan. This invention is applicable to the actual production process of new energy battery products, enabling enterprises to formulate reasonable production plans and scheduling schemes within a limited time, providing scientific decision support.

[0220] 2. This invention addresses the characteristics of new energy battery product processing production models by proposing an integration problem of multi-cycle production planning and distributed assembly line scheduling. An improved particle swarm optimization algorithm based on a differential perturbation strategy is designed. The differential strategy enhances the diversity of the particle swarm by adding a differential term to the particle velocity update formula, helping to escape local optima. The perturbation strategy enhances the algorithm's global search capability. This improvement increases the algorithm's convergence speed and solution quality.

[0221] 3. Based on actual production conditions, the embodiments of the present invention consider the distributed assembly line workshop scheduling problem in the lower-level scheduling, and provide corresponding heuristic algorithms to solve the corresponding problems. Finally, it can be applied to the actual production process of power batteries for new energy vehicles.

[0222] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0223] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A production planning and scheduling coordination method based on an improved particle swarm optimization algorithm, characterized in that, include: To 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. With the goal of minimizing the total cost, an upper-level planning model is constructed that applies to all production planning cycles. With the goal of minimizing the maximum completion time, a lower-level scheduling model is constructed that applies to a single production scheduling cycle. An 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 for each production scheduling cycle. A heuristic algorithm is used to solve the lower-level scheduling model to obtain the optimal scheduling scheme within a single production scheduling cycle, so as to meet the corresponding optimal production plan. The upper-level planning model includes: Wherein, equation (1) represents minimizing the total cost, including inventory holding costs and penalty costs for 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 product quantity; U p Indicates the unit inventory holding cost of product class p; I pt C represents the inventory holdings of product class p at the end of period t; p R represents the unit late delivery penalty cost per cycle for product class p; pt This represents the number of product category p that is out of stock due to delayed delivery at the end of period t. Constraint (2) represents the inventory level I at the end of period t. pt equal to the previous period's inventory level I p(t-1) Add the production / assembly quantity Q of the current period pt Subtract the current product demand D pt ; Constraint (3) gives the upper limit of production capacity within the cycle; B pt This is a binary variable; if product p is produced within period t, it is 1; otherwise, it is 0. pt This represents the production / assembly volume Q of product type p within period t. pt The upper limit; Constraints (4) and (5) respectively give the variable Q pt B pt The domain of definition.

2. The production planning and scheduling coordination method as described in claim 1, characterized in that, The lower-level scheduling model includes: My C max (6) Equation (6) represents minimizing the maximum completion time; C max This 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 This is a binary variable. If workpiece i is assigned to the h-th processing sequence of factory f, it is 1; otherwise, it is 0. Constraint (8) means that a workpiece can only be assigned to one processing sequence in one factory; Constraints (9) and (10) indicate that a workpiece can only begin processing 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 p represents the h-th processing sequence of the workpiece on machine j-1 and machine j in factory f, respectively; ij This represents the processing time of workpiece i on machine j; Constraint (11) represents the time relationship between the completion of machining of adjacent workpieces; C j(h-1)f This indicates the (h-1)th processing sequence of the workpiece on machine j in factory f; p ij This represents the processing time of workpiece i on machine j; Constraints (12) and (13) indicate that during the assembly stage, a product has one and only one predecessor product and no more than one successor product; Y pq Represented as a binary variable, it is 1 if product q immediately follows product p, and 0 otherwise; Constraint (14) indicates that the assembly work of the product will only begin after all parts of the product have been manufactured; Ca p C represents the completion time of product p during the assembly stage; iM G represents the time when workpiece i is completed on the last machine M in the factory; ip This is a binary variable; if workpiece i belongs to product p, it is 1; otherwise, it is 0. p This indicates the assembly time of product p during the assembly stage; Constraint (15) specifies the assembly completion time of the product; C h Y represents the assembly completion time of the h-th processing sequence in the factory; ph The variable represents a binary number. If the processing order h in the factory immediately follows the product p, the value is 1; otherwise, it is 0. W represents a sufficiently large positive number. Constraint (16) specifies the order relationship between products; C h-1 This represents the assembly completion time for the (h-1)th processing sequence in the factory. Constraint (17) means that the maximum completion time is equal to the assembly completion time of the last product; Constraints (18) to (22) give the variable C respectively. jhf , Ca p X ihf Y pq G ip The domain of definition.

3. The production planning and scheduling coordination method as described in claim 1, 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 for each production scheduling cycle; including: S31. Set the iteration count k = 0, and initialize the population size, particle velocity and position, fitness, and individual historical best solution P. best and the global optimal solution G best Initialize the particle swarm optimization algorithm parameters; where the position of each particle is obtained by encoding a possible production plan. S32. Based on equation (1), calculate the fitness of each particle in the population and update the individual's historical optimal solution P. best and the global optimal solution G best And calculate the average fitness value of the current particle swarm. S33. Update the position and velocity of the particles using a difference strategy and a perturbation strategy: From better than the average fitness value Let x be the position of a randomly selected particle from the set of particles. u From inferior to the average fitness value Let x be the position of a randomly selected particle from the set of particles. l , with x u -x l As a difference term, the position and velocity of the current particle are updated using a difference strategy, and the updated position and velocity of the current particle are denoted as s1 and v1, respectively. And using a perturbation strategy to perturb the global optimal solution G best This is used to update the position and velocity of the current particle, and the updated position and velocity of the current particle are denoted 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 whether it is better than the global best solution G best , and if so, 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 no further significant improvement is achieved, the algorithm terminates and outputs the globally optimal solution G. best And decode to obtain the optimal production plan for each production scheduling cycle.

4. The production planning and scheduling coordination method as described in claim 3, 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 the particle with index i belonging to the k-th iteration is represented as... K represents the maximum number of iterations, k = 1, 2, ..., K; In this context, the position of each particle corresponds to a possible production plan; Q represents the production plan matrix, and the matrix has a dimension of P×T.

5. The production planning and scheduling coordination method as described in claim 3, characterized in that, The method of updating the position and velocity of particles using a difference strategy and a perturbation strategy specifically includes the following update formulas: (1) Particle position update formula: x i (k+1)=x i (k)+v i (k+1) (23) (2) Introducing the particle velocity update formula for the differential strategy: (3) Particle velocity update formula with perturbation strategy: 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) Where, x i (k+1),x i (k) represents the position of particle i in the (k+1)th and kth iterations, respectively; v i (k+1), v i (k) represents the velocity of particle i in the (k+1)th and kth iterations, respectively; ω is the inertia weight, representing the weight of the current particle's influence from the previous iteration; r1, r2, and r3 are random numbers between (0, 1); c1 and c2 are both learning factors, representing the degree to which a particle depends on its own historical best position and global best position, respectively. c3 is a control factor, representing the weight that adjusts the particle's flight direction, and is used to control the difference term (x). u -x l The effect on particle velocity updates; G′ best This indicates the position after perturbing the current global optimal solution; N(G best ,σ) denotes a solution with global optimality G best It follows a normal distribution with mean σ and standard deviation σ. σ max This represents the initial value of the maximum disturbance amplitude, set to a constant value to control the initial strength of the disturbance. This represents the ratio between the current iteration number k and the maximum iteration number K; c is a control factor that controls the nonlinear decreasing rate of σ with the number of iterations; the value of c is a constant.

6. The production planning and scheduling coordination method as described in claim 2, characterized in that, The process involves employing a heuristic algorithm to solve the lower-level scheduling model and obtain the optimal scheduling scheme within a single production scheduling cycle to meet the corresponding production plan; this includes: S41. Generate product workpiece sequence: The NEH heuristic algorithm, based on the shortest processing time rule, is used to generate product p. l workpiece sequence π l =[π l (1),π l (2),…,π l (π l )],n l It is product p l The number of workpieces included; S42. Generate product sequence: Using the NR2 rule, product p l workpiece sequence π l =[π l (1),π l (2),…,π l (n l Assign to the factory and calculate product p. l The earliest possible start time of assembly E l ,l=1,2,…,P; Based on E l The non-descending sort results generate a product sequence σ = [σ(1), σ(2), ..., σ(P)]; among which, for products with the same earliest possible start assembly time, products with fewer workpieces are processed first. S43. Generate the final scheduling sequence of the workpieces: Based on product p l workpiece sequence π l =[π l (1),π l (2),…,π l (n l The product sequence σ = [σ(1), σ(2), ..., σ(P)] generates the final scheduling sequence δ = [δ(1), δ(2), ..., δ(N)]. S44. Assign the workpiece to the factory: Using the NR2 rule, the final scheduling sequence δ=[δ(1),δ(2),…,δ(N)] of the workpieces is assigned to each factory to determine the workpiece processing order in each factory; 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 order of the results generates the final assembly sequence σ′=[σ′(1),σ′(2),…,σ′(P)]; where for products with the same earliest possible start time for assembly, products with fewer workpieces are processed first.

7. A production planning and scheduling collaborative system based on an improved particle swarm optimization algorithm, characterized in that, For executing the production planning and scheduling coordination method as described in claim 1, including: The acquisition module is used to acquire production resources and product demand. The construction module is used to divide the production planning cycle into several production scheduling cycles evenly based on the production resources and product demand, with the goal of minimizing the total cost, to construct an upper-level planning model applicable to all production planning cycles, and with the goal of minimizing the maximum completion time, to construct a lower-level scheduling model applicable to a single production scheduling cycle. The solution module is used to solve the upper-level planning model using an improved particle swarm optimization algorithm based on differential perturbation strategy, and to obtain the optimal production plan in each production scheduling cycle. And it is used to solve the lower-level scheduling model using heuristic algorithms to obtain the optimal scheduling scheme within a single production scheduling cycle, so as to meet the corresponding optimal production plan.

8. A storage medium, characterized in that, It stores a computer program for production planning and scheduling coordination based on an improved particle swarm optimization algorithm, wherein the computer program causes the computer to execute the production planning and scheduling coordination method as described in any one of claims 1 to 6.

9. 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 configured to be executed by the one or more processors, the programs including methods for performing production planning and scheduling coordination as described in any one of claims 1 to 6.

Images