Multi-target scheduling method and system for distributed assembly flow shop

Abstract

The invention provides a multi-target scheduling method and system for a distributed assembly flow shop, and relates to the technical field of production scheduling, and the method comprises the steps: collecting the technological parameters of the distributed assembly flow shop; based on the process parameters, determining scheduling constraint conditions by taking minimization of total energy consumption and completion time as targets; under the constraint of a scheduling constraint condition, generating an initial feasible scheduling scheme, calculating the maximum completion time and total energy consumption of the initial feasible scheduling scheme, and establishing a distributed assembly flow shop scheduling mixed integer linear optimization model comprising a workpiece processing sequence, machine start and stop, a machine processing rotating speed and a workpiece assembly sequence; in combination with a heuristic algorithm and a local search algorithm, optimizing the distributed assembly flow shop scheduling mixed integer linear optimization model, and outputting a Pareto optimal file representing an optimal scheduling scheme; and performing multi-target scheduling of the distributed assembly flow shop according to the Pareto optimal file.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and particularly to a multi-objective scheduling method and system for a distributed assembly flow shop. Background Art

[0002] The Distributed Assembly Flow Shop Problem (DAPFSP) is a typical combinatorial optimization problem in the field of manufacturing systems. The problem model includes multiple geographically dispersed manufacturing plants, each equipped with multiple parallel processing devices and a dedicated assembly device to complete the processing and final assembly tasks of workpieces. With the rapid growth of energy consumption, a series of problems such as global warming, resource depletion, and environmental deterioration are intensifying. The energy-saving problem in production scheduling has received increasing attention from enterprises and scholars. Therefore, the energy-efficient distributed assembly permutation flow-shop scheduling problem (EEDAPFSP) with energy consumption as one of the optimization objectives has emerged. EEDAPFSP is a typical NP-hard multi-objective combinatorial optimization problem, and its solution space and computational complexity are higher than those of DAPFSP.

[0003] Currently, for the EEDAPFSP problem, some scholars focus on using multi-objective optimization for scheduling. One is a brainstorm optimization method based on reinforcement learning and an improved iterative greedy method, which are respectively used to solve the energy-efficient scheduling problem of the distributed assembly non-waiting flow shop and the energy-efficient scheduling problem of the distributed assembly blocking flow shop. The other is a knowledge-based bi-objective collaborative optimization method, and an energy-saving strategy based on speed reduction is designed. By reducing the operation speed of workpieces on non-critical paths, the goal of energy consumption optimization is achieved while ensuring production efficiency. These methods provide a new and effective way to solve the multi-objective optimization problem involving energy consumption.

[0004] However, current algorithms generally use a direct numerical comparison method to evaluate multi-objective solutions and update the Pareto front, ignoring the diversity and evolution potential of solutions in the potential search space, which easily leads to premature convergence of the search process to local optima and limits the global distribution and quality of the solution set. On the other hand, most studies only use a single energy-saving method, lacking the collaborative consideration of multiple energy-saving mechanisms such as shutting down and restarting idle devices and load balancing, and are unable to fully explore multi-dimensional energy-saving opportunities, making it difficult to meet the demand for comprehensive optimization of system energy efficiency in the actual manufacturing environment. Summary of the Invention

[0005] To address the technical issues that current algorithms generally use direct numerical comparison to evaluate multi-objective solutions and update the Pareto front, ignoring the diversity and evolution potential of solutions in the potential search space, which easily leads to premature convergence of the search process to local optima and restricts the global distribution and quality of the solution set. On the other hand, most studies only adopt a single energy-saving measure, lacking coordinated consideration of multiple energy-saving mechanisms such as shutdown and restart of idle devices and load balancing, unable to fully explore multi-dimensional energy-saving opportunities and difficult to meet the requirements of comprehensive optimization of system energy efficiency in the actual manufacturing environment, the present invention provides a multi-objective scheduling method and system for a distributed assembly flow shop.

[0006] The technical solutions provided by the embodiments of the present invention are as follows:

[0007] First aspect:

[0008] A multi-objective scheduling method for a distributed assembly flow shop provided by an embodiment of the present invention includes:

[0009] S1: Collect the process parameters of the distributed assembly flow shop;

[0010] S2: Based on the process parameters, with the goal of minimizing the total energy consumption and the makespan, determine the scheduling constraint conditions;

[0011] S3: Under the constraints of the scheduling constraint conditions, generate an initial feasible scheduling plan, calculate the makespan and total energy consumption of the initial feasible scheduling plan, and establish a distributed assembly flow shop scheduling mixed integer linear optimization model including workpiece processing sequence, machine start and stop, machine processing speed, and workpiece assembly sequence;

[0012] S4: Combine a heuristic algorithm and a local search algorithm to optimize the distributed assembly flow shop scheduling mixed integer linear optimization model, and output a Pareto optimal archive representing the optimal scheduling plan;

[0013] S5: According to the Pareto optimal archive, perform multi-objective scheduling of the distributed assembly flow shop.

[0014] Second aspect:

[0015] A multi-objective scheduling system for a distributed assembly flow shop provided by an embodiment of the present invention includes:

[0016] A processor;

[0017] A memory, on which computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, the multi-objective scheduling method for a distributed assembly flow shop as described in the first aspect is implemented.

[0018] Third aspect:

[0019] A computer-readable storage medium provided by an embodiment of the present invention stores a computer program thereon. When the program is executed by a processor, it implements the multi-objective scheduling method for a distributed assembly flow shop as described in the first aspect.

[0020] The beneficial effects brought by the technical solution provided by the embodiment of the present invention at least include:

[0021] In the embodiment of the present invention, by introducing a cooperative mechanism of a heuristic algorithm and a local search algorithm in the scheduling optimization process and replacing the traditional numerical comparison method of the objective function with a Pareto optimal archive, a comprehensive exploration and optimization of the solution set in multiple objective dimensions are realized, significantly improving the distribution breadth and diversity of the solution set. At the same time, by collecting key process parameters of the distributed assembly flow shop, a scheduling optimization model integrating elements such as workpiece processing sequence, equipment start-stop control, processing speed adjustment, and assembly timing is constructed, realizing the cooperative integration of multiple energy-saving control strategies. At the same time, minimizing energy consumption is taken as one of the core objectives in the optimization process, comprehensively considering the dynamic relationship between the machine operating state and energy consumption fluctuations, thereby improving the energy efficiency adaptation ability and energy-saving optimization depth of the system in the actual production scenario, effectively breaking through the limitation of the traditional method that only relies on a single energy-saving means. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0023] Figure 1 It is a schematic flowchart of a multi-objective scheduling method for a distributed assembly flow shop provided by an embodiment of the present invention;

[0024] Figure 2 It is a schematic structural diagram of a multi-objective scheduling system for a distributed assembly flow shop provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] The following describes the technical solutions in the present invention with reference to the drawings.

[0026] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to give examples, illustrations or explanations. Any embodiment or design solution described as an "example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of the word "example" is intended to present concepts in a specific manner. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two.

[0027] In the embodiments of the present invention, "image" and "picture" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same. "Of", "corresponding", and "corresponding" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same.

[0028] In the embodiments of the present invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meanings they express are the same.

[0029] To make the technical problems to be solved, technical solutions and advantages of the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0030] Refer to the attached Figure 1 , which shows a schematic flow chart of a multi-objective scheduling method for a distributed assembly flow shop provided by the embodiments of the present invention.

[0031] The embodiments of the present invention provide a multi-objective scheduling method for a distributed assembly flow shop. This method can be implemented by a multi-objective scheduling device for a distributed assembly flow shop. The multi-objective scheduling device for a distributed assembly flow shop can be a terminal or a server. The processing flow of the multi-objective scheduling method for a distributed assembly flow shop can include the following steps:

[0032] S1: Collect the process parameters of the distributed assembly flow shop.

[0033] Among them, the distributed assembly flow shop refers to a manufacturing system composed of multiple geographically dispersed factories (or workshops). Each factory contains several processing machines. After some workpieces are processed in their respective factories, they are finally assembled centrally in one or more central nodes (such as an assembly workshop) in a process production system.

[0034] In a possible implementation manner, the process parameters specifically include:

[0035] The number of workpieces, the number of products, the number of machines, the number of factories, the number of adjustable discrete speeds of machines, the subordination relationship between workpieces and products, the distribution method of workpieces, the distribution method of workpieces, the processing sequence of workpieces, the processing time and speed of workpieces on each machine, the energy consumption per unit time of the machine in the processing state, the energy consumption per unit time in the idle state, and the energy consumption of each machine shutdown and restart.

[0036] In the embodiment of the present invention, comprehensively collecting process parameters is the basis of the entire distributed scheduling optimization model, which ensures the accuracy of the model, the feasibility of the scheduling scheme, the interpretability of the optimization result, and the effectiveness of the energy-saving decision.

[0037] S2: Based on the process parameters, with the goal of minimizing the total energy consumption and the completion time, determine the scheduling constraint conditions.

[0038] In a possible implementation manner, the scheduling constraint conditions specifically include:

[0039] Each workpiece can only be processed at one location in the factory at any moment and cannot be transferred between factories during the processing:

[0040]

[0041] Among them, N represents the total number of workpieces, R represents the total number of factories, represents whether the i-th workpiece is processed on the j-th machine, represents that the i-th workpiece is processed on the j-th machine, represents that the i-th workpiece is not processed on the j-th machine.

[0042] Each process can only use a fixed processing speed:

[0043]

[0044] Among them, D represents the total number of discrete speeds, represents whether the processing speed of the i-th workpiece on the j-th machine is v d , v d represents the discrete processing speed, represents that the processing speed of the i-th workpiece on the j-th machine is v d , represents that the processing speed of the i-th workpiece on the j-th machine is not v d .

[0045] Ensure the orderly progress of the processing of workpieces in their corresponding factories and ensure the feasibility of the generated scheduling scheme:

[0046]

[0047]

[0048] where X ki indicates whether the k-th workpiece is a direct predecessor of the i-th workpiece. X ki Xik = 1 indicates that the k-th workpiece is a direct predecessor of the i-th workpiece. X ki Xik = 0 indicates that the k-th workpiece is not a direct predecessor of the i-th workpiece. X 0i Xi0 indicates whether workpiece 0 is a direct predecessor of the i-th workpiece. X 0i Xi0 = 1 means that workpiece 0 is a direct predecessor of the i-th workpiece. X 0i Xi0 = 0 means that workpiece 0 is not a direct predecessor of the i-th workpiece. X k0 Xk0 indicates whether workpiece k is a direct predecessor of workpiece 0. X k0 Xk0 = 1 means that workpiece k is a direct predecessor of workpiece 0. X k0 Xk0 = 0 means that workpiece k is not a direct predecessor of workpiece 0. X kj Xkj indicates whether workpiece k is a direct predecessor of the i-th workpiece. X kj Xkj = 1 means that workpiece k is a direct predecessor of the i-th workpiece. X kj Xkj = 0 means that workpiece k is not a direct predecessor of the i-th workpiece. X jk Xjk indicates whether workpiece j is a direct predecessor of the k-th workpiece. X jk Xjk = 1 indicates that workpiece j is a direct predecessor of the k-th workpiece. X jk Xjk = 0 indicates that workpiece j is not a direct predecessor of the k-th workpiece. Tij(v) represents the actual processing time of the i-th workpiece on the j-th machine at speed v d Ci - 1,j(v) represents the completion time of the (i - 1)-th workpiece on the j-th machine at speed v d Sij(v) represents the actual processing time of the i-th workpiece on the j-th machine at speed v d S ij tij represents the start time of the i-th workpiece on the j-th machine. Cij(v) represents the completion time of workpiece i on machine j at speed v d M represents an infinitely large positive integer.

[0049] When the energy consumption during the current idle period of the machine is greater than the energy consumption for starting and stopping the machine, the shutdown operation is allowed to be executed:

[0050]

[0051] where e off represents the energy consumption for restarting the machine, yj represents the energy consumption of the j-th machine when it is idle, y j yj indicates whether there is idle time before the j-th machine starts processing. y​​j = 1 indicates that there is idle time before the j-th machine starts processing, y j = 0 indicates that there is no idle time before the j-th machine starts processing, f j indicates whether the j-th machine is in the off state, f j = 1 indicates that the j-th machine is in the off state, f j = 0 indicates that the j-th machine is in the running state.

[0052] The machine must be in the running state before the next workpiece starts processing:

[0053]

[0054] Among them, indicates the shutdown time of the j-th machine, y ij indicates whether there is idle time before the j-th machine starts processing, y ij = 1 indicates that there is idle time before the j-th machine starts processing, y ij = 0 indicates that there is no idle time before the j-th machine starts processing, f ij indicates whether the j-th machine is in the off state, f ij = 1 indicates whether the j-th machine is in the off state, f ij = 0 indicates whether the j-th machine is in the off state.

[0055] The actual completion time of the workpiece after speed regulation cannot exceed the processing start time of the next workpiece:

[0056]

[0057] Among them, S i+1j indicates the processing start time of the (i + 1)-th workpiece on the j-th machine.

[0058] The energy consumption during the speed-regulated time period needs to decrease:

[0059]

[0060] Among them, indicates the unit energy consumption of machine j at speed v d for processing, indicates indicates the unit energy consumption of machine j at speed v base for processing.

[0061] In the embodiments of the present invention, by setting constraint conditions on aspects such as workpiece processing position, speed, sequential dependence, machine state transition, and speed regulation effect, the feasible solution space of the scheduling problem is effectively limited, ensuring that the optimization scheme has physical feasibility and process rationality, and at the same time providing a strategy basis for energy consumption control and multi-objective balance.

[0062] S3: Under the constraints of scheduling constraints, generate an initial feasible scheduling plan, calculate the makespan and total energy consumption of the initial feasible scheduling plan, and establish a distributed assembly flow shop scheduling mixed-integer linear optimization model including job processing sequence, machine start / stop, machine processing speed, and job assembly sequence.

[0063] Among them, the initial feasible scheduling plan refers to a feasible scheduling result generated based on process parameters on the premise of meeting all scheduling constraints, which is used as the starting solution of the optimization algorithm. This plan determines the processing sequence of each job, the corresponding machine allocation, processing speed, processing start and completion times, and satisfies basic constraints such as process sequence, resource uniqueness, speed regulation rules, and energy consumption logic.

[0064] Among them, the distributed assembly flow shop scheduling mixed-integer linear optimization model is a mathematical model for scheduling optimization constructed for an assembly manufacturing system with multiple geographically dispersed factories, multiple processing resources, and a centralized assembly node. This model comprehensively considers two core objectives of production efficiency and energy consumption, and is expressed in the form of mixed-integer linear programming (MILP) on the basis of meeting various scheduling constraints, and finally realizes the generation of an optimal or approximately optimal scheduling plan.

[0065] In a possible implementation manner, S3 specifically includes:

[0066] S301: Set the actual processing time of the job after speed regulation to:

[0067]

[0068] Among them, represents the actual processing time of the -th job on the j-th machine at speed v d , represents the actual processing time of the -th job on the j-th machine at the reference speed of 1, represents whether the processing speed of the -th job on the j-th machine is v d , represents that the processing speed of the -th job on the j-th machine is v d , represents that the processing speed of the -th job on the j-th machine is not v d .

[0069] S302: Set the actual processing completion time of the job after speed regulation to:

[0070]

[0071] Among them, represents the actual completion time of the -th workpiece processed on the j-th machine at speed v d . represents the actual completion time of the -th workpiece processed on the j-th machine at speed v d . represents the actual completion time of the -th workpiece processed on the (j - 1)-th machine at speed v d . represents the actual processing time of the -th workpiece processed on the j-th machine at speed v d .

[0072] S303: Set the completion time of all corresponding workpieces for assembling a single product on the last machine to be:

[0073]

[0074] Among them, represents the maximum completion time of the workpieces for assembling product on the last machine Q, represents the -th workpiece, and Ω h represents the set of product workpieces.

[0075] S304: The product can start to be assembled only when all the workpieces for assembling the product are processed and the assembly machine is idle:

[0076]

[0077] Among them, represents the completion time of product on the assembly machine M A , max represents maximization, represents the completion time of product on the assembly machine M A , represents the assembly time of product .

[0078] S305: Determine the makespan of the initial feasible scheduling plan to be:

[0079]

[0080] Among them, C max (Γ) represents the makespan of the initial feasible scheduling plan.

[0081] In the embodiment of the present invention, by dynamically modeling the processing time and completion time of workpieces at different processing speeds, combining the judgment of assembly conditions and the extraction of product completion time, a complete initial scheduling time system is established. This system can accurately reflect the time relationship between the processing and assembly nodes of each workpiece, ensuring the timing consistency of the scheduling logic. At the same time, through the evaluation of the makespan, a key target value is provided for the subsequent optimization process. The above settings not only improve the executability and simulation accuracy of the model, but also lay a foundation for speed control, assembly coordination, and multi-objective scheduling optimization.

[0082] S306: Set the total processing energy consumption as:

[0083]

[0084]

[0085] Among them, APE(Γ) represents the total processing energy consumption of the initial feasible scheduling scheme, represents whether the processing speed of the i-th workpiece on the j-th machine is v d , v d represents the discrete processing speed, represents that the processing speed of the i-th workpiece on the j-th machine is v d , represents that the processing speed of the i-th workpiece on the j-th machine is not v d , represents that the i-th workpiece is processed on the j-th machine at the speed v d for the actual processing time, represents that the i-th workpiece is processed on the j-th machine at the speed v d for the actual unit energy consumption of processing, R represents the total number of factories, N f represents the total number of workpieces in the current factory, Q represents the number of machines in each factory, and D represents the total number of discrete speeds.

[0086] S307: Set the total machine idle energy consumption as:

[0087]

[0088] Among them, AIE(Γ) represents the total machine idle energy consumption of the initial feasible scheduling scheme, C f represents the makespan of the f-th factory, represents the shutdown time of the j-th machine, represents the energy consumption when the j-th machine is idle.

[0089] S308: Set the total start-stop energy consumption as:

[0090] AOE(Γ) = SDt·e off

[0091] Among them, AOE(Γ) represents the total energy consumption of machine start-up and shutdown of the initial feasible scheduling plan, SD t represents the total number of start-up and shutdown times, and e off represents the energy consumption of machine restart.

[0092] S309: According to the total energy consumption of processing, the total energy consumption of machine idle time, and the total energy consumption of start-up and shutdown, determine that the total energy consumption of the initial feasible scheduling plan is:

[0093] AE(Γ) = APE(Γ) + AIE(Γ) + AOE(Γ).

[0094] S310: According to the total energy consumption of the initial feasible scheduling plan and the makespan, establish a distributed assembly flow shop scheduling mixed integer linear optimization model.

[0095] In the embodiments of the present invention, by separately modeling and calculating the energy consumption during the processing process, the energy consumption of machine idle time, and the energy consumption of start-up and shutdown behaviors, the total energy consumption level of the initial feasible scheduling plan can be comprehensively evaluated. The processing energy consumption reflects the direct energy consumption of the equipment in the actual production task, the idle energy consumption measures the energy waste caused by the scheduling gap, and the start-up and shutdown energy consumption quantifies the additional energy consumption brought by the machine switch, providing an accurate energy evaluation basis for subsequent scheduling optimization.

[0096] In a possible implementation manner, the distributed assembly flow shop scheduling mixed integer linear optimization model is specifically:

[0097] min{C max (Γ), AE(Γ)}

[0098] Among them, min represents minimization, C max (Γ) represents the makespan of the initial feasible scheduling plan, and AE(Γ) represents the total energy consumption of the initial feasible scheduling plan.

[0099] In the embodiments of the present invention, in this implementation manner, by constructing a distributed assembly flow shop scheduling mixed integer linear optimization model with the goal of minimizing the makespan and the total energy consumption, unified modeling of scheduling efficiency and energy consumption control is achieved. This model can quantitatively evaluate the overall quality of the scheduling plan, which is not only beneficial to supporting the execution of multi-objective optimization algorithms, but also helps to balance the scheduling goals of efficient production and green energy conservation in practical applications.

[0100] S4: Combine the heuristic algorithm and the local search algorithm to optimize the distributed assembly flow shop scheduling mixed integer linear optimization model, and output the Pareto optimal archive representing the optimal scheduling plan.

[0101] Among them, the heuristic algorithm generates a strategy for the operation sequence based on scheduling rules, and quickly constructs a scheduling scheme with good objective performance in the feasible solution space. This algorithm does not need to enumerate all scheduling combinations, can significantly reduce the computational complexity, improve the solution efficiency, and is especially suitable for distributed scheduling optimization problems with multiple factories, multiple tasks, and complex constraints.

[0102] Among them, the local search algorithm is used to optimize and improve the initial scheduling solution. By defining neighborhood operations (such as swapping, inserting, reversing, etc.) for the product assembly sequence and workpiece processing sequence, the solution structure is gradually adjusted under a fixed objective function (such as the minimum completion time or total energy consumption). When the neighborhood solution is better than the current solution, it is updated, gradually approaching the local optimal solution, and significantly improving the quality of the scheduling result and the energy-saving effect.

[0103] Among them, the Pareto optimal archive is used to store the set of non-dominated solutions generated during the scheduling optimization process. Each solution has the characteristic that it cannot be simultaneously surpassed by other solutions in terms of objectives such as completion time and energy consumption. This archive is dynamically updated during the algorithm iteration process, used to track the evolution process of the optimal solution, and provide a multi-objective trade-off scheme reference for the selection of the final scheduling scheme, so as to achieve the balance control between scheduling efficiency and energy consumption.

[0104] In a possible implementation manner, S4 specifically includes:

[0105] S401: Set the position of the first assembled product in the product sequence, the initial population with an initial size of the number of products, and algorithm parameters. Among them, the algorithm parameters include the dominant population ratio, learning rate, local search algorithm segmentation number, and the number of iterations.

[0106] S402: Determine the time global probability matrix of the time-dominant product subsequence and the energy consumption global probability matrix of the energy consumption-dominant product subsequence:

[0107]

[0108] Among them, Ψ(g) represents the time global probability matrix, and Ψ ab (g) represents the probability value of operation a at the b-th position in the g-th generation heuristic sequence of the time global probability matrix, a ∈ 1, 2, … N TDP , b ∈ 1, 2, … N TDP , N TDP represents the length of the heuristic sequence of the time-dominant product subsequence, Υ(g) represents the energy consumption global probability matrix, and Υ ab (g) represents the probability value of operation a at the b-th position in the g-th generation heuristic sequence of the energy consumption global probability matrix, N EDP represents the length of the heuristic sequence of the energy consumption-dominant product subsequence.

[0109] S403: Initialize the global time probability matrix and the global energy consumption probability matrix, and evenly distribute the elements in the global time probability matrix and the global energy consumption probability matrix:

[0110]

[0111] Among them, Ψ ab (0) represents the probability value of operation a at the b-th position in the time-dominated heuristic sequence of the g-th generation, N1 represents the number of heuristic algorithms in the time-dominated product heuristic sequence, and Υ ab (0) represents the probability value of operation a at the b-th position in the energy consumption-dominated heuristic sequence of the g-th generation, and N2 represents the number of heuristic algorithms in the energy consumption-dominated product heuristic sequence.

[0112] In the embodiments of the present invention, by initializing the scheduling population and constructing the global probability matrix, a diversity basis for solutions and a learnable search direction control mechanism are provided for the scheduling optimization algorithm. Among them, the initial population ensures the coverage of the scheduling solution space, and the global probability matrix guides the usage frequency and position distribution of heuristic operations in the scheduling construction, forming an adaptive search strategy framework. This combination improves the search efficiency, reduces blindness, and provides a stable starting point and sense of direction for subsequent iterative optimization.

[0113] S404: Traverse each position of the heuristic operator sequence in turn, and calculate the cumulative probability sets of the global time probability matrix and the global energy consumption probability matrix:

[0114]

[0115] Among them, Hs_P b represents the cumulative probability of the b-th heuristic operator in the global time probability matrix, Hs_J b represents the cumulative probability of the b-th heuristic operator in the global energy consumption probability matrix, and l represents the index of the heuristic operator.

[0116] S405: Generate a random number. By traversing the cumulative probability sets of the global time probability matrix and the global energy consumption probability matrix, determine the interval where the random number is located, and calculate the time heuristic sequence and the energy consumption heuristic sequence through the following formula:

[0117]

[0118] Among them, S1[c] represents the operation at the c-th position in the time-dominated heuristic sequence, rnd1 represents the random number, and S2[c] represents the operation at the c-th position in the energy consumption-dominated heuristic sequence.

[0119] In the embodiment of the present invention, by using the global probability matrix to generate a time and energy consumption oriented heuristic operation sequence, the scheduling optimization has a structured search strategy and a flexible evolution path. This mechanism combines random sampling and cumulative probability control, making each generation of operation sequences both random and able to reflect the historical optimal solution experience, ensuring that the search has the characteristics of both diversity and directionality, and providing a reasonable initial mutation basis for subsequent neighborhood search and local optimization.

[0120] S406: With the goal of minimizing the makespan, sequentially perform neighborhood search on the initial population according to the sequence numbers in the time heuristic sequence, output the updated first target population, and compare the solutions in the initial population and the solutions in the first target population. If C max (ε' M ) < C max (ε M ) and rnd ≥ e -Δ , accept the solution in the first target population. Otherwise, continue to use the solution in the initial population.

[0121] In a possible implementation, the calculation formula of Δ is:

[0122]

[0123] where Δ represents a constant, C max (ε' M ) represents the makespan of the initial solution, C max (ε M ) represents the makespan of the target solution, and Temp represents an adjustable annealing rate parameter.

[0124] In a possible implementation, the neighborhood search for the initial population in S406 specifically includes:

[0125] S4061: When the sequence number in the time heuristic sequence is the first sequence number, randomly exchange the positions of a time-dominated product P a and an energy consumption-dominated product P b in the product assembly sequence, where a and b represent the product numbers.

[0126] S4062: When the sequence number in the time heuristic sequence is the second sequence number, select a time-dominated product P a and an energy consumption-dominated product P b . If b is greater than a, insert P a before P b .

[0127] S4063: When the sequence number in the time heuristic sequence is the third sequence number, select a time-dominated product P a and an energy consumption-dominated product Pb , if b is greater than a, insert P a into P b after that.

[0128] S4064: When the serial number in the time heuristic sequence is the fourth serial number, select a time-dominated product P a and an energy consumption-dominated product P b , reverse the product subsequence between product P a and product P b .

[0129] S4065: When the serial number in the time heuristic sequence is the fifth serial number, randomly swap the positions of two time-dominated products.

[0130] S4066: When the serial number in the time heuristic sequence is the sixth serial number, randomly select a time-dominated product and uniformly adjust the speeds of all workpieces used to assemble the current product to a preset level.

[0131] S4067: When the serial number in the time heuristic sequence is not the first serial number to the sixth serial number, do not operate on the time-dominated product subsequence and the energy consumption-dominated product subsequence.

[0132] S407: With the goal of minimizing the total energy consumption, sequentially perform neighborhood search on the first target population according to the serial number in the energy consumption heuristic sequence, output the updated second target population, and compare the solutions in the first target population and the second target population. If C max (ε' M ) < C max (ε M ) and rnd ≥ e -Δ , accept the solution in the second target population; otherwise, continue to use the solution in the first target population.

[0133] In a possible implementation, the specific process of performing neighborhood search on the first target population in S407 includes:

[0134] S4071: When the serial number in the energy consumption heuristic sequence is the first serial number, randomly swap the positions of energy consumption-dominated products P c and P d .

[0135] S4072: When the serial number in the energy consumption heuristic sequence is the second serial number, select two energy consumption-dominated products P c and P d , if c is greater than d, insert P d before P c .

[0136] S4073: When the serial number in the energy consumption heuristic sequence is the third serial number, select two energy consumption dominant products P c and P d , if c is greater than d, insert P d after P c .

[0137] S4074: When the serial number in the energy consumption heuristic sequence is the fourth serial number, select two energy consumption dominant products P c and P d , reverse the product subsequence between product P c and product P d .

[0138] S4075: When the serial number in the energy consumption heuristic sequence is the fifth serial number, randomly swap the positions of two adjacent time dominant products.

[0139] S4076: When the serial number in the energy consumption heuristic sequence is the sixth serial number, randomly select two workpieces J c in a time dominant product P c and J d , and swap the positions of workpiece J c and J d .

[0140] S4077: When the serial number in the energy consumption heuristic sequence is the seventh serial number, randomly select two workpieces J c and J d in a time dominant product, if c is greater than d, insert workpiece J c before J d .

[0141] S4078: When the serial number in the energy consumption heuristic sequence is the eighth serial number, randomly select two workpieces J c and J d in a time dominant product, if c is greater than d, insert workpiece J c after J d .

[0142] S4079: When the serial number in the energy consumption heuristic sequence is the ninth serial number, randomly select two workpieces J c and J d in an energy consumption dominant product, and reverse the workpiece subsequence between the two workpieces.

[0143] S407A: When the serial number in the energy consumption heuristic sequence is the tenth serial number, randomly select two adjacent workpieces J c and J d in an energy consumption dominant product, and swap their positions.

[0144] S407B: When the sequence number in the energy consumption heuristic sequence is not the first to the tenth sequence numbers, no operations are performed on the time-dominated job subsequence and the energy consumption-dominated job subsequence.

[0145] In the embodiments of the present invention, a neighborhood search mechanism driven by two objectives of makespan and total energy consumption is adopted to perform two-way refined adjustment on the current scheduling scheme. Through various neighborhood operations (such as swapping, inserting, reversing, etc.), the local optimality of the scheduling solution in the two objective dimensions is effectively improved, single-objective deviation is avoided, and the coordination between efficiency and energy consumption of the scheduling scheme is strengthened.

[0146] S408: Calculate the L2 metric for each solution in the second objective population:

[0147]

[0148] where min represents minimization, f1(x) represents the objective function value of the makespan of the current solution, f2(x) represents the objective function value of the total energy consumption of the current solution, represents the ideal value of the total energy consumption, and λ represents the weight of the makespan.

[0149] S409: Sample the first candidate individual and the second candidate individual, compare the L2 metrics of the first candidate individual and the second candidate individual, and select the candidate individual with a smaller L2 metric value to enter the dominant subgroup to form the first dominant subpopulation.

[0150]

[0151] Sups = P_size * η

[0152] where, Sup_vec i represents the individual number at the d-th position of the dominant subpopulation, C1 represents the first candidate individual, C2 represents the second candidate individual, Sups represents the size of the dominant subpopulation, P_size represents the size of the population, and η represents the proportion of dominant solutions.

[0153] S410: Update the time global probability matrix and the energy consumption global probability matrix for each generation according to the first dominant subpopulation:

[0154]

[0155] where, Ψ ij (g + 1) represents the probability value of operation a at the b-th position in the g + 1-th generation heuristic sequence in the time global probability matrix, γ represents the learning rate, Υ ij (g + 1) represents the probability value of operation a at the b-th position in the g + 1-th generation heuristic sequence in the energy consumption global probability matrix, Indicates whether the operation of operation a at position b in the heuristic sequence has a positive effect on finding a solution with better quality. Indicates that the operation of operation a at position b in the heuristic sequence has a positive effect on finding a solution with better quality. Indicates that the operation of operation a at position b in the heuristic sequence has no positive effect on finding a solution with better quality.

[0156] In the embodiment of the present invention, by evaluating the L2 comprehensive index of the individual solution, screening to form a dominant sub-population, and then combining with the learning update of the probability matrix, the dynamic optimization of the solution and the generation-by-generation strengthening of the search direction are realized. This mechanism not only retains the current excellent scheduling structure, but also gradually adjusts the generation probability of the heuristic operation through the learning mechanism, thereby guiding the search of the next generation to concentrate on a better area, realizing an evolutionary optimization control of "the excellent guiding the search", and improving the convergence speed and quality of the overall solution set.

[0157] S411: Insert each workpiece in each solution of the first dominant sub-population into the first remaining position different from the current position in turn, calculate the makespan after inserting the workpiece, and judge whether the makespan after inserting the workpiece is less than the current makespan in the dominant sub-population. If so, update the current solution and start the search again. Otherwise, keep the current order and continue with the insertion operation of the next workpiece until all workpieces are processed, and output the updated second dominant sub-population.

[0158] S412: Divide the energy consumption-dominated workpiece subsequence corresponding to the solution in the second dominant sub-population into multiple sub-workpiece segments, insert the workpieces within each workpiece segment into the second remaining position within the current workpiece segment in turn, calculate the total energy consumption after inserting the workpiece, and judge whether the total energy consumption after inserting the workpiece is reduced. If so, continue the search. Otherwise, keep the current order and continue with the insertion operation of the next workpiece until all workpieces are processed, and output the updated third dominant sub-population.

[0159] In the embodiment of the present invention, a local insertion strategy is adopted to perform structural reconstruction within the workpiece subsequence and workpiece segment, further optimizing the scheduling scheme from two directions of time and energy consumption. This strategy focuses on feasible adjustments at the micro level, and deeply optimizes the arrangement order and speed combination of workpieces without destroying the original overall structure, effectively improving the executability, compactness and energy-saving performance of the scheduling scheme.

[0160] S413: Compare the objective values of the solutions in the third dominant sub-population with the objective values of the solutions in the current Pareto archive, update the current Pareto archive, and output the optimal Pareto archive.

[0161] S414: Delay the starting time of the workpiece under the constraint that the latest completion time of the workpiece cannot exceed the earliest starting time of the next workpiece and the earliest starting assembly time of the product to which it belongs.

[0162] S415: Accelerate the machining speed of the machine to a preset multiple, and compare whether the idle energy consumption before acceleration is greater than the sum of the start-stop energy consumption of the machine after acceleration and the increased machining energy consumption. If so, perform the shutdown operation. Otherwise, go to S416:

[0163] S416: When the energy consumption during the adjusted speed period decreases, perform an acceleration operation on the machine. When the actual completion time of the workpiece after speed adjustment does not exceed the machining start time of the next workpiece, perform a deceleration operation on the machine. Otherwise, keep the machine in an idle state.

[0164] In the embodiment of the present invention, on the premise of maintaining process feasibility, by delaying the machining start time, judging the energy consumption critical value, and performing speed adjustment or shutdown operations, the dynamic coordination of the production rhythm and energy consumption behavior is realized. This stage not only avoids the idle energy consumption generated by the machine starting in advance, but also intelligently judges whether to start, stop or adjust the speed according to the actual energy-saving effect, truly realizing the scheduling control goal of "saving energy without delaying work", which is a key strategic link in the green manufacturing scheduling system.

[0165] S417: Judge whether the current algorithm execution time is greater than the maximum algorithm execution time. If so, end the iteration and output the Pareto optimal archive. Otherwise, increment the iteration count by 1 and return to S404.

[0166] S5: Perform multi-objective scheduling for the distributed assembly flow shop according to the Pareto optimal archive.

[0167] Specifically, by screening the non-dominated solutions in the Pareto optimal archive, select the scheduling plan that comprehensively considers the makespan and total energy consumption as the final execution plan. The selected scheduling plan contains key information such as the workpiece processing sequence, equipment start-stop and speed adjustment strategies, and product assembly sequence, and is distributed to each distributed factory and assembly node. Each execution unit performs resource scheduling control according to this plan.

[0168] In the embodiment of the present invention, by selecting and implementing the scheduling plan according to the Pareto optimal archive, the optimal implementation of the multi-objective scheduling result is effectively realized. This plan can flexibly respond to different trade-off requirements between time and energy consumption, ensuring the efficient coordinated execution of production tasks among different factories. The workpiece sequence, equipment start-stop and speed adjustment strategies in the scheduling plan have been optimized and configured, and the system can execute precisely according to the instructions, reducing the intervention cost. At the same time, combined with the real-time feedback mechanism, the overall robustness and adaptability of the scheduling are improved. This method not only improves the scheduling execution efficiency, but also significantly optimizes the energy utilization level.

[0169] The beneficial effects brought by the technical solution provided by the embodiment of the present invention at least include:

[0170] In the embodiment of the present invention, by introducing the cooperation mechanism of the heuristic algorithm and the local search algorithm in the scheduling optimization process, and replacing the traditional numerical comparison method of the objective function with the Pareto optimal archive, the comprehensive exploration and optimization of the solution set in multiple objective dimensions are realized, and the distribution breadth and diversity of the solution set are significantly improved. At the same time, by collecting the key process parameters of the distributed assembly flow shop, a scheduling optimization model integrating elements such as the workpiece processing sequence, equipment start-stop control, processing speed adjustment, and assembly time sequence is constructed, realizing the collaborative integration of multiple energy-saving control strategies. At the same time, minimizing energy consumption is taken as one of the core objectives in the optimization process, and the dynamic relationship between the machine operating state and energy consumption fluctuation is comprehensively considered, thereby improving the energy efficiency adaptation ability and energy-saving optimization depth of the system in the actual production scenario, and effectively breaking through the limitation of the traditional method relying only on a single energy-saving means.

[0171] Refer to the attached Figure 2 illustrates a schematic structural diagram of a multi-objective scheduling system for a distributed assembly flow shop provided by the present invention.

[0172] The present invention also provides a multi-objective scheduling system 20 for a distributed assembly flow shop, which is applied to the above-mentioned multi-objective scheduling method for a distributed assembly flow shop, and includes:

[0173] A processor 201.

[0174] A memory 202, on which computer-readable instructions are stored. When the computer-readable instructions are executed by the processor 201, the multi-objective scheduling method for a distributed assembly flow shop as in the method embodiment is realized.

[0175] The multi-objective scheduling system 20 for a distributed assembly flow shop provided by the present invention can execute the above-mentioned multi-objective scheduling method for a distributed assembly flow shop and achieve the same or similar technical effects. To avoid repetition, the present invention will not be elaborated herein.

[0176] The beneficial effects brought by the technical solution provided by the embodiment of the present invention at least include:

[0177] In the embodiments of the present invention, by introducing a cooperative mechanism of a heuristic algorithm and a local search algorithm in the scheduling optimization process, and replacing the traditional numerical comparison method of the objective function with a Pareto optimal archive, a comprehensive exploration and optimization of the solution set in multiple objective dimensions are realized, significantly improving the distribution breadth and diversity of the solution set. At the same time, by collecting the key process parameters of the distributed assembly flow shop, a scheduling optimization model integrating elements such as workpiece processing sequence, equipment start-stop control, processing speed adjustment, and assembly timing is constructed, realizing the cooperative integration of multiple energy-saving control strategies. At the same time, minimizing energy consumption is taken as one of the core objectives in the optimization process, comprehensively considering the dynamic relationship between the machine operating state and energy consumption fluctuations, thereby improving the energy efficiency adaptation ability and energy-saving optimization depth of the system in the actual production scenario, effectively breaking through the limitation of traditional methods relying only on a single energy-saving means.

[0178] It should be understood that the processor in the embodiments of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0179] It should also be understood that the memory in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0180] The above embodiments can be implemented in whole or in part by software, hardware (such as circuits), firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. A computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions according to the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wired (such as infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that contains one or more collections of available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, or a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0181] It should be understood that the term "and / or" in this document is merely a description of the association relationship between associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. Here, A and B can be singular or plural. In addition, the character " / " in this document generally represents an "or" relationship between the associated objects before and after, but it may also represent an "and / or" relationship, which can be specifically understood with reference to the context before and after.

[0182] In the present invention, "at least one" means one or more, and "a plurality" means two or more. "At least one of the following" or its similar expressions refer to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b, or c can represent: a, b, c, a - b, a - c, b - c, or a - b - c, where a, b, and c can be single or multiple.

[0183] It should be understood that in various embodiments of the present invention, the magnitudes of the sequence numbers of the above processes do not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0184] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. A professional technician can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0185] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the devices, apparatuses, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0186] In several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling, direct coupling, or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of devices or units can be in an electrical, mechanical, or other form.

[0187] The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0188] In addition, the functional units in each embodiment of the present invention can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit.

[0189] If a function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs that can store program codes.

[0190] An embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the multi-objective scheduling method for a distributed assembly flow shop as in the method embodiment.

[0191] The computer-readable storage medium provided by the present invention can implement the steps and effects of the multi-objective scheduling method for a distributed assembly flow shop in the above method embodiment. To avoid repetition, the present invention will not elaborate further.

[0192] The beneficial effects brought by the technical solution provided by the embodiments of the present invention at least include:

[0193] In the embodiments of the present invention, by introducing a collaborative mechanism of a heuristic algorithm and a local search algorithm in the scheduling optimization process and replacing the traditional numerical comparison method of the objective function with a Pareto optimal archive, a comprehensive exploration and optimization of the solution set in multiple objective dimensions are realized, significantly improving the distribution breadth and diversity of the solution set. At the same time, by collecting the key process parameters of the distributed assembly flow shop, a scheduling optimization model integrating elements such as workpiece processing sequence, equipment start-stop control, processing speed adjustment, and assembly timing is constructed, realizing the collaborative integration of multiple energy-saving control strategies. At the same time, minimizing energy consumption is taken as one of the core objectives in the optimization process, comprehensively considering the dynamic relationship between the machine operating state and energy consumption fluctuations, thereby improving the energy efficiency adaptation ability and energy-saving optimization depth of the system in actual production scenarios and effectively breaking through the limitation of traditional methods relying only on a single energy-saving means.

[0194] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

[0195] The following points need to be explained:

[0196] (1) The accompanying drawings of the embodiments of the present invention only relate to the structures involved in the embodiments of the present invention, and other structures can refer to the general design.

[0197] (2) For clarity, in the accompanying drawings used to describe the embodiments of the present invention, the thickness of layers or regions is enlarged or reduced, that is, these drawings are not drawn to actual scale. It can be understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element can be "directly" on or under the other element or there can be intervening elements.

[0198] (3) Without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0199] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A multi-objective scheduling method for a distributed assembly flow shop, characterized in that Including: S1: Collect the process parameters of the distributed assembly flow shop; S2: Based on the process parameters, determine the scheduling constraints with the goal of minimizing the total energy consumption and the makespan; S3: Under the constraints of the scheduling constraints, generate an initial feasible scheduling plan, calculate the makespan and the total energy consumption of the initial feasible scheduling plan, and establish a distributed assembly flow shop scheduling mixed integer linear optimization model including the workpiece processing sequence, machine start / stop, machine processing speed, and workpiece assembly sequence; S4: Combine the heuristic algorithm and the local search algorithm to optimize the distributed assembly flow shop scheduling mixed integer linear optimization model, and output the Pareto optimal archive representing the optimal scheduling plan; S5: According to the Pareto optimal archive, perform multi-objective scheduling of the distributed assembly flow shop.

2. The multi-objective scheduling method for a distributed assembly flow shop according to claim 1, wherein The process parameters specifically include: The number of workpieces, the number of products, the number of machines, the number of factories, the number of adjustable discrete speeds of the machines, the subordinate relationship between the workpieces and the products, the allocation method of the workpieces, the allocation method of the workpieces, the processing sequence of the workpieces, the processing time and speed of the workpieces on each machine, the energy consumption per unit time of the machine in the processing state, the energy consumption per unit time in the idle state, and the energy consumption of each machine shutdown and restart.

3. The multi-objective scheduling method for a distributed assembly flow shop according to claim 1, wherein The scheduling constraints specifically include: Each workpiece can only be processed at one location in the factory at any time and cannot be transferred between factories during the processing; Each process can only use a fixed processing speed; Ensure the orderly progress of the processing of the workpieces in their corresponding factories and ensure the feasibility of the generated scheduling plan; When the idle energy consumption of the machine in the current time period is greater than the start / stop energy consumption of the machine, the shutdown operation is allowed to be executed; The machine must be in the running state before the next workpiece starts to be processed; The actual completion time of the workpiece after speed adjustment cannot exceed the start time of the next workpiece; The energy consumption during the time period after speed adjustment needs to decrease.

4. The multi-objective scheduling method for a distributed assembly flow shop according to claim 3, characterized in that The specific content of S3 includes: S301: Set the actual processing time of the workpiece after speed adjustment as: Among them, represents the actual processing time of the d i-th workpiece on the j-th machine at speed v, represents the actual processing time of the i-th workpiece on the j-th machine at the reference speed of 1, represents whether the processing speed of the d i-th workpiece on the j-th machine is v ; represents that the processing speed of the d i-th workpiece on the j-th machine is v ; represents that the processing speed of the d i-th workpiece on the j-th machine is not v S302: Set the actual processing completion time of the workpiece after speed adjustment as: Among them, represents the actual completion time of the -th workpiece processed on the j-th machine at speed v d . represents the actual completion time of the -th workpiece processed on the j-th machine at speed v d . represents the actual completion time of the -th workpiece processed on the (j - 1)-th machine at speed v d . represents the actual processing time of the -th workpiece processed on the j-th machine at speed v d . S303: Set the processing completion time of all corresponding workpieces for assembling a single product on the last machine as: Among them, represents the maximum completion time of the workpiece for assembling the product on the last machine Q, represents the th workpiece, Ω h represents the set of product workpieces; S304: When all the workpieces for assembling the product are processed and the assembly machine is idle, the product can start to be assembled: Among them, represents the completion time of the product on the assembly machine M A where max represents maximization, represents the completion time of the product on the assembly machine M A and represents the assembly time of the product ; S305: Determine the makespan of the initial feasible scheduling plan as: Among them, C max (Γ) represents the makespan of the initial feasible scheduling plan; S306: Set the total processing energy consumption as: Among them, APE(Γ) represents the total energy consumption of the initial feasible scheduling plan. Indicates whether the processing speed of the i-th workpiece on the j-th machine is v d , v d Represents the discrete processing speed. Indicates that the processing speed of the i-th workpiece on the j-th machine is v d , Indicates that the processing speed of the i-th workpiece on the j-th machine is not v d , Indicates that the i-th workpiece is processed on the j-th machine at a speed of v d The actual processing time. Indicates that the i-th workpiece is processed on the j-th machine at a speed of v d The actual unit energy consumption of processing. R represents the total number of factories, N f Represents the total number of workpieces in the current factory, Q represents the number of machines in each factory, and D represents the total number of discrete speeds. S307: Set the total idle energy consumption of the machine as: Among them, AIE(Γ) represents the total energy consumption of machine idle time in the initial feasible scheduling plan, and C f represents the makespan of the f-th factory, represents the shutdown time of the j-th machine, represents the energy consumption when the j-th machine is idle; S308: Set the total start / stop energy consumption as: AOE(Γ) = SDt·e off Among them, AOE(Γ) represents the total energy consumption of machine startup and shutdown in the initial feasible scheduling scheme, SD t represents the total number of startup and shutdown times, and e off represents the energy consumption of machine restart; S309: According to the total processing energy consumption, the total idle energy consumption of the machine, and the total start / stop energy consumption, determine the total energy consumption of the initial feasible scheduling plan as: AE(Γ) = APE(Γ) + AIE(Γ) + AOE(Γ); S310: According to the total energy consumption and the makespan of the initial feasible scheduling plan, establish a distributed assembly flow shop scheduling mixed integer linear optimization model.

5. The multi-objective scheduling method for a distributed assembly flow shop according to claim 4, wherein The specific form of the distributed assembly flow shop scheduling mixed integer linear optimization model is: min{C max (Γ), AE(Γ)}; where min represents minimization, and C max (Γ) represents the makespan of the initial feasible scheduling scheme, and AE(Γ) represents the total energy consumption of the initial feasible scheduling scheme.

6. The multi-objective scheduling method for a distributed assembly flow shop according to claim 1, wherein The specific content of S4 includes: S401: Set the position of the first assembled product in the product sequence, an initial population with an initial size equal to the number of products, and algorithm parameters, where the algorithm parameters include the dominant population ratio, learning rate, number of segments of the local search algorithm, and number of iterations; S402: Determine the time global probability matrix of the time-dominant product subsequence and the energy consumption global probability matrix of the energy consumption-dominant product subsequence: Among them, Ψ(g) represents the time global probability matrix, and Ψ ab (g) represents the probability value of operation a at the b-th position in the g-th generation heuristic sequence in the time global probability matrix, where a ∈ 1, 2, … N TDP , b ∈ 1, 2, … N TDP , N TDP represents the length of the heuristic sequence of the time dominant product subsequence, Υ(g) represents the energy consumption global probability matrix, and Υ ab (g) represents the probability value of operation a at the b-th position in the g-th generation heuristic sequence in the energy consumption global probability matrix, N EDP represents the length of the heuristic sequence of the energy consumption dominant product subsequence; S403: Initialize the time global probability matrix and the energy consumption global probability matrix, and uniformly distribute the elements in the time global probability matrix and the energy consumption global probability matrix: Among them, Ψ ab (0) represents the probability value of operation a at the b-th position in the g-th generation of the time-dominated heuristic sequence, N1 represents the number of heuristic algorithms in the time-dominated product heuristic sequence, Υ ab (0) represents the probability value of operation a at the b-th position in the g-th generation of the energy consumption-dominated heuristic sequence, N2 represents the number of heuristic algorithms in the energy consumption-dominated product heuristic sequence; S404: Traverse each position of the heuristic operator sequence in turn, and calculate the cumulative probability sets of the time global probability matrix and the energy consumption global probability matrix: Among them, Hs_P b represents the cumulative probability of the b-th heuristic operator in the time global probability matrix, and Hs_J b represents the cumulative probability of the b-th heuristic operator in the energy consumption global probability matrix, where l represents the index of the heuristic operator; S405: Generate a random number. By traversing the cumulative probability sets of the time global probability matrix and the energy consumption global probability matrix, determine the interval where the random number is located, and calculate the time heuristic sequence and the energy consumption heuristic sequence using the following formula: where S1[c] represents the operation at the c-th position in the time-dominant heuristic sequence, rnd1 represents the random number, and S2[c] represents the operation at the c-th position in the energy consumption-dominant heuristic sequence; S406: With the goal of minimizing the makespan, sequentially perform neighborhood search on the initial population according to the sequence numbers in the time heuristic sequence, output the updated first objective population, and compare the solutions in the initial population with the solutions in the first objective population. If C max (ε' M ) < C max (ε M ) and rnd ≥ e -Δ , accept the solution in the first objective population; otherwise, continue to use the solution in the initial population; S407: With the goal of minimizing the total energy consumption, sequentially perform neighborhood search on the first target population according to the sequence numbers in the energy consumption heuristic sequence, output the updated second target population, and compare the solutions in the first target population with the solutions in the second target population. If C max (ε' M ) < C max (ε M ) and rnd ≥ e -Δ , accept the solution in the second target population; otherwise, continue to use the solution in the first target population; S408: Calculate the L2 metric for each solution in the second target population: Among them, min represents minimization, f1(x) represents the objective function value of the makespan of the current solution, and f2(x) represents the objective function value of the total energy consumption of the current solution. represents the ideal value of the total energy consumption, and λ represents the weight of the makespan. S409: Sample the first candidate individual and the second candidate individual, compare the L2 metrics of the first candidate individual and the second candidate individual, and select the candidate individual with a smaller L2 metric value to enter the dominant subgroup to form the first dominant subpopulation; Sups = P_size * η Among them, Sup_vec d represents the individual number at the d-th position of the dominant sub-population, C1 represents the first candidate individual, C2 represents the second candidate individual, Sups represents the size of the dominant sub-population, P_size represents the size of the population, and η represents the proportion of dominant solutions; S410: Update the time global probability matrix and the energy consumption global probability matrix for each generation according to the first dominant subpopulation: Among them, Ψ ab (g + 1) represents the probability value of operation a at the b-th position in the (g + 1)-th generation heuristic sequence in the time global probability matrix, γ represents the learning rate, Υ ab (g + 1) represents the probability value of operation a at the b-th position in the (g + 1)-th generation heuristic sequence in the energy consumption global probability matrix, represents whether the operation of operation a at position b in the heuristic sequence has a positive effect on finding a solution with better quality, represents that the operation of operation a at position b in the heuristic sequence has a positive effect on finding a solution with better quality, represents that the operation of operation a at position b in the heuristic sequence has no positive effect on finding a solution with better quality; S411: Insert each workpiece in each solution of the first dominant subpopulation into the first remaining position different from the current position in turn, calculate the makespan after inserting the workpiece, and determine whether the makespan after inserting the workpiece is less than the current makespan in the dominant subpopulation; if so, update the current solution and start the search again; otherwise, keep the current order and continue with the insertion operation for the next workpiece until all workpieces are processed, and output the updated second dominant subpopulation; S412: Divide the energy consumption-dominant workpiece subsequence corresponding to the solutions in the second dominant subpopulation into multiple sub-workpiece segments, insert the workpieces within each workpiece segment into the second remaining positions within the current workpiece segment in turn, calculate the total energy consumption after inserting the workpiece, and determine whether the total energy consumption after inserting the workpiece is reduced; if so, continue the search; otherwise, keep the current order and continue with the insertion operation for the next workpiece until all workpieces are processed, and output the updated third dominant subpopulation; S413: Compare the objective values of the solutions in the third dominant subpopulation with the objective values of the solutions in the current Pareto archive, update the current Pareto archive, and output the optimal Pareto archive; S414: Under the constraint that the latest completion time of the workpiece cannot exceed the latest start time of the next workpiece and the earliest start assembly time of the product to which it belongs, postpone the start processing time of the workpiece; S415: Accelerate the machine processing speed to a preset multiple, and compare whether the idle energy consumption before acceleration is greater than the sum of the machine start-stop energy consumption and the increased processing energy consumption after acceleration; if so, perform the shutdown operation; otherwise, proceed to S416: S416: When the energy consumption decreases within the time period after speed adjustment, perform an acceleration operation on the machine. When the actual completion time of the workpiece after speed adjustment does not exceed the processing start time of the next workpiece, perform a deceleration operation on the machine; otherwise, keep the machine in an idle state; S417: Determine whether the current algorithm execution time is greater than the maximum algorithm execution time; if so, end the iteration and output the Pareto optimal archive; otherwise, increment the iteration count by 1 and return to S404.

7. The multi-objective scheduling method for a distributed assembly flow shop according to claim 6, characterized in that, The specific neighborhood search for the initial population in S406 includes: S4061: When the serial number in the time heuristic sequence is the first serial number, randomly swap the positions of a time-dominated product P a and a power consumption-dominated product P b where a and b represent the product numbers; S4062: When the serial number in the time heuristic sequence is the second serial number, select a time-dominated product P a and an energy consumption-dominated product P b , if b is greater than a, insert P a before P b ; S4063: When the serial number in the time heuristic sequence is the third serial number, select a time-dominated product P a and an energy consumption-dominated product P b , if b is greater than a, insert P a after P b ; S4064: When the serial number in the time heuristic sequence is the fourth serial number, select a time-dominated product P a and an energy consumption-dominated product P b , reverse the product subsequence between product P a and product P b ; S4065: When the serial number in the time heuristic sequence is the fifth serial number, randomly swap the positions of two time-dominated products; S4066: When the serial number in the time heuristic sequence is the sixth serial number, randomly select a time-dominated product and uniformly adjust the speeds of all workpieces used to assemble the current product to a preset level; S4067: When the serial number in the time heuristic sequence is not one of the first to the sixth serial numbers, do not operate on the time-dominated product subsequence and the energy consumption-dominated product subsequence.

8. The multi-objective scheduling method for a distributed assembly flow shop according to claim 6, wherein The calculation formula of Δ is: where Δ represents a constant, C max (ε' M ) represents the makespan of the initial solution, C max (ε M ) represents the makespan of the target solution, and Temp represents the adjustable annealing rate parameter.

9. The multi-objective scheduling method for a distributed assembly flow shop according to claim 6, characterized in that, The specific neighborhood search for the first target population in S407 includes: S4071: When the serial number in the energy consumption heuristic sequence is the first serial number, randomly exchange the positions of the energy consumption dominant products P c and P d . S4072: When the serial number in the energy consumption heuristic sequence is the second serial number, select two energy consumption dominant products P c and P d . If c is greater than d, insert P d before P c . S4073: When the serial number in the energy consumption heuristic sequence is the third serial number, select two energy consumption dominant products P c and P d . If c is greater than d, insert P d after P c . S4074: When the serial number in the energy consumption heuristic sequence is the fourth serial number, select two energy consumption dominant products P c and P d , and reverse the product subsequence between product P c and product P d ; S4075: When the serial number in the energy consumption heuristic sequence is the fifth serial number, randomly swap the positions of two adjacent time-dominated products; S4076: When the serial number in the energy consumption heuristic sequence is the sixth serial number, randomly select two workpieces J c in c c and J d , and exchange the positions of workpiece J c and J d ; S4077: When the serial number in the energy consumption heuristic sequence is the seventh serial number, randomly select two workpieces J in a time-dominant product c and J d . If c is greater than d, insert workpiece J c before J d ; S4078: When the serial number in the energy consumption heuristic sequence is the eighth serial number, randomly select two workpieces J in a time-dominant product c and J d . If c is greater than d, insert workpiece J c after J d . S4079: When the serial number in the energy consumption heuristic sequence is the ninth serial number, randomly select two workpieces J c and J d in a dominant energy consumption product, and reverse the workpiece subsequence between the two workpieces; S407A: When the serial number in the energy consumption heuristic sequence is the tenth serial number, randomly select two adjacent workpieces J c and J d in an energy consumption dominant product, and exchange their positions; S407B: When the serial number in the energy consumption heuristic sequence is not one of the first to the tenth serial numbers, do not operate on the time-dominated workpiece subsequence and the energy consumption-dominated workpiece subsequence.

10. A multi-objective scheduling system for a distributed assembly flow shop, characterized in that, Including: A processor; A memory, on which computer-readable instructions are stored. When the computer-readable instructions are executed by the processor, the multi-objective scheduling method for a distributed assembly flow shop as described in any one of claims 1 to 9 is implemented.

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