Distributed heterogeneous assembly flexible job shop scheduling method with transfer

Abstract

The invention discloses a distributed heterogeneous assembly flexible job shop scheduling method with transfer. The method comprises the following steps of: setting assumption and basic parameters, proposing corresponding constraint conditions according to a researched problem, and constructing a dual-objective optimization model taking minimization of maximum completion time and minimization of total processing energy consumption as objectives; the dual-objective optimization model is used for scheduling optimization of the assembly flexible job shop considering the factory processing capacity, the transportation stage and the workpiece transfer; designing a three-segment coding mode and a decoding mode corresponding to the dual-objective optimization model based on a process sequence, processing factory selection and processing machine selection; and based on a three-segment coding mode and a decoding mode, an improved multi-target genetic algorithm based on Q-Learning is adopted, and an optimal scheduling scheme is solved. According to the method, factors of workshop processing capacity, workshop collaborative processing and transportation stage time are considered, and a process processing sequence, process processing factories, process processing machines and assembly workshop selection are arranged from the perspective of global optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing and production optimization, and in particular to a distributed heterogeneous assembly flexible job shop scheduling method with transfer. Background Art

[0002] In order to meet the challenges of diversified market demand, the mass production model has gradually transformed into a flexible production model with multiple varieties and small batches. In addition, with the deepening development of economic globalization, the traditional single-factory production model can no longer meet the growing market demand. More and more companies are cooperating with each other to integrate the production capacity of production bases in different regions, improve production efficiency and reduce costs.

[0003] In this context, the scheduling problem of assembly flexible job shops, which consists of two stages, manufacturing and assembly, has received increasing attention and has been successfully applied to the manufacturing of die-casting molds, ball valves, and various complex electromechanical products.

[0004] However, in the prior art, the scheduling technology of the assembly flexible workshop has the following problems:

[0005] First, existing studies all assume that different factories have the same manufacturing capabilities, that is, homogeneous factories. In fact, in a multi-factory production environment, not all factories have the ability to produce any product. In particular, only core enterprises have the ability and authority to process core components.

[0006] Second, existing studies all assume that workpieces can only be processed in one factory. However, in actual production, if the distance allows, in order to improve the utilization of equipment resources and balance the load of equipment in each factory, and at the same time shorten the total processing time of the product, some processes of the product may be handed over to the collaborative workshop for processing;

[0007] Third, the influencing factors such as the transportation time in the transportation stage are not considered. In the actual assembly production system, the time for collecting raw materials and transportation and distribution is considerable and cannot be ignored. Summary of the invention

[0008] In view of the shortcomings of the prior art, the present invention proposes a distributed heterogeneous assembly flexible job shop scheduling method with transfer, which takes into account the factors of workshop processing capacity, workshop collaborative processing and transportation stage time, and arranges the process processing sequence, process processing factory, process processing machine, and assembly workshop selection from a global optimization perspective within a reasonable time to minimize the maximum completion time and minimize the total processing energy consumption.

[0009] To achieve the above object, the present invention is designed to provide a distributed heterogeneous assembly flexible job shop scheduling method with transfer, which is particularly characterized in that it includes the following steps:

[0010] S1) setting assumptions and basic parameters, proposing corresponding constraints on workshop processing capacity, workshop collaborative processing and transportation phase time, and constructing a dual-objective optimization model with the goals of minimizing the maximum completion time and minimizing the total processing energy consumption. The dual-objective optimization model is used for scheduling optimization of assembly flexible job shops considering factory processing capacity, transportation phase and workpiece transfer;

[0011] The objective optimization model of minimizing the maximum completion time is expressed as follows:

[0012]

[0013] In the formula,

[0014] C max is the maximum completion time,

[0015] b indicates product,

[0016] a represents the assembly workshop,

[0017] Indicates the completion time of product b in assembly workshop a;

[0018] The target optimization model for minimizing the total energy consumption of machining is expressed by the following formula:

[0019] mincost=C1+C2+C3+C4+C5

[0020] In the formula,

[0021] C1 represents the total energy consumption of the processing workshop, including the workpiece processing energy consumption and the fixed energy consumption of the processing workshop.

[0022] C2 represents the total energy consumption of the assembly workshop, including product assembly energy consumption and fixed energy consumption of the assembly workshop.

[0023] C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop.

[0024] C4 represents the total transportation energy consumption during the workpiece production process, including the energy consumption of transportation between different machines and between different workshops.

[0025] C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop;

[0026] The total transportation energy consumption C4 during the workpiece production process is expressed by the following formula:

[0027]

[0028] In the formula,

[0029] C4 represents the total energy consumption of transportation during the production process of workpieces.

[0030] X j,p-1,i,r Indicates whether the p-1th process of product j is processed on the i-th machine in the r-th factory. If so, then X j,p-1,i,r is 1, otherwise it is 0.

[0031] X jpi'r Indicates whether the p-th process of product j is processed on the i'th machine in the r-th factory. If so, then X jpi'r is 1, otherwise it is 0.

[0032] represents the unit energy consumption of transferring product j from machine i to machine i' in factory r,

[0033] Y jpr' Indicates whether the pth process of product j is processed in factory r'. If so, then Y jpr' is 1, otherwise it is 0.

[0034] Y j,p-1,r Indicates whether the p-1th process of product j is processed in factory r. If so, then Y j,p-1,r is 1, otherwise it is 0.

[0035] represents the energy consumption transferred from plant r to r';

[0036] S2) designing a three-segment encoding mode and a three-segment decoding mode corresponding to the dual-objective optimization model based on the process sequence, processing plant selection and processing machine selection;

[0037] S3) Based on the three-segment encoding mode and the three-segment decoding mode, an improved multi-objective genetic algorithm based on Q-Learning is used to solve the optimal scheduling solution of the dual-objective optimization model.

[0038] Furthermore, in S1), the assumptions set include: each job can only be assigned to one factory; different processes of a job can be completed by different factories in collaboration; core components can only be processed by core factories; each machine can only process one job at a time; all processes belonging to the same job should be processed in a predetermined order; once the operation starts, no interruption is allowed; and machine startup time is not considered.

[0039] Furthermore, in S1), the constraints proposed include: one process of each workpiece can only be assigned to one manufacturing plant; each product can only be assigned to one assembly plant; each process of the workpiece can only be completed by one available machine in a factory with corresponding processing capabilities; the completion time of each process is equal to the start time of the process plus the processing time of the process; the start processing time of a process is not less than the completion time of the previous process plus the transportation time; each machine can only process one process at the same time; the manufacturing completion time of the product is not less than the completion time of the product process plus the transportation time of the raw materials of each workpiece in the product; the start assembly time of the product is not less than the manufacturing completion time of the product plus the transportation time from the production workshop to the assembly workshop; the assembly completion time of the product is the assembly start time of the product plus the assembly time.

[0040] Furthermore, in S1), the total energy consumption C1 of the processing workshop is expressed by the following formula:

[0041]

[0042] In the formula,

[0043] C1 represents the total energy consumption of the processing workshop,

[0044] P jpir Indicates process O jp The processing time on machine i in plant r,

[0045] represents the unit processing energy consumption on machine i in factory r,

[0046] X jpir Indicates process O jp Is it processed on machine i in factory r? If so, then X jpir is 1, otherwise it is 0.

[0047] represents the unit processing energy consumption of factory r,

[0048] M r represents the total processing time of processing factory r;

[0049] The total energy consumption C2 of the assembly workshop is expressed by the following formula

[0050]

[0051] In the formula,

[0052] C2 represents the total energy consumption of the assembly workshop,

[0053] represents the unit assembly energy consumption of the assembly workshop,

[0054] Aba Indicates the assembly time,

[0055] Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1, otherwise it is 0.

[0056] represents the unit fixed energy consumption of assembly workshop a,

[0057] A a represents the total assembly time of assembly shop a;

[0058] The total energy consumption C3 of transporting the raw materials of each workpiece to the corresponding processing workshop is expressed by the following formula:

[0059]

[0060] In the formula,

[0061] C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop.

[0062] Represents the energy consumption of transporting raw materials to the processing plant,

[0063] Y jpr Indicates process O jp Is it processed in factory r? If so, then Y jpr is 1, otherwise it is 0; the total energy consumption C5 of transporting products from the processing workshop to the assembly workshop is expressed by the following formula

[0064]

[0065] In the formula,

[0066] C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop.

[0067] V jra Indicates whether product j needs to be transported from processing factory r to assembly factory a. If yes, it is 1, otherwise it is 0.

[0068] It represents the unit transportation energy consumption from the processing plant to the assembly workshop.

[0069] Further, in S2), the three coding modes include a factory allocation coding mode, a machine selection coding mode, and a process sequencing coding mode.

[0070] Furthermore, in S2), the design steps of the three-segment decoding mode are as follows:

[0071] S21) determining the operation sequence of all the processes to be processed according to the process sequence vector;

[0072] S22) reading the factory, machine and corresponding process processing time assigned to the corresponding process;

[0073] S23) first determine whether it is the first process on the machine and whether it is the first process of the workpiece; if both conditions are met, directly arrange the process to the first position of the machine;

[0074] S24) Determine whether the process sequence vector has been read. If not, go to step S22; if yes, arrange the scheduling plan for the assembly stage, that is, sort the workpieces in each product from small to large according to the maximum completion time, and distribute them to the assembly plants in sequence according to the minimum load principle.

[0075] Furthermore, in S23), if the condition that the process is the first process on the machine but not the first process on the workpiece is satisfied, the earliest processable time of the process is T a =max{C j,p-1 +TM+TF,TS t}, the completion time of the process is T a +P ijpr ;

[0076] If it does not meet the condition of being the first process on the machine, but meets the condition of being the first process of the workpiece, there may be idle time on the machine, and a greedy decoding method is used to further shorten the maximum completion time.

[0077] Further, in S3), the steps of solving the optimal scheduling solution of the dual-objective optimization model by using the improved multi-objective genetic algorithm based on Q-Learning are as follows:

[0078] S31) according to the initial population size and encoding method, a hybrid initialization method is used to generate a high-quality initial population to promote rapid convergence of the algorithm;

[0079] S32) using a tournament selection method to select individuals from the population for subsequent crossover and mutation operations;

[0080] S33) adaptively adjusting key parameters of the algorithm through Q-Learning, wherein the key parameters include crossover probability and mutation probability;

[0081] S34) using a two-step crossover strategy to perform a global search;

[0082] S35) using a four-step mutation strategy for local search;

[0083] S36) using a neighborhood search strategy to further explore the solution space;

[0084] S37) When the set maximum number of iterations or the deadline is reached, the optimal solution is output, otherwise the new population is used as the initial population and steps S32) to S35) are re-executed.

[0085] Furthermore, in S31), the hybrid initialization method includes: for the process layer, a random initialization method is adopted; for the factory layer, each process gives priority to selecting an optional factory with a large number of centralized processing machines. If the number is the same, a factory with a short average processing time is selected; for the machine layer, machines with low machine load are given priority.

[0086] The advantages of the present invention are:

[0087] 1. The present invention further considers multiple realistic constraints (workshop processing capacity, workshop collaborative processing and transportation phase time), constructs a dual-objective optimization model that minimizes the maximum completion time and minimizes the total processing energy consumption, and finally solves the optimal scheduling scheme of the dual-objective optimization model to improve workshop production efficiency; the optimal scheduling scheme simultaneously solves the four problems of processing plant selection, processing machine selection, processing sequence sorting and assembly workshop selection in the manufacturing workshop;

[0088] 2. Since the existing solution algorithms are inefficient in solving this type of problem, the present invention proposes an improved multi-objective genetic algorithm (QL-IMOGA) based on Q-Learning to solve the optimal scheduling scheme of the dual-objective optimization model of minimizing the maximum completion time and minimizing the total processing energy consumption. A mixed population initialization method, a two-step crossover operator, a four-step mutation operator and six neighborhood search strategies are adopted, among which the two-step crossover improves the global search capability, the four-step mutation and neighborhood search strategies improve the local search capability, and the mixed initialization strategy accelerates the convergence of the algorithm;

[0089] The distributed heterogeneous assembly flexible job shop scheduling method with transfer of the present invention aims to minimize the maximum completion time and minimize the total processing energy consumption, considers the factors of workshop processing capacity, workshop collaborative processing and transportation stage time, and arranges the process processing sequence, process processing factory, process processing machine, and assembly workshop selection from the perspective of global optimization within a reasonable time. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of the distributed heterogeneous assembly flexible job shop scheduling method with transfer of the present invention;

[0091] Figure 2 This is a flow chart of the QL-IMOGA algorithm used in the present invention;

[0092] Figure 3 A schematic diagram of the comparison results of target values ​​of different algorithms provided by an embodiment of the present invention;

[0093] Figure 4 A schematic diagram of the comparison results of evaluation indicators of different algorithms provided by the embodiment of the present invention;

[0094] Figure 5 A schematic diagram of the comparison results of the Wilcoxon test of different algorithms provided in an embodiment of the present invention;

[0095] Figure 6 It is a schematic diagram comparing the operation results of the distributed heterogeneous assembly flexible job shop scheduling method with transfer and the distributed heterogeneous assembly flexible job shop scheduling method without transfer of the present invention. DETAILED DESCRIPTION

[0096] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0097] The present invention provides a distributed heterogeneous assembly flexible job shop scheduling method with transfer, comprising the following steps:

[0098] S1) Set assumptions and basic parameters, propose corresponding constraints on workshop processing capacity, workshop collaborative processing and transportation stage time, and build a dual-objective optimization model with the goals of minimizing the maximum completion time and minimizing the total processing energy consumption. The dual-objective optimization model is used for scheduling optimization of assembly flexible job shops considering factory processing capacity, transportation stage and workpiece transfer.

[0099] Specifically, the assumptions set include: each job can only be assigned to one factory; different processes of a job can be completed by different factories in collaboration; core components can only be processed by core factories; each machine can only process one job at a time; all processes belonging to the same job should be processed in a predetermined order; once the operation starts, no interruption is allowed; and machine startup time is not considered.

[0100] Specifically, the proposed constraints include:

[0101] Condition 1: Each workpiece can only be assigned to one manufacturing plant:

[0102]

[0103] In the formula,

[0104] Y jpr Indicates process O jp Is it processed in factory r? If yes, then Y jpr is 1 if the value is true, otherwise it is 0.

[0105] Condition 2: Each product can only be assigned to one assembly plant:

[0106]

[0107] In the formula,

[0108] Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1 if the value is true, otherwise it is 0.

[0109] Condition 3: Each operation of the workpiece can only be completed by one available machine in the factory with corresponding processing capacity:

[0110]

[0111] In the formula,

[0112] X jpir Indicates process O jp Is it processed on machine i in factory r? If so, then X jpir is 1, otherwise it is 0.

[0113] U jpir Indicates process O jp Can it be processed on machine i in factory r? If so, then U jpir is 1 if the value is true, otherwise it is 0.

[0114] Condition 4: The completion time of each process is equal to the start time of the process plus the processing time of the process:

[0115]

[0116] In the formula,

[0117] C jp Indicates process O jp The completion time,

[0118] S jp Indicates process O jp The start time of

[0119] P jpir Indicates process O jp The processing time on machine i in plant r,

[0120] represents a very large number,

[0121] X jpir Indicates process O jp Is it assigned to machine i in factory r? If so, then X jpir is 1 if the value is true, otherwise it is 0.

[0122] Condition 5: The start processing time of the process is not less than the completion time of the previous process plus the transportation time:

[0123]

[0124] In the formula,

[0125] S jp Indicates process O jp The start time of

[0126] C j，p-1 Indicates process O j,p-1 The completion time,

[0127] represents the transfer time from machine i to machine i' in factory r,

[0128] X j,p-1,i',r Indicates process O j,p-1 Is it assigned to machine i' in factory r? If so, then X j,p-1,i',r is 1, otherwise it is 0.

[0129] X jpir Indicates process O jp Is it assigned to machine i in factory r? If so, then X jpir is 1, otherwise it is 0.

[0130] represents the transfer time from factory r to factory r',

[0131] Y j,p-1,r' Indicates process O j,p-1 Is it assigned to factory r'? If so, then Y j,p-1,r' is 1, otherwise it is 0.

[0132] Y jpr Indicates process O j,p Is it assigned to factory r? If so, then Y jpr is 1, otherwise it is 0.

[0133] Condition 6: Each machine can only process one process at a time:

[0134]

[0135] In the formula,

[0136] C jp Indicates process O jp The completion time,

[0137] C j’p’ Indicates process O j’p’ Completion time

[0138] P jpir Indicates process O jp Processing time on machine i in plant r

[0139] P j’p’i’r’ Indicates process O j’p’ Processing time on machine i' in plant r'

[0140] X jpir Indicates process O jp Is it assigned to machine i in factory r? If so, then X jpir is 1, otherwise it is 0.

[0141] X j’p’i’r’ Indicates process O j’p’ Is it assigned to machine i' of r'? If so, then X j’p’i’r’ is 1, otherwise it is 0.

[0142] represents a very large number,

[0143] η jpj,p, Indicates process O j,p, On the same machine before process O jp Processing, if yes, then η jpj,p, is 1 if the value is true, otherwise it is 0.

[0144] Condition 7: The manufacturing completion time of the product shall not be less than the process completion time of the product plus the transportation time of the raw materials of each workpiece in the product:

[0145]

[0146] In the formula,

[0147] represents the completion time of product b in factory r,

[0148] C jp Indicates process O jp The completion time,

[0149] R jb Indicates whether workpiece j belongs to product b. If so, then R jb is 1, otherwise it is 0.

[0150] Y jpr Indicates process O jp Is it processed in factory r? If yes, then Y jpr is 1, otherwise it is 0.

[0151] represents the transportation time of workpiece j from the transportation of raw materials to the processing factory,

[0152] Y j，1，r Indicates process O j,1 Is it assigned to factory r? If so, then Yj，1，r is 1 if the value is true, otherwise it is 0.

[0153] Condition 8: The start time of product assembly shall not be less than the product manufacturing completion time plus the transportation time from the production workshop to the assembly workshop:

[0154]

[0155] In the formula,

[0156] Indicates the start assembly time of product b,

[0157] represents the completion time of product b in factory r,

[0158] represents the transit time from processing plant r to assembly plant a,

[0159] Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1 if the value is true, otherwise it is 0.

[0160] Condition 9: The assembly completion time of a product is the assembly start time of the product plus the assembly time.

[0161]

[0162] In the formula,

[0163] represents the completion time of product b,

[0164] Indicates the start assembly time of product b,

[0165] Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1, otherwise it is 0.

[0166] A ba Represents the assembly time of product b in assembly factory a.

[0167] Specifically, the objective optimization model for minimizing the maximum completion time is expressed as follows:

[0168]

[0169] In the formula,

[0170] C max is the maximum completion time,

[0171] b indicates product,

[0172] a represents the assembly workshop,

[0173] Indicates the completion time of product b in assembly workshop a.

[0174] Specifically, the target optimization model for minimizing the total energy consumption of machining is expressed by the following formula:

[0175] mincost=C1+C2+C3+C4+C5

[0176] In the formula,

[0177] C1 represents the total energy consumption of the processing workshop, including the workpiece processing energy consumption and the fixed energy consumption of the processing workshop.

[0178] C2 represents the total energy consumption of the assembly workshop, including product assembly energy consumption and fixed energy consumption of the assembly workshop.

[0179] C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop.

[0180] C4 represents the total transportation energy consumption during the workpiece production process, including the energy consumption of transportation between different machines and between different workshops.

[0181] C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop.

[0182] Specifically, the total energy consumption C1 of the processing workshop is expressed by the following formula:

[0183]

[0184] In the formula,

[0185] C1 represents the total energy consumption of the processing workshop,

[0186] P jpir Indicates process O jp The processing time on machine i in plant r,

[0187] represents the unit processing energy consumption on machine i in factory r,

[0188] X jpir Indicates process O jp Is it processed on machine i in factory r? If so, then X jpir is 1, otherwise it is 0.

[0189] represents the unit processing energy consumption of factory r,

[0190] M r Represents the total processing time of processing factory r.

[0191] The total energy consumption C2 of the assembly workshop is expressed by the following formula

[0192]

[0193] In the formula,

[0194] C2 represents the total energy consumption of the assembly workshop,

[0195] represents the unit assembly energy consumption of the assembly workshop,

[0196] A ba Indicates the assembly time,

[0197] Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1, otherwise it is 0.

[0198] represents the unit fixed energy consumption of assembly workshop a,

[0199] A a Represents the total assembly time of assembly shop a.

[0200] The total energy consumption C3 of transporting the raw materials of each workpiece to the corresponding processing workshop is expressed by the following formula:

[0201]

[0202] In the formula,

[0203] C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop.

[0204] Represents the energy consumption of transporting raw materials to the processing plant,

[0205] Y jpr Indicates process O jp Is it processed in factory r? If so, then Y jpr is 1 if the value is true, otherwise it is 0.

[0206] The total transportation energy consumption C4 during the workpiece production process is expressed by the following formula:

[0207]

[0208] In the formula,

[0209] C4 represents the total energy consumption of transportation during the production process of workpieces.

[0210] X j,p-1,i,r Indicates whether the p-1th process of product j is processed on the i-th machine in the r-th factory. If so, then X j,p-1,i,r is 1, otherwise it is 0.

[0211] X jpi'r Indicates whether the p-th process of product j is processed on the i'th machine in the r-th factory. If so, then X jpi'r is 1, otherwise it is 0.

[0212] represents the unit energy consumption of transferring product j from machine i to machine i' in factory r,

[0213] Y jpr' Indicates whether the pth process of product j is processed in factory r'. If so, then Y jpr' is 1, otherwise it is 0.

[0214] Y j,p-1,r Indicates whether the p-1th process of product j is processed in factory r. If so, then Y j,p-1,r is 1, otherwise it is 0.

[0215] represents the energy consumption transferred from plant r to r'.

[0216] The total energy consumption C5 of transporting products from the processing workshop to the assembly workshop is expressed by the following formula

[0217]

[0218] In the formula,

[0219] C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop.

[0220] V jra Indicates whether product j needs to be transported from processing factory r to assembly factory a. If yes, it is 1, otherwise it is 0.

[0221] It represents the unit transportation energy consumption from the processing plant to the assembly workshop.

[0222] S2) Based on the process sequence, processing plant selection and processing machine selection, a three-segment encoding mode and a three-segment decoding mode corresponding to the dual-objective optimization model are designed.

[0223] Specifically, the three coding modes include a factory allocation coding mode (US), a machine selection coding mode (MS), and a process sequencing coding mode (OS).

[0224] In this embodiment, US is represented by {1,1,2,1,1,2,2,2,2}, where each element is the index of the selected factory in the optional factory set of the corresponding process. Similarly, each element in MS also represents the index of the selected machine in the optional machine set of the corresponding process. OS uses a process-based expression method, represented by {1,3,1,1,3,2,4,2}. If the element at the kth position is i and it is the jth time that i appears in OS, then OS ij is the kth scheduled process.

[0225] Specifically, the design steps of the three-segment decoding mode are as follows:

[0226] S21) Determine the operation sequence of all the processes to be processed according to the process sequence vector.

[0227] S22) Read the factory, machine and corresponding process processing time assigned to the corresponding process.

[0228] S23) first determine whether it is the first process on the machine and whether it is the first process of the workpiece; if both conditions are met, directly arrange the process to the first position of the machine;

[0229] If it satisfies the condition of being the first process on the machine but not the first process on the workpiece, the earliest processable time of the process is T a =max{C j,p-1 +TM+TF,TS t}, the completion time of the process is T a +P ijpr ;

[0230] If it does not meet the condition of being the first process on the machine, but meets the condition of being the first process of the workpiece, there may be idle time on the machine, and a greedy decoding method is used to further shorten the maximum completion time. That is, if it is the first process of the workpiece, in order to minimize the maximum completion time, the process is directly inserted into the first idle time period.

[0231] But if the above conditions are not met, then the judgment condition T needs to be met. a +P jpi ≤TE t , the process can be put into the corresponding idle time period.

[0232] S24) Determine whether the process sequence vector has been read. If not, go to step S22; if yes, arrange the scheduling plan for the assembly stage, that is, sort the workpieces in each product from small to large according to the maximum completion time, and distribute them to the assembly plants in sequence according to the minimum load principle.

[0233] S3) Based on the three-segment encoding mode and the three-segment decoding mode, an improved multi-objective genetic algorithm QL-IMOGA based on Q-Learning is used to solve the optimal scheduling solution of the dual-objective optimization model.

[0234] Specifically, the steps of solving the optimal scheduling solution of the dual-objective optimization model using the improved multi-objective genetic algorithm based on Q-Learning are as follows:

[0235] S31) According to the initial population size and encoding method, a hybrid initialization method is used to generate a high-quality initial population to promote rapid convergence of the algorithm.

[0236] Wherein, the hybrid initialization method includes:

[0237] a. The first method uses random initialization for the process layer; for the factory layer, each process is given priority to selecting the factory with more centralized processing machines. If the number is the same, the factory with the shortest average processing time is selected, using the following formula:

[0238]

[0239] In the formula,

[0240] A fj represents the average processing time of the jth job on the selectable machines in the fth factory,

[0241] Indicates the machine processing time,

[0242] m represents the number of processable machines;

[0243] For the machine layer, preference is given to machines with low machine load.

[0244] b. The second method uses random initialization for the process layer; for the factory layer, based on the factory allocation knowledge of the process, this study proposes a method to balance the factory load and the uniform distribution of each workpiece of the product, using the following formula:

[0245] k f =N fpj I fp F f

[0246] In the formula,

[0247] k f represents the importance coefficient of factory f,

[0248] N fpj Indicates the number of processes assigned to each workpiece of product p in factory f,

[0249] Ifp represents the importance weight matrix of factory f with respect to product p,

[0250] F f Indicates the load of each plant;

[0251] For the machine layer, preference is given to machines with low machine load.

[0252] c. The third method uses random initialization for the process level, factory level, and machine level.

[0253] S32) A tournament selection method is used to select individuals from the population for subsequent crossover and mutation operations.

[0254] S33) adaptively adjusting key algorithm parameters through Q-Learning, wherein the key parameters include crossover probability (Pc) and mutation probability (Pm).

[0255] It usually consists of five elements, namely the agent, the environment, the action set, the state set, and the reward function, forming a five-tuple (A, E, C, S, R). At each decision time point, the agent selects the appropriate action based on the current state of the environment, and then updates the state-action mapping table (Q table) according to the reward function. At the same time, the ε greedy selection method is used to select the best strategy based on the Q table. The update equation of the Q table is as follows.

[0256]

[0257] In the formula,

[0258] Q(s t ,a t ) indicates state s t Next action a t The Q value,

[0259] α is the learning rate,

[0260] γ represents the discount factor,

[0261] r t+1 is in state s t Take action t The rewards gained from the environment,

[0262] Indicates state s t+1 The maximum Q value in the Q table is

[0263] Q(s t ,a) indicates the state s t The Q value in the Q table at this time.

[0264] For the state design, in order to maintain the diversity and cutting-edge of the population, an environmental state based on the average fitness of the population, the diversity of the population and the optimal fitness is proposed.

[0265] The following formula represents the calculation of average fitness:

[0266]

[0267] In the formula,

[0268] represents the fitness of the i-th individual in the t-th generation,

[0269] represents the fitness of the i-th individual in the first generation.

[0270] The following formula represents the calculation of population diversity:

[0271]

[0272] In the formula,

[0273] d represents population diversity,

[0274] represents the fitness of the i-th individual in the t-th generation,

[0275] represents the fitness of the first individual in the jth generation,

[0276] Ns is the population size.

[0277] The following formula represents the calculation of the optimal fitness:

[0278]

[0279] In the formula,

[0280] represents the maximum fitness of the i-th individual in the t-th generation,

[0281] It represents the maximum fitness of the first individual in the tth generation.

[0282] The following formula represents the calculation of the total status value:

[0283] s=w1f+w2d+w3m

[0284] In the formula,

[0285] s represents the total state value,

[0286] f represents the average fitness of the population,

[0287] d represents population diversity,

[0288] m represents the optimal fitness of the population,

[0289] w1 is set to 0.35,

[0290] w2 is set to 0.35,

[0291] w3 is set to 0.3.

[0292] The state set S is divided into 20 states, S = [S1, S2…S19, S20], where the interval value is 0.05. For example, when S∈[0,0.05], S = S1.

[0293] For the design of actions, in each generation of population, the agent performs various actions to determine the appropriate crossover probability (Pc) and mutation probability (Pm). In this embodiment, there are 10 possible choices for these actions. Generally, the crossover probability Pc ranges from 0.4 to 0.9, and the interval between each action is 0.05. For example, if action a1 is selected, a value needs to be randomly selected in [0.4, 0.45]. Similarly, the mutation probability Pm ranges from 0.1 to 0.3, and the interval between each action is 0.02.

[0294] For the design of exploration strategy, the ε-greedy strategy is an action selection strategy that balances global search and local search. It is expressed by the following formula:

[0295]

[0296] In the formula,

[0297] ε is called the utilization rate,

[0298] r 0-1 is a random value between 0 and 1.

[0299] When ε≥r 0-1 When , select the action with the largest reward value; when ε <r 0-1 , conduct exploration and choose a random action.

[0300] In the classic ε-greed strategy, ε is a fixed value, which limits the adaptability of Q-Learning. Therefore, the decay factor β is introduced to automatically adjust the value of ε. It is expressed by the following formula:

[0301] ε=0.9-0.85×β,β=(i / Maxgen) / 10

[0302] In the formula,

[0303] i is the number of iterations,

[0304] Maxgen is the maximum number of iterations.

[0305] In the initial stage of the algorithm, the value of ε is set to the maximum value to improve the algorithm's ability to explore new solutions. As the algorithm progresses, the value of β gradually increases, causing ε to decrease. This allows the agent to more likely choose the action with the highest Q value and retain previous historical experience.

[0306] S34) A two-step crossover strategy is used for global search.

[0307] For the process order vector, the widely used Priority Operation Crossover (POX) is applied to generate feasible solutions. For example, all jobs are randomly arranged in two non-empty complementary sets Q1{1,3} and Q2{2,4}. For offspring 1, the genes {1,3,1,1,3} belonging to Q1 remain unchanged in their positions in parent 1, and the genes belonging to Q2 follow the order of parent 2, so {2,2,4,4} are filled into offspring 1.

[0308] For the factory allocation vector, an improved multi-point protected crossover (MPX) is used. Specifically, a string of 0s and 1s with a length equal to the total number of factory vectors is randomly generated, and for workpieces J1 and J3 with a value of 0, the index number of the processing factory is exchanged. For example, {1,1,2} and {2,2,2} of J1 are exchanged to generate offspring. However, it should be noted that this operation may result in illegal solutions to the machine vector, and the offspring needs to be strictly checked to ensure that the machine can be selected in the new factory. For example, for offspring 1, J1 cannot be processed by machine 1 in factory 2, so it needs to be replaced by other feasible machines.

[0309] S35) A four-step mutation strategy is used for local search.

[0310] Specifically, for the process mutation operation, it means randomly selecting two positions in the OS, such as Position 1 and Position 2, and then disrupting the order of the processes {1,1,3} between them to generate a new process scheduling code {1,3,1}. For the process exchange operation, it means randomly selecting two positions in the OS, and then exchanging the processes {3,2} at the two positions to {2,3}.

[0311] For the key machine replacement mutation, it means selecting the machine with the highest machine load rate in the factory with the highest machine load rate in the current factory, randomly selecting a process on this machine, and then replacing the machine of this process with the machine with the lowest machine load rate in the current factory.

[0312] For the key plant replacement mutation, it means randomly selecting a process in the plant with the largest current plant load rate, and then replacing the plant of the process with the plant with the smallest plant load rate.

[0313] The plant load factor is defined as:

[0314] f_r(r)=f_load(r) / max(f_load)

[0315] Where f_load(r) represents the maximum completion time of each factory.

[0316] Step S36: Adopting neighborhood search strategy to further explore the solution space. In the present invention, six neighborhood search strategies are adopted to further explore the solution space, as follows:

[0317] Critical factory operator: transfers the processes of non-critical products on the critical path to the factory with the lowest factory load rate, and selects the machine with the shortest processing time.

[0318] Critical machine operator: In the critical factory, a process is randomly selected from the machine with the highest utilization rate and transferred to the machine with the lowest machine load rate.

[0319] Critical process operator: Exchange the critical processes on the critical path.

[0320] Plant load operator: Sort the plant load rates from largest to smallest, and randomly select one from each plant in the first half of the sequence and insert it into the plant in the second half.

[0321] Process allocation operator: Based on the knowledge of the processing order of the process, the processes of each workpiece under each product should be concentrated as much as possible to complete each workpiece as soon as possible. Therefore, for workpieces that exceed the maximum processing time, for the OS vector, its last process is inserted forward.

[0322] Energy consumption operator: randomly select a process with the highest energy consumption in processing time, and select a machine with the lowest energy consumption from the set of optional machines to replace it.

[0323] S37) When the set maximum number of iterations or the deadline is reached, the optimal solution is output, otherwise the new population is used as the initial population and steps S32) to S35) are re-executed.

[0324] like Figure 2 As shown in FIG. 1 , it is a flowchart of the QL-IMOGA algorithm used in the present invention. Among them, QL-IMOGA represents an improved multi-objective genetic algorithm based on Q-Learning. Figure 2In the algorithm, the initial population is first determined, and individuals are selected according to the tournament strategy. The appropriate crossover rate (Pc) and mutation rate (Pm) are determined according to Q-Learning. Then, the two-step crossover strategy, four-step mutation and neighborhood search strategy are selected for the selected individuals. Finally, the external archive set is updated. If the termination condition is met, the optimal solution is output. Otherwise, the above steps are repeated for the updated population until the termination condition is met.

[0325] In order to verify the effectiveness and superiority of the present invention, the constraints of the transportation stage and the assembly stage are added with reference to the benchmark case proposed by Brandimarte et al., and a test example of the embodiment of the present application is established. Specifically, the number of assembly workshops follows a uniform distribution U[2,5], the inter-factory transportation time of each process follows a uniform distribution U[1,3], the raw material transportation time and the transportation time between factories follow a uniform distribution U[4,6], the assembly time follows a uniform distribution U[6,10], the unit processing energy consumption of each process follows a uniform distribution U[1,2], the unit fixed energy consumption of the processing plant follows a uniform distribution U[2,3], the unit fixed energy consumption of the assembly plant and the unit assembly energy consumption follow a uniform distribution U[1,3], the unit transportation energy consumption within the factory follows a uniform distribution U[0.5,1], the unit transportation energy consumption outside the factory follows a uniform distribution U[1,1.5], the unit transportation energy consumption of raw materials and the unit transportation energy consumption from the processing workshop to the assembly workshop follow a uniform distribution U[1,2].

[0326] The improved non-dominated sorting genetic algorithm (NSGA-II), multi-objective evolutionary algorithm based on decomposition (MOEA / D), improved strength Pareto evolutionary algorithm (SPEA-II) and improved memetic algorithm (IMA) are used as comparison algorithms to solve the distributed heterogeneous assembly flexible job shop scheduling problem with transfer, with the objectives of minimizing the maximum completion time and minimizing the total processing energy consumption.

[0327] All algorithms are run using MATLAB R2020b on an AMD Ryzen 76800H 3.20GHz PC with 16GB RAM. For fairness, the CPU running time is set to J·M, where J represents the number of workpieces and M represents the number of machines. At the same time, all algorithms use the same initialization method, decoding method, and crossover mutation strategy.

[0328] In order to evaluate the performance of the multi-objective algorithm, Inverted Generational Distance (IGD) and Hypervolume (HV) were selected as evaluation indicators. IGD is an indicator for evaluating the convergence and diversity of the Pareto front. The following formula can be used to calculate IGD:

[0329]

[0330] In the formula,

[0331] |Ω * | represents the number of items on the true Pareto front,

[0332] D i (Ω * ,Ω) represents the solution in Ω and Ω * The minimum Euclidean distance between the solutions i in .

[0333] The smaller the IGD value, the better the convergence of the algorithm.

[0334] Hypervolume (HV) is a widely used indicator for evaluating the convergence and distribution of the Pareto front. The following formula can be used to calculate HV.

[0335]

[0336] In the formula,

[0337] Ns is the number of non-dominated solutions obtained by the algorithm,

[0338] v i is the volume / area formed by the ith solution in the non-dominated solution in units of the reference point.

[0339] The higher the HV value, the greater the diversity of the algorithm.

[0340] like Figures 3 to 5 As shown, Figure 3 A schematic diagram of the comparison results of target values ​​of different algorithms provided by an embodiment of the present invention; Figure 4 A schematic diagram of the comparison results of evaluation indicators of different algorithms provided by the embodiment of the present invention; Figure 5 A schematic diagram of the comparison results of the Wilcoxon test using different algorithms provided in an embodiment of the present invention.

[0341] It can be seen from the experimental results that in the 15 test instances, the QL-IMOGA algorithm almost showed the best results for the maximum completion time and the total processing energy consumption, while NSGA-II only achieved the optimal solution for a single target in instances 4, 6 and 12. MOEA / D achieved the optimal value of a single target in instances 4, 8, 9 and 13, while SPEA-II and IMA did not obtain the optimal value, which illustrates the superiority of QL-IMOGA. At the same time, the advantages in the HV and IGD indicators indicate that the Pareto front obtained by QL-IMOGA is closer to the real Pareto front, and has better distribution and convergence than other algorithms. Finally, for the Wilcoxon test, it can be found that different algorithms directly have significant differences, which further proves the superiority of the algorithm of the present invention.

[0342] In order to verify the impact of workpiece transfer on actual production, the maximum completion time, overall energy consumption (Cost) and factory load rate (LB) obtained from the distributed heterogeneous assembly flexible job shop scheduling problem with and without workpiece transfer are compared. In order to ensure fairness, the solution algorithm for the distributed heterogeneous assembly flexible job shop scheduling problem without workpiece transfer also uses Q-Learning to optimize key parameters. The difference is that in the factory encoding part, each workpiece is constrained to be assigned to only one processing factory, and the corresponding crossover, mutation and neighborhood search operators are changed. These two methods are run independently 20 times on each instance, and the results are as follows: Figure 6 As shown. It can be found that the solution that allows workpiece transfer reduces the maximum completion time by an average of 7.5%, reduces the overall energy consumption by an average of 3.9%, and increases the factory load rate by an average of 8.4%. It can be found that the capacity of the processing plant is obviously more fully utilized, and better results are achieved on Makespan. The production of the processing workshop and the assembly workshop is more concentrated, with less idle time, which ensures that the production time is fully utilized while minimizing energy consumption. This proves that overall, allowing workpiece transfer can break the production bottleneck of the entire processing stage and enable each product to be assembled faster.

[0343] The distributed heterogeneous assembly flexible job shop scheduling method with transfer of the present invention aims to minimize the maximum completion time and minimize the total processing energy consumption, considers the factors of workshop processing capacity, workshop collaborative processing and transportation stage time, and arranges the process processing sequence, process processing factory, process processing machine, and assembly workshop selection from the perspective of global optimization within a reasonable time.

[0344] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A distributed heterogeneous assembly flexible job shop scheduling method with transfer, characterized in that: The steps include: S1) setting assumptions and basic parameters, proposing corresponding constraints on workshop processing capacity, workshop collaborative processing and transportation phase time, and constructing a dual-objective optimization model with the goals of minimizing the maximum completion time and minimizing the total processing energy consumption. The dual-objective optimization model is used for scheduling optimization of assembly flexible job shops considering factory processing capacity, transportation phase and workpiece transfer; The objective optimization model of minimizing the maximum completion time is expressed as follows: In the formula, C max is the maximum completion time, b indicates product, a represents the assembly workshop, Indicates the completion time of product b in assembly workshop a; The target optimization model for minimizing the total energy consumption of machining is expressed by the following formula: mincost=C1+C2+C3+C4+C5 In the formula, C1 represents the total energy consumption of the processing workshop, including the workpiece processing energy consumption and the fixed energy consumption of the processing workshop. C2 represents the total energy consumption of the assembly workshop, including product assembly energy consumption and fixed energy consumption of the assembly workshop. C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop. C4 represents the total transportation energy consumption during the workpiece production process, including the energy consumption of transportation between different machines and between different workshops. C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop; The total transportation energy consumption C4 during the workpiece production process is expressed by the following formula: In the formula, C4 represents the total energy consumption of transportation during the production process of workpieces. X j，p-1，i，r Indicates whether the p-1th process of product j is processed on the i-th machine in the r-th factory. If so, then X j，p-1，ir is 1, otherwise it is 0. X jpi’r Indicates whether the p-th process of product j is processed on the i'th machine in the r-th factory. If so, then X jpi’r is 1, otherwise it is 0. represents the unit energy consumption of transferring product j from machine i to machine i' in factory r, Y jpr’ Indicates whether the pth process of product j is processed in factory r'. If so, then Y ipr’ is 1, otherwise it is 0. Y j,p-1,r Indicates whether the p-1th process of product j is processed in factory r. If so, then Y j，p-1，r is 1, otherwise it is 0. represents the energy consumption of transferring from plant r to r; S2) designing a three-segment encoding mode and a three-segment decoding mode corresponding to the dual-objective optimization model based on the process sequence, processing plant selection and processing machine selection; S3) Based on the three-segment encoding mode and the three-segment decoding mode, an improved multi-objective genetic algorithm based on Q-Learning is used to solve the optimal scheduling solution of the dual-objective optimization model.

2. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 1 is characterized by: In S1), the assumptions set include: each job can only be assigned to one factory; different processes of a job can be completed by different factories in collaboration; core components can only be processed by core factories; each machine can only process one job at a time; all processes belonging to the same job should be processed in a predetermined order; once the operation starts, no interruption is allowed; and machine startup time is not considered.

3. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 2 is characterized by: S1), the constraints proposed include: one process of each workpiece can only be assigned to one manufacturing plant; each product can only be assigned to one assembly plant; each process of the workpiece can only be completed by one available machine in a plant with corresponding processing capabilities; the completion time of each process is equal to the start time of the process plus the processing time of the process; the start processing time of a process is not less than the completion time of the previous process plus the transportation time; each machine can only process one process at the same time; the manufacturing completion time of the product is not less than the completion time of the product process plus the transportation time of the raw materials of each workpiece in the product; the start assembly time of the product is not less than the manufacturing completion time of the product plus the transportation time from the production workshop to the assembly workshop; the assembly completion time of the product is the assembly start time of the product plus the assembly time.

4. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 3 is characterized by: S1), the total energy consumption C1 of the processing workshop is expressed by the following formula In the formula, C1 represents the total energy consumption of the processing workshop, P jpir Indicates process O jp The processing time on machine i in plant r, represents the unit processing energy consumption on machine i in factory r, X jpir Indicates process O jp Is it processed on machine i in factory r? If so, then X jpir is 1, otherwise it is 0. represents the unit processing energy consumption of factory r, M r represents the total processing time of processing factory r; The total energy consumption C2 of the assembly workshop is expressed by the following formula In the formula, C2 represents the total energy consumption of the assembly workshop, represents the unit assembly energy consumption of the assembly workshop, A ba Indicates the assembly time, Z ba Indicates whether product b is assembled in assembly workshop a. If so, then Z ba is 1, otherwise it is 0. represents the unit fixed energy consumption of assembly workshop a, A a represents the total assembly time of assembly shop a; The total energy consumption C3 of transporting the raw materials of each workpiece to the corresponding processing workshop is expressed by the following formula: In the formula, C3 represents the total energy consumption of transporting the raw materials of each workpiece to the corresponding processing workshop. Represents the energy consumption of transporting raw materials to the processing plant, Y jpr Indicates process O jp Is it processed in factory r? If so, then Y jpr is 1, otherwise it is 0; The total energy consumption C5 of transporting products from the processing workshop to the assembly workshop is expressed by the following formula In the formula, C5 represents the total energy consumption of transporting products from the processing workshop to the assembly workshop. V jra Indicates whether product j needs to be transported from processing factory r to assembly factory a. If yes, it is 1, otherwise it is 0. It represents the unit transportation energy consumption from the processing plant to the assembly workshop.

5. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 1 is characterized by: In S2), the three coding modes include a factory allocation coding mode, a machine selection coding mode, and a process sequencing coding mode.

6. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 5 is characterized by: In S2), the design steps of the three-segment decoding mode are as follows: S21) determining the operation sequence of all the processes to be processed according to the process sequence vector; S22) reading the factory, machine and corresponding process processing time assigned to the corresponding process; S23) first determine whether it is the first process on the machine and whether it is the first process of the workpiece; if both conditions are met, directly arrange the process to the first position of the machine; S24) Determine whether the process sequence vector has been read. If not, go to step S22; if yes, arrange the scheduling plan for the assembly stage, that is, sort the workpieces in each product from small to large according to the maximum completion time, and distribute them to the assembly plants in sequence according to the minimum load principle.

7. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 6 is characterized by: S23), If it satisfies the condition of being the first process on the machine but not the first process on the workpiece, the earliest processable time of the process is T a =max{C j,p-1 +TM+TF,TS t }, the completion time of the process is T a +P ijpr ; If it does not meet the condition of being the first process on the machine, but meets the condition of being the first process of the workpiece, there may be idle time on the machine, and a greedy decoding method is used to further shorten the maximum completion time.

8. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 1 is characterized by: In S3), the steps of solving the optimal scheduling solution of the dual-objective optimization model using the improved multi-objective genetic algorithm based on Q-Learning are as follows: S31) according to the initial population size and encoding method, a hybrid initialization method is used to generate a high-quality initial population to promote rapid convergence of the algorithm; S32) using a tournament selection method to select individuals from the population for subsequent crossover and mutation operations; S33) adaptively adjusting key parameters of the algorithm through Q-Learning, wherein the key parameters include crossover probability and mutation probability; S34) using a two-step crossover strategy to perform a global search; S35) using a four-step mutation strategy for local search; S36) using a neighborhood search strategy to further explore the solution space; S37) When the set maximum number of iterations or the deadline is reached, the optimal solution is output, otherwise the new population is used as the initial population and steps S32) to S35) are re-executed.

9. The distributed heterogeneous assembly flexible job shop scheduling method with transfer according to claim 8 is characterized by: S31), the hybrid initialization method includes: for the process layer, a random initialization method is adopted; for the factory layer, each process gives priority to selecting an optional factory with a large number of centralized processing machines. If the number is the same, a factory with a short average processing time is selected; for the machine layer, machines with low machine load are given priority.

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