Agv cooperative scheduling method based on non-cooperative evolutionary game for flexible job shop

Abstract

The application discloses a flexible job shop machine AGV collaborative scheduling method based on non-cooperative evolutionary game, and specifically is: a flexible job shop machine-AGV collaborative scheduling model is constructed under a double-layer multi-agent system architecture; an improved negotiation mechanism is designed based on the non-cooperative game theory; workpieces, machines and AGVs are independent agents in three non-cooperative games, and matching and conflict resolution among resources are realized through strategy game and local negotiation mechanism, so that a Nash equilibrium solution is obtained; an evolutionary game mechanism is introduced, selection, diffusion, innovation and iteration operations are carried out on the feasible solution set generated by multiple non-cooperative games, so that the population diversity and global search ability of the algorithm are improved, and a better evolutionary stable equilibrium solution is obtained; and the intelligent solution of the flexible job shop machine-AGV collaborative scheduling is realized through the improved NCAEG algorithm. The application can significantly improve the scheduling precision and system stability, and effectively realize multi-resource collaboration, conflict avoidance and global optimization.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing and production scheduling, and in particular relates to a collaborative scheduling method for flexible workshop AGVs based on non-cooperative evolutionary game theory. Background Technology

[0002] In the context of customized production with multiple varieties and small batches, intelligent logistics equipment such as Automated Guided Vehicles (AGVs) have become core equipment for material handling in smart workshops. However, current workshop scheduling research often neglects or simplifies logistics elements, leading to poor coordination between production and logistics resources, which in turn restricts the overall production management efficiency of the workshop. Therefore, the collaborative scheduling between machines and AGVs is of great significance for improving the resource allocation capability and production efficiency of the production system. Current research on FJSP (Functionally Selected, Simply Selected) mainly focuses on the optimal allocation of processing machine resources, generally neglecting the transportation time of workpieces between different machines. However, in the context of customized production with multiple varieties and small batches, especially in complex product production scenarios with long process chains and close process connections, the proportion of logistics transportation time in the production cycle is gradually increasing. Taking the manufacturing of electronic components, represented by chips, as an example, its production process is characterized by numerous processes and diverse machine types, and it usually relies on Automated Guided Vehicles (AGVs) to complete the material transfer between processes. In this context, if a scheduling method that ignores transportation time is still adopted, it will lead to a significant deviation between the actual production execution and the scheduling plan, resulting in production delays or bottleneck drift, which will seriously restrict the overall production efficiency of the workshop.

[0003] The flexible job shop scheduling problem is a classic NP-hard problem. Existing solutions mainly include exact solutions and solutions using metaheuristic algorithms. Metaheuristic algorithms, due to their strong optimization capabilities and the widespread application of various swarm intelligence algorithms in combinatorial optimization problems, including train scheduling, the traveling salesman problem, and the job shop scheduling problem, are chosen for this invention. Building upon the traditional job shop scheduling problem, this invention considers the impact of automated guided vehicles (AGVs) on the planning of flexible job shops, making the problem space more complex. Therefore, this invention selects an improved metaheuristic algorithm to solve the problem, addressing the shortcomings of existing algorithms and improving both efficiency and accuracy. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies in solving the scheduling problem of flexible workshops, this invention provides a collaborative scheduling method for AGVs in flexible workshops based on non-cooperative evolutionary game theory.

[0005] The present invention provides a flexible workshop AGV collaborative scheduling method based on non-cooperative evolutionary game theory, comprising the following steps:

[0006] Step 1: Construct a flexible workshop machine-AGV collaborative scheduling model under the two-layer multi-agent system (MAS) architecture; with minimizing the maximum completion time as the optimization objective, comprehensively consider multiple constraints such as machine allocation, process sequencing, AGV path and task allocation to achieve unified modeling of production and logistics resources.

[0007] (1) Problem description.

[0008] The Flexible Workshop Machine-AGV Cooperative Scheduling Problem (FJMACSP) based on MAS is described as follows: The number of processing machines, the number of AGVs, and the workshop layout are all known; the production order includes several workpieces to be processed; each machine, AGV, and workpiece constitutes a machine agent, an AGV agent, and a workpiece agent, respectively, which together with other management agents and workshop agents form the MAS; each workpiece agent consists of several processes, each process is considered a task, which can be decomposed into processing tasks and transfer tasks; the machine agents that can perform processing tasks and the corresponding processing time are known, and each machine agent has a buffer for storing workpieces with unlimited capacity; transfer tasks are divided into empty-load processes and loaded processes. The empty-load process is when the AGV agent travels from its current position to the starting point of the loaded process, and the loaded process is when the AGV agent travels from the loading / unloading station or the position of the machine processed in the previous process to the position of the machine to be processed in the current process. The travel time of the AGV agent depends on the actual distance traveled. The processing task can only be executed after the transfer task of each process is completed; the arrival position of the new workpiece agent and the AGV... The Agent's initial position is at the loading / unloading station L / U. The L / U station has sufficient input / output buffer space. After completing the current transfer task, the AGV Agent stops next to the nearest machine or loading / unloading station.

[0009] (2) Objective function: The optimization objective is to minimize the maximum completion time;

[0010] (1)

[0011] Among them, C i Let be the completion time of Agent i.

[0012] (3) Constraints:

[0013] (2)

[0014] (3)

[0015] (4)

[0016] (5)

[0017] (6)

[0018] (7)

[0019] (8)

[0020] Among them, OST i,j,k OCT i,j,k Indicates process O i,j The start and end times of processing on machine agent k, EST i,j,r ECT i,j,r Indicates process O i,j LST is the start and end time of the empty transfer before the transfer on the AGV Agent r. i,j,r LCT i,j,r Indicates process O i,j The start and end times of load transfer on the AGV Agent r, tt i,j,r Indicates process O i,j Transfer time on AGV Agent r, tt i,j,r = et i,j,r + lt i,j,r et i,j,r Represents the idle transfer time, lt i,j,r Indicates load transfer time, pt i,j,k Indicates process O i,j Processing time on machine Agent k ,in Represents preparation time. Indicates processing time, x i,j,k , z i,j,r Denotes the decision variable, if process O i,j x is processed on machine agent k. i,j,k = 1, otherwise x i,j,k = 0; if process O i,j Transferring via AGVAgent r then z i,j,r = 1, otherwise z i,j,r = 0.

[0021] Equation (2) represents the processing sequence constraint of each process of the workpiece agent on the machine agent; Equations (3) and (4) represent the transfer sequence constraint of each process of the workpiece agent on the AGV agent; Equation (5) represents the sequence constraint between the idle time of the processing task, the transfer task and the load time of the transfer task; Equation (6) represents that all processing tasks are assigned to a specific machine agent; Equation (7) represents that all transfer tasks are assigned to a specific AGV agent; Equation (8) is a decision variable constraint, which means that the processing task of each process of the workpiece agent can only be executed on one machine agent and the transfer task can only be executed on one AGV agent.

[0022] Step 2: Based on non-cooperative game theory, an improved negotiation mechanism is designed. The workpiece, machine and AGV, as independent agents, achieve resource matching and conflict resolution through strategy game and local negotiation mechanism in three non-cooperative games, thereby obtaining the Nash equilibrium solution.

[0023] (1) Improve the MAS negotiation mechanism for non-cooperative games.

[0024] The idea of ​​using a non-cooperative game negotiation mechanism to solve scheduling problems is based on real-time manufacturing information in the workshop. At each moment, workpieces actively "compete" for transferable AGVs and processing machines based on their real-time status information. According to the canonical formulation of game theory, a standard game G between agents can be described as a triple:

[0025] (9)

[0026] Where N represents the set of players, S represents the set of feasible strategies for players, and U represents the payoff function for players.

[0027] An improvement was made to the non-cooperative game process. The improved game negotiation process for the machine-AGV collaborative scheduling problem includes the non-cooperative game negotiation process for selecting the machine and AGV for the workpiece, and for the AGV to complete the transfer task and the machine to complete the processing task. The three game processes are represented by G1, G2 and G3, respectively.

[0028] In each round of decision-making, each workpiece selects all suitable transfer AGVs and processing machines for the current process through the first non-cooperative game G1. All AGVs selected in G1 select suitable workpieces for transfer through the second non-cooperative game G2, and all machines selected in G1 select suitable workpieces for processing through the third non-cooperative game G3. After G1, G2, and G3 make their respective choices, the workpieces, AGVs, and machines selected by each other are confirmed by the relevant agents managed at the upper level to achieve coordination among the three games of workpieces, machines, and AGVs. Only when the choices made by G1, G2, and G3 are consistent is the game considered valid and used to generate the final scheduling plan; otherwise, it participates in the next round of decision-making.

[0029] When a workpiece selects a machine and an AGV, the non-cooperative game process G1 between the workpieces can be described by the following three-term expression:

[0030] (10)

[0031] (11)

[0032] When an AGV selects a transfer task, the non-cooperative game process G2 among the AGVs is described by the following three-term expression:

[0033] (12)

[0034] (13)

[0035] When a machine selects a processing task, the non-cooperative game process G3 between machines is described by the following three-term expression:

[0036] (14)

[0037] (15)

[0038] In the formula, C i AC r and MC k These represent the completion time of the workpiece process, the completion time of the AGV transfer task, and the completion time of the machining task, respectively.

[0039] The set of feasible strategies for a workpiece refers to the machines and AGVs selected through the workpiece's processes; the feasible strategies for machines and AGVs refer to the processes selected by the machines and AGVs; each player's objective is to maximize their personal gain and allocate workpieces to appropriate AGVs and appropriate machines; the payoff function is the minimum of the optimization objective, therefore the reciprocal of the objective function is chosen as the player's payoff.

[0040] (2) Local consultation mechanism.

[0041] In non-cooperative game theory, a local negotiation mechanism is introduced to balance the final choice results when a choice conflict occurs between agents. The local negotiation mechanism is that when two or more agents choose the same strategy, the two agents communicate with each other to compare their payoffs, so that the agent with the higher payoff chooses the strategy, while the other agents choose the other strategy.

[0042] Step 3: Introduce an evolutionary game mechanism to perform selection, diffusion, innovation, and iteration operations on the feasible solution set generated by multiple non-cooperative games, so as to improve the diversity of the algorithm population and the global search capability, and obtain a better evolutionary stable equilibrium solution.

[0043] An evolutionary game process is added to the non-cooperative game theory framework to improve the optimization performance of MAS. Through selection, diffusion, innovation, and evolution, an evolutionary game equilibrium solution is obtained in the continuous game process. During the evolutionary process, if players use the same strategy combination within a finite time, then that strategy combination is in a "stable" state. To obtain an evolutionary stable equilibrium solution, random disturbances are needed to cause the game to deviate from its original "stable" state. This process is repeated until the maximum number of evolutionary games reaches a set value, and the final "stable" state is the evolutionary stable equilibrium solution of the evolutionary game.

[0044] The evolutionary game process can be described as follows:

[0045] (16)

[0046] In the formula, N represents the set of players, S represents the strategy space, U represents the payoff function, γ represents the selection operator, ψ represents the diffusion operator, ζ represents the innovation operator, and τ represents the maximum number of evolutionary iterations.

[0047] Through multiple non-cooperative game processes, multiple Nash equilibria are formed, thus constituting the initial population. Through selection, crossover, and mutation interference operations, repeated operations are performed until the maximum number of iterations is reached, thereby obtaining an evolutionarily stable equilibrium solution.

[0048] Step 4: Implement intelligent solution for machine-AGV collaborative scheduling in flexible workshop based on improved non-cooperative-evolutionary game theory collaborative optimization algorithm.

[0049] Furthermore, the specific process for improving the MAS negotiation mechanism in non-cooperative games is as follows:

[0050] Step S1: JA selects the optimal equipment combination from different combinations of machines and AGVs, records the suitable processing machine and suitable transfer AGV for workpiece i, and adds them to the strategy set s. Ji In the process, the information of the process to be processed is sent to the relevant MA and AA.

[0051] Step S2: AA simultaneously receives all pending processing information and adds it to the transferable processing set. Select transfer tasks from the set, and AUA will select them based on each s Ar Assigning transfer tasks: When the number of elements in a certain AA set is greater than 1, the AGV Agent inside the AUA conducts local negotiation and uses the greedy principle to assign the process to AGVs without competition as much as possible, so that more processes are assigned to more suitable AGVs for transfer to maximize benefits.

[0052] Step S3: MA receives process information and selects processing tasks to add to strategy set s Mk MUA according to each s Mk Assigning processing tasks: When the number of elements in a certain MA set is greater than 1, the MA within the processing service unit Agent conducts local negotiation and uses the greedy principle to assign the process to a machine with a set of no competing optional strategies containing 1 element, so that more processes are assigned to more suitable processing machines.

[0053] Step S4: AUA and MUA conduct local negotiations to coordinate the selection results of AGVs and machines to ensure that the AGVs and machines are assigned to the finally selected AGVs and machines for each processing step; AUA and MUA issue transfer tasks and processing tasks to the finally selected AGVs and machines respectively, and the AGVs and machines execute the transfer tasks and processing tasks.

[0054] Step S5: Repeat the above process until all processes for all workpieces are transferred and processed, obtaining the Nash equilibrium solution {s}. l}

[0055] Furthermore, in the non-cooperative game process, the initial population size is set to 50, the selection probability γ is set to 0.1, the diffusion probability ψ is set to 0.8, the innovation probability ζ is set to 0.1, and the maximum number of evolutionary iterations τ is set to 200. The selection operator adopts two types: elite selection and tournament selection. The diffusion operator process sequence adopts two types: POX and JBX crossover. The machine and AGV sequence adopts two-point crossover. The innovation operator adopts two types: exchange type and neighborhood type.

[0056] The beneficial technical effects of this invention compared to the prior art are as follows:

[0057] (1) This invention considers the collaborative relationship between machine processing and AGV transportation in flexible workshop scheduling, and establishes a collaborative scheduling model based on a two-layer multi-agent system architecture. This model integrates multiple constraints such as machine allocation, process sequencing, AGV path and task scheduling, and can effectively solve the resource conflict and efficiency loss caused by the asynchrony between production plan and logistics plan, so that the scheduling results are more in line with the actual operating characteristics of the manufacturing system.

[0058] (2) This invention employs a Non-Cooperative-Evolutionary Game Theory (NCAEG) to solve the model. This algorithm introduces three non-cooperative game processes among the workpiece, machine, and AGV to achieve competitive game and dynamic matching among resources. It also incorporates an evolutionary game mechanism to select, diffuse, innovate, and evolve feasible solutions generated from multiple games, thereby improving the algorithm's global search capability and population diversity. The algorithm designs a local negotiation mechanism to resolve conflicts between agents and enhances the quality of evolutionarily stable equilibrium solutions through elite selection, crossover, and mutation strategies. Compared to traditional heuristic or single optimization algorithms, this algorithm has a faster convergence speed and higher solution accuracy, enabling efficient collaborative scheduling of machines and AGVs in flexible work workshops. Attached Figure Description

[0059] Figure 1 The overall flow of the FJMACSP scheduling method based on the improved NCAEG is as follows.

[0060] Figure 2 It is a non-cooperative game negotiation mechanism.

[0061] Figure 3 This is an example of a non-cooperative game negotiation mechanism.

[0062] Figure 4 To improve the negotiation mechanism in non-cooperative games.

[0063] Figure 5 An example of improving the negotiation mechanism in non-cooperative games.

[0064] Figure 6 To improve the flowchart of non-cooperative game theory.

[0065] Figure 7 This is a non-cooperative game process for machine-AGV collaborative scheduling.

[0066] Figure 8 This is a comparison chart of the experimental results of the first 40 Bilge examples.

[0067] Figure 9 This is a comparison chart of the experimental results of 42 cases following the Bilge case.

[0068] Figure 10 This is a comparison chart of the experimental results for the Deroussi example. Detailed Implementation

[0069] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0070] This invention addresses the challenges of scheduling and coordinating machines and Automated Guided Vehicles (AGVs) in complex manufacturing environments, including intense resource competition and uneven task allocation. Using minimizing the maximum completion time as the optimization objective function, it establishes a flexible machine-AGV collaborative scheduling model for a workshop within a two-layer multi-agent system architecture. This model comprehensively considers various constraints such as machine allocation, process sequencing, AGV path and task assignment, achieving unified modeling of production and logistics resources. An improved non-cooperative game theory negotiation mechanism (MAS) is employed to solve the model. The resulting reasonable scheduling scheme not only better reflects actual production scenarios but also significantly improves the automation, intelligence, and production efficiency of the workshop.

[0071] The present invention provides a flexible workshop AGV collaborative scheduling method based on non-cooperative evolutionary game theory, the details of which are as follows:

[0072] Problem Description

[0073] The Flexible Job Shop Machine-AGV Collaborative Scheduling Problem (FJMACSP) based on MAS is described as follows: The number of processing machines, the number of AGVs, and the shop layout are all known; the production order includes several workpieces to be processed; each machine, AGV, and workpiece constitutes a machine agent, an AGV agent, and a workpiece agent, respectively, which together with other management agents and shop agents form the MAS; each workpiece agent consists of several processes, each process is considered a task, which can be decomposed into processing tasks and transfer tasks; the machine agents that can perform processing tasks and the corresponding processing time are known, and each machine agent has a buffer for storing workpieces with unlimited capacity; the transfer tasks are divided into empty-load processes and loaded processes. The empty-load process is when the AGV agent travels from its current position to the starting point of the loaded process, and the loaded process is when the AGV agent travels from the loading / unloading station or the position of the machine processed in the previous process to the position of the machine to be processed in the current process. The travel time of the AGV agent depends on the actual distance traveled. The processing task can only be executed after the transfer task of each process is completed; the arrival position of the new workpiece agent and the AGV... The Agent's initial position is at the loading / unloading station L / U. The L / U station has sufficient input / output buffer space. After completing the current transfer task, the AGV Agent stops next to the nearest machine or loading / unloading station.

[0074] To establish the FJMACSP mathematical model, the relevant symbols and variables are defined as shown in Table 1:

[0075] Table 1 Symbol Definition Table

[0076]

[0077] Objective function: Minimizing the maximum completion time is the optimization objective;

[0078] (1)

[0079] Constraints:

[0080] (2)

[0081] (3)

[0082] (4)

[0083] (5)

[0084] (6)

[0085] (7)

[0086] (8)

[0087] Equation (2) represents the processing sequence constraint of each process of the workpiece agent on the machine agent; Equations (3) and (4) represent the transfer sequence constraint of each process of the workpiece agent on the AGV agent; Equation (5) represents the sequence constraint between the idle time of the processing task, the transfer task and the load time of the transfer task; Equation (6) represents that all processing tasks are assigned to a specific machine agent; Equation (7) represents that all transfer tasks are assigned to a specific AGV agent; Equation (8) is a decision variable constraint, which means that the processing task of each process of the workpiece agent can only be executed on one machine agent and the transfer task can only be executed on one AGV agent.

[0088] A machine-AGV cooperative scheduling method based on an improved NCAEG (Non-Cooperative and Adaptive Evolutionary Game).

[0089] When applying non-cooperative game theory to production scheduling in a workshop (MAS), a feasible solution can be generated through a single non-cooperative game process, based on the players' strategy choices. However, the uncertainty of the players' strategy choices often leads to poor quality and instability of the final solution. Therefore, multiple non-cooperative games can be used to generate multiple feasible solutions, from which a better solution can be selected. How to find a better solution, or even explore a superior solution, from multiple solutions is a problem that needs to be solved. Evolutionary game theory, utilizing the idea of ​​"survival of the fittest," can achieve higher quality and more stable solutions through learning, imitation, and evolution. Therefore, this invention adds an evolutionary game process using multiple solutions generated from non-cooperative games after the non-cooperative game process. Based on this, this invention designs a flexible workshop machine-AGV collaborative scheduling method that combines non-cooperative and evolutionary game theory approaches, as shown in the attached figure. Figure 1 As shown.

[0090] First, after obtaining the workshop information, register all required Agents, construct a two-layer MAS, and initialize the state of all Agents. Second, conduct non-cooperative game theory to complete the allocation of process processing machines and transfer AGVs. After each game, put the game result into the feasible solution set and repeat the non-cooperative game process until there are enough feasible solutions. Finally, conduct evolutionary game theory to obtain the evolutionary game equilibrium solution for generating the production plan. Therefore, the NCAEG method proposed in this invention mainly includes the following two parts: 1) Improving the non-cooperative game negotiation mechanism for the three sub-problems of machine selection, AGV selection and workpiece selection in machine-AGV cooperative scheduling, obtaining a more beneficial strategy for the global scheduling result through three games between workpiece, AGV and machine agent respectively, and introducing a local negotiation mechanism to resolve conflicts between agents, so that the non-cooperative game has a stronger global optimization capability; 2) Adding an evolutionary game process to the non-cooperative game to improve the quality of the scheduling scheme, combining the advantages of efficient distributed methods and high-precision centralized search algorithms, the non-cooperative game search performance is improved through selection, diffusion, innovation and evolution processes, and the evolutionary game equilibrium solution is obtained to generate the final scheduling scheme.

[0091] Improve the MAS negotiation mechanism in non-cooperative games.

[0092] The idea of ​​using a non-cooperative game negotiation mechanism to solve scheduling problems is based on real-time manufacturing information in the workshop. At each moment, workpieces actively "compete" for transferable AGVs and processing machines based on their real-time status information. According to the canonical formulation of game theory, a standard game G between agents can be described as a triple:

[0093] (9)

[0094] Where N represents the set of players, S represents the set of feasible strategies for each player, and U represents the payoff function for each player. The non-cooperative game negotiation mechanism of FJMACSP is attached. Figure 2 As shown in the diagram, each workpiece corresponds to a player in the game. Each workpiece attempts to choose the optimal AGV and machine to complete the transfer and processing of the operation and maximize its own profit. Here, the reciprocal of the maximum completion time is chosen as the profit function for each workpiece. The set of strategies ultimately chosen in the workpiece game is represented as the Nash equilibrium. At each time step, each player chooses the optimal strategy according to the priority rule, and the optimal strategy combination of all players is the Nash equilibrium solution. (Appendix) Figure 3 This is an example of how a non-cooperative game negotiation mechanism can achieve a final scheduling scheme.

[0095] In this game negotiation mechanism, the allocation of processes is completed after only one negotiation. However, due to the randomness of the players' strategy choices, the quality of the Nash equilibrium solution is poor and unstable. To solve this problem, this invention improves the non-cooperative game process, as shown in the appendix. Figure 4 As shown. The non-cooperative game negotiation mechanism of FJMACSP designed in this invention was used three times. The game negotiation process of the improved machine-AGV cooperative scheduling problem includes the non-cooperative game negotiation process of selecting the machine and AGV for the workpiece, and the AGV completing the transfer task and the machine completing the processing task. The three game processes are represented by G1, G2 and G3 respectively.

[0096] Appendix Figure 5 This is an example of improving a non-cooperative game negotiation mechanism to obtain a final scheduling solution. In each round of decision-making, each workpiece selects all suitable transfer AGVs and processing machines for the current process through the first non-cooperative game G1 (as shown in the attached...). Figure 5 (a) All AGVs selected in G1 choose suitable workpieces for transfer through a second non-cooperative game G2 (as shown in the appendix). Figure 5 (b) All machines selected in G1 choose suitable workpieces for processing through the third non-cooperative game G3 (as shown in the appendix). Figure 5 (c) After G1, G2, and G3 make their respective choices, the selected workpieces, AGVs, and machines are confirmed by the relevant agents (JMA, AUA, MUA) at the upper level to achieve coordination among the three rounds of the game involving workpieces, machines, and AGVs. Only when the choices made by G1, G2, and G3 are consistent is the game considered valid and used to generate the final scheduling plan; otherwise, it participates in the next round of decision-making (as shown in the appendix). Figure 5 (d) Through this process of three non-cooperative games and mutual selection among workpieces, AGVs, and machines, the final Nash equilibrium solution is obtained.

[0097] Comparing the negotiation mechanism before and after the improvement with the final generated scheduling scheme, we can find that: 1) In the negotiation mechanism before the improvement, each JA only retains one optimal selection strategy, but this strategy is not necessarily the best choice for the final global scheduling result. After the improvement, each JA can retain multiple better strategies, and then the AGV or machine can select the strategy that is more beneficial to the global scheduling result; 2) The scheduling scheme before the improvement is generated by the unidirectional selection of workpieces, while the improved scheduling scheme avoids the situation where different workpieces select the same AGV or machine at the same time through the mutual selection between workpieces and equipment, which can improve the imbalance of equipment load and shorten the completion time.

[0098] When a workpiece selects a machine and an AGV, the non-cooperative game process G1 between the workpieces can be described by the following three-term expression:

[0099] (10)

[0100] (11)

[0101] When an AGV selects a transfer task, the non-cooperative game process G2 among the AGVs is described by the following three-term expression:

[0102] (12)

[0103] (13)

[0104] When a machine selects a processing task, the non-cooperative game process G3 between machines is described by the following three-term expression:

[0105] (14)

[0106] (15)

[0107] In the formula, C i AC r and MC k These represent the completion time of the workpiece process, the completion time of the AGV transfer task, and the completion time of the machining task, respectively.

[0108] The feasible strategy set for a workpiece refers to the machine and AGV selected through the workpiece's process; the feasible strategy for a machine and AGV refers to the process selected by the machine and AGV; each player's goal is to maximize their personal gain and allocate the workpiece to the appropriate AGV and appropriate machine; the payoff function is the minimum of the optimization objective, therefore the reciprocal of the objective function is chosen as the player's payoff.

[0109] Improve the MAS negotiation mechanism process for non-cooperative games, such as... Figure 6 As shown, specifically:

[0110] Step S1: JA selects the optimal equipment combination from different combinations of machines and AGVs, records the suitable processing machine and suitable transfer AGV for workpiece i, and adds them to the strategy set s. Ji In the process, the information of the process to be processed is sent to the relevant MA and AA.

[0111] Step S2: AA simultaneously receives all pending processing information and adds it to the transferable processing set. Select transfer tasks from the set, and AUA will select them based on each s Ar Assigning transfer tasks: When the number of elements in a certain AA set is greater than 1, the AGV Agent inside the AUA conducts local negotiation and uses the greedy principle to assign the process to AGVs without competition as much as possible, so that more processes are assigned to more suitable AGVs for transfer to maximize benefits.

[0112] Step S3: MA receives process information and selects processing tasks to add to strategy set s Mk MUA according to each s Mk Assigning processing tasks: When the number of elements in a certain MA set is greater than 1, the MA within the processing service unit Agent conducts local negotiation and uses the greedy principle to assign the process to a machine with a set of no competing optional strategies containing 1 element, so that more processes are assigned to more suitable processing machines.

[0113] Step S4: AUA and MUA conduct local negotiations to coordinate the selection results of AGVs and machines to ensure that the AGVs and machines are assigned to the finally selected AGVs and machines for each processing step; AUA and MUA issue transfer tasks and processing tasks to the finally selected AGVs and machines respectively, and the AGVs and machines execute the transfer tasks and processing tasks.

[0114] Step S5: Repeat the above process until all processes for all workpieces are transferred and processed, obtaining the Nash equilibrium solution {s}. l}

[0115] The non-cooperative game process of the machine-AGV collaborative scheduling problem is a continuous process of allocating workpiece operations to processing machines and transfer AGVs, as shown in the appendix. Figure 7As shown, the workpiece management agent JMA sends the first unprocessed operation of all workpieces to the workshop agent SA. SA divides the operation into logistics tasks and processing tasks and distributes them to the logistics service unit agent AUA and the processing service unit agent MUA. MUA and AUA, as well as their respective internal device agents, communicate and negotiate to allocate the logistics tasks and processing tasks to the AGV agent AA and the machine agent MA, respectively. AA and MA then add the assigned tasks to their own transfer task or processing task queue, and repeat this game process until all operations of all workpieces are assigned.

[0116] To address the conflict arising from agents adopting the same strategy, this invention introduces a local negotiation mechanism in the non-cooperative game process. When a choice conflict occurs between agents, local negotiation is conducted to balance the final selection outcome. The local negotiation mechanism involves communication between two or more agents when they choose the same strategy. The agents with the higher payoff choose that strategy, while the other agents choose a different strategy. The specific algorithm pseudocode for the non-cooperative game process is shown in Table 2.

[0117] Table 2. Pseudocode for Non-Cooperative Game Theory Algorithms

[0118]

[0119] MAS performance enhancement mechanism based on fusion evolutionary game theory.

[0120] To address the problem of poor global optimization performance caused by intense competition among individual agents in non-cooperative game theory, this invention adds an evolutionary game process to the non-cooperative game theory framework to improve MAS optimization performance. Through selection, diffusion, innovation, and evolution, an evolutionary game equilibrium solution is obtained through continuous game interaction. During the evolutionary process, if players use the same strategy combination within a finite time, then that strategy combination is in a "stable" state. To obtain an evolutionary stable equilibrium solution, random disturbances are needed to cause the game to deviate from its original "stable" state. This process is repeated until the maximum number of evolutionary games reaches a set value, and the final "stable" state is the evolutionary stable equilibrium solution of the evolutionary game. The pseudocode for the evolutionary game process algorithm is shown in Table 3.

[0121] Table 3. Pseudocode for Evolutionary Game Theory Algorithms

[0122]

[0123] The evolutionary game process can be described as follows:

[0124] (16)

[0125] In the formula, N represents the set of players, S represents the strategy space, U represents the payoff function, γ represents the selection operator, ψ represents the diffusion operator, ζ represents the innovation operator, and τ represents the maximum number of evolutionary iterations.

[0126] Through multiple non-cooperative game processes, multiple Nash equilibria are formed, constituting the initial population. Interference operations such as selection, diffusion (crossover), and innovation (mutation) are repeated iteratively until the maximum number of iterations is reached, thus obtaining an evolutionarily stable equilibrium. In this invention, the initial population size is 50, the selection probability γ is 0.1, the diffusion probability ψ is 0.8, the innovation probability ζ is 0.1, and the maximum number of evolutionary iterations τ is 200. Two selection operators are used: elite selection and tournament selection. Two diffusion operator sequence methods are used: POX and JBX crossover. Two-point crossover is used for the machine and AGV sequence. Two innovation operators are used: exchange-based and neighborhood-based.

[0127] Example:

[0128] 1. Experimental Design

[0129] This algorithm is written in Java and uses a virtual multi-agent system built on the JADE platform based on the JDK 8.0 development environment to simulate a real-world production workshop scenario. The experimental environment is a PC with an Intel(R) Core(TM) i5@2.40GHz and 16GB RAM. To fully verify the effectiveness of the method, the following sets of standard examples were selected as test data.

[0130] (1) Bilge's first 40 standard examples. The first 40 standard examples of the proposed flexible manufacturing system scheduling problem. This set of examples has a low ratio of transport time to processing time, i.e. <0.25, where This represents the average transit time in the matrix. This represents the average time of all jobs in the job set. In this set of experiments, the present invention selected three existing scheduling rules (Shortest travel distance - STD, First-Come, First-Served - FCFS, Longest travel distance - LTD), four distributed methods (BDSA, IMAS, MAS, HRA), and two centralized intelligent optimization algorithms (IDDE and IGA) for comparison.

[0131] (2) The last 42 standard examples of Bilge's proposed flexible manufacturing system scheduling problem. This set of examples has a high ratio of transportation time to processing time, i.e. >0.25. The last digit of the example code, "0" or "1", indicates that the processing time is doubled or tripled, respectively. In this case, the transportation time is halved. The superiority of the scheduling method of this invention over heuristic rules has been verified in the first case. Therefore, this group of experiments only compares it with four distributed methods (BDSA, IMAS, MAS, and HRA) and two centralized intelligent optimization algorithms (IDDE and IGA).

[0132] (3) Deroussi Examples. Ten standard examples were proposed. These examples are characterized by several available machines, a few transportation resources, and fixed processing time for each process step, with allocation problems for both processing and transportation tasks. Compared to the Bilge examples, these examples are more flexible. This group of experiments mainly compares with algorithms such as GATS, GTSB, BRKGA, HA, BDSA, IMAS, IDDE, and IGA.

[0133] 2. Algorithm Result Comparison and Solution Demonstration

[0134] (1) Bilge's first 40 examples

[0135] The experimental results of this group are shown in Table 4. It can be seen that, among the scheduling rules, for the optimization objective of this invention to minimize the maximum completion time, "Shortest Travel Distance" (STD) performs best, followed by "First-Come, First-Served" (FCFS), and "Longest Travel Distance" (LTD) performs worst. However, due to the poor optimization ability of the heuristic rules, the quality of the solutions is poor and they cannot outperform other algorithms. In 40 cases, the algorithm of this invention outperforms the three rules by 18.54%, 21.55%, and 25.61%, respectively, proving the effectiveness of the scheduling method of this invention. After calculation, the experimental results of the algorithm of this invention on 40 cases are better than other algorithms to varying degrees. The highest performance is 23.39% better than the BDSA algorithm, the lowest performance is 2.76% better than the IDDE algorithm, and the average performance is 13.36% better than other algorithms. The calculation results can prove the superiority of the algorithm of this invention.

[0136] Table 4. Experimental results of the first 40 Bilge examples.

[0137]

[0138] The results of this invention's algorithm, compared with those of several distributed methods and intelligent optimization algorithms, are shown in the attached figure. Figure 8 As can be seen from the figure, the algorithm of this invention can achieve the optimal solution relative to other algorithms in most cases, which proves that the algorithm of this invention improves the search ability for high-quality solutions compared to existing distributed methods, and improves the quality of the population compared to centralized intelligent optimization algorithms. Therefore, it has higher computational accuracy and better scheduling ability.

[0139] (2) The last 42 examples of Bilge

[0140] The experimental results of this group are shown in Table 5, and the comparison graph of the results is attached. Figure 9 As shown.

[0141] Table 5. Experimental results for the last 42 cases after the Bilge example.

[0142]

[0143] Experimental results show that, compared to other algorithms, the algorithm of this invention outperforms the BDSA algorithm by up to 10.60% and the IDDE algorithm by down to 0.33% in the last 42 examples, with an average outperformance of 4.73% over other algorithms. Although the algorithm of this invention also outperforms other algorithms in these 42 examples, the superiority is not as high as in the first 40 examples, indicating that the algorithm of this invention has high computational accuracy when the ratio of transportation time to processing time is high. Therefore, it proves that the algorithm of this invention performs better relative to problems with a relatively high ratio of transportation time to processing time, and the algorithm shows better performance as the ratio increases, indicating that the algorithm of this invention has a greater advantage in solving the bottleneck problem of AGV scheduling. This is because the present invention considers production scheduling and AGV scheduling simultaneously, and achieves coordination between machines and AGVs by improving the non-cooperative game process, which can solve the problem of extended completion time caused by insufficient machine-AGV coordination to a certain extent.

[0144] (3) Deroussi calculation example

[0145] The experimental results of the Deroussi example are shown in Table 6 and Appendix. Figure 10 As shown in the table, the instance features (M - number of machines, J - number of workpieces, O - number of operations, and A - average number of selectable machines per operation), the comparison algorithms, and the experimental results of the algorithm of this invention are presented. In the table, Best represents the optimal value of 20 experiments, and Mean represents the mean of 20 experiments. Calculations show that the algorithm of this invention achieves the optimal solution on 4 cases, and on average outperforms GATS, GTSB, BRKGA, and HA by 3.66% on 10 cases, and on average outperforms BDSA, IMAS, IGA, and IDDE by 11.03%, further verifying the algorithm's superiority. From the optimal and mean values ​​of the experimental results, the algorithm of this invention achieves good results, indicating that it is also applicable to scheduling scenarios where both processing and transportation tasks have allocation problems. It can complete transfer and processing tasks through the game process between workpieces, AGVs, and machine agents, exhibiting higher computational accuracy and stability.

[0146] Table 6. Experimental Results of the Deroussi Example

[0147]

[0148] Based on 92 examples from three sets of experiments, the NCAEG algorithm proposed in this invention outperforms three commonly used rules, four distributed methods, and two intelligent optimization algorithms by an average of 15.66% in terms of solution accuracy. This demonstrates that: 1) Compared to heuristic rules, the algorithm of this invention leverages the advantages of distributed autonomous decision-making, avoiding the reduction in computational accuracy caused by a single or inappropriately selected scheduling rule; 2) The improved non-cooperative game process enables the coordination of workshop manufacturing resources during three non-cooperative game processes, and enhances the algorithm's optimization capability through the evolutionary game process; 3) The algorithm of this invention achieves higher accuracy than existing intelligent optimization algorithms, which is due to the higher quality of the population during the evolutionary process, thereby improving the algorithm's solution quality.

Claims

1. A flexible job shop AGV collaborative scheduling method based on non-cooperative evolutionary game theory, characterized in that, Includes the following steps: Step 1: Construct a flexible workshop machine-AGV collaborative scheduling model under the two-layer multi-agent system (MAS) architecture; with minimizing the maximum completion time as the optimization objective, comprehensively consider multiple constraints such as machine allocation, process sequencing, AGV path and task allocation to achieve unified modeling of production and logistics resources; (1) Problem description; The FJMACSP (Flexible Job Shop Machine-AGV Cooperative Scheduling Problem) based on MAS (Machine-Assisted System) describes the following: The number of processing machines, the number of AGVs, and the shop layout are all known; production orders include several workpieces to be processed; each machine, AGV, and workpiece constitutes a machine agent, an AGV agent, and a workpiece agent, respectively, forming a MAS with other management agents and shop agents; each workpiece agent consists of several processes, each process is considered a task, which can be decomposed into processing tasks and transfer tasks; the machine agents that can perform processing tasks and the corresponding processing time are known; each machine agent has a buffer for storing workpieces with unlimited capacity; transfer tasks are divided into idle processes and loaded processes. The idle process is when the AGV agent travels from its current position to the starting point of the loaded process; the loaded process is when the AGV agent travels from the loading / unloading station or the position of the machine processed in the previous process to the position of the machine processed in the current process. The agent's travel time depends on the actual distance traveled. The processing task can only be executed after the transfer task of each process is completed. The arrival position of the new workpiece agent and the initial position of the AGV agent are both at the loading / unloading station L / U. The L / U station has sufficient input / output buffer space. The AGV agent completes the current transfer task and stops next to the nearest machine or loading / unloading station. (2) Objective function: The optimization objective is to minimize the maximum completion time; （1） Among them, C i The completion time of Agent i; (3) Constraints: （2） （3） （4） （5） （6） （7） （8） Among them, OST i,j,k OCT i,j,k Indicates process O i,j The start and end times of processing on machine agent k, EST i,j,r ECT i,j,r Indicates process O i,j LST is the start and end time of the empty transfer before the transfer on the AGV Agent r. i,j,r LCT i,j,r Indicates process O i,j The start and end times of load transfer on the AGV Agent r, tt i,j,r Indicates process O i,j Transfer time on AGV Agent r, tt i,j,r = et i,j,r + lt i,j,r et i,j,r Represents the idle transfer time, lt i,j,r Indicates load transfer time, pt i,j,k Indicates process O i,j Processing time on machine Agent k ,in Represents preparation time. Indicates processing time, x i,j,k , z i,j,r Denotes the decision variable, if process O i,j x is processed on machine agent k. i,j,k = 1, otherwise x i,j,k = 0; if process O i,j Transferring goods on the AGV Agentr is z i,j,r = 1, otherwise z i,j,r = 0; Equation (2) represents the processing sequence constraint of each process of the workpiece agent on the machine agent; Equations (3) and (4) represent the transfer sequence constraint of each process of the workpiece agent on the AGV agent; Equation (5) represents the sequence constraint between the idle time of the processing task, the transfer task and the load time of the transfer task; Equation (6) represents that all processing tasks are assigned to a specific machine agent; Equation (7) represents that all transfer tasks are assigned to a specific AGV agent; Equation (8) is a decision variable constraint, which means that the processing task of each process of the workpiece agent can only be executed on one machine agent, and the transfer task can only be executed on one AGV agent. Step 2: Based on non-cooperative game theory, an improved negotiation mechanism is designed. The workpiece, machine and AGV, as independent agents, achieve resource matching and conflict resolution in three non-cooperative games through strategy game and local negotiation mechanism, thereby obtaining the Nash equilibrium solution. (1) Improve the MAS negotiation mechanism in non-cooperative games; The idea of ​​using a non-cooperative game negotiation mechanism to solve scheduling problems is based on real-time manufacturing information in the workshop. At each moment, workpieces actively "compete" for transferable AGVs and processing machines based on their real-time status information. According to the canonical formulation of game theory, a standard game G between agents can be described as a triple: （9） Where N represents the set of players, S represents the set of feasible strategies for players, and U represents the payoff function for players; The non-cooperative game process was improved. The improved game negotiation process of the machine-AGV cooperative scheduling problem includes the workpiece selection machine and AGV, and the non-cooperative game negotiation process of AGV completing the transfer task and machine completing the processing task. The three game processes are represented by G1, G2 and G3 respectively. In each round of decision-making, each workpiece selects all suitable transfer AGVs and processing machines for the current process through the first non-cooperative game G1. All AGVs selected in G1 select suitable workpieces for transfer through the second non-cooperative game G2, and all machines selected in G1 select suitable workpieces for processing through the third non-cooperative game G3. After G1, G2, and G3 make their respective choices, the workpieces, AGVs, and machines selected by each other are confirmed by the relevant agents managed at the upper level to achieve coordination among the three games of workpieces, machines, and AGVs. Only when the choices made by G1, G2, and G3 are consistent is the game considered valid and used to generate the final scheduling plan; otherwise, it participates in the next round of decision-making. When a workpiece selects a machine and an AGV, the non-cooperative game process G1 between the workpieces can be described by the following three-term expression: （10） （11） When an AGV selects a transfer task, the non-cooperative game process G2 among the AGVs is described by the following three-term expression: （12） （13） When a machine selects a processing task, the non-cooperative game process G3 between machines is described by the following three-term expression: （14） （15） In the formula, C i AC r and MC k These represent the completion time of the workpiece process, the completion time of the AGV transfer task, and the completion time of the machining task, respectively. The feasible strategy set for a workpiece refers to the machine and AGV selected through the workpiece's process; the feasible strategy for a machine and AGV refers to the process selected by the machine and AGV; each player's goal is to maximize their personal gain and allocate the workpiece to the appropriate AGV and appropriate machine; the payoff function is the minimum of the optimization objective, therefore the reciprocal of the objective function is chosen as the player's payoff; (2) Local consultation mechanism; In non-cooperative game theory, a local negotiation mechanism is introduced to balance the final choice results when a choice conflict occurs between agents. The local negotiation mechanism is that when two or more agents choose the same strategy, the two agents communicate with each other to compare their payoffs, so that the agent with the higher payoff chooses the strategy, while the other agents choose the other strategy. Step 3: Introduce an evolutionary game mechanism to perform selection, diffusion, innovation and iteration operations on the feasible solution set generated by multiple non-cooperative games, so as to improve the diversity of the algorithm population and the global search capability, and obtain a better evolutionary stable equilibrium solution. An evolutionary game process is added to the non-cooperative game theory framework to improve the optimization performance of MAS. Through selection, diffusion, innovation, and evolution, an evolutionary game equilibrium solution is obtained in the continuous game process. During the evolutionary process, if players use the same strategy combination within a finite time, then that strategy combination is in a "stable" state. To obtain an evolutionary stable equilibrium solution, random disturbances are needed to cause the game to deviate from its original "stable" state. This process is repeated until the maximum number of evolutionary games reaches a set value, and the final "stable" state is the evolutionary stable equilibrium solution of the evolutionary game. The evolutionary game process can be described as follows: （16） In the formula, N represents the set of players, S represents the strategy space, U represents the payoff function, γ represents the selection operator, ψ represents the diffusion operator, ζ represents the innovation operator, and τ represents the maximum number of evolutionary iterations. After multiple non-cooperative game processes, multiple Nash equilibrium solutions are formed to form the initial population. Through selection, crossover and mutation interference operations, the operations are repeated to iterate until the maximum number of iterations is reached, thereby obtaining an evolutionarily stable equilibrium solution. Step 4: Implement intelligent solution for machine-AGV collaborative scheduling in flexible workshop based on improved non-cooperative-evolutionary game theory collaborative optimization algorithm.

2. The method for collaborative scheduling of AGVs in a flexible job shop based on non-cooperative evolutionary game theory as described in claim 1, characterized in that, The specific process of the improved MAS negotiation mechanism for non-cooperative games is as follows: Step S1: JA selects the optimal equipment combination from different combinations of machines and AGVs, records the suitable processing machine and suitable transfer AGV for workpiece i, and adds them to the strategy set s. Ji In the process, the information of the process to be processed is sent to the relevant MA and AA; Step S2: AA simultaneously receives all pending processing information and adds it to the transferable processing set. Select transfer tasks from the set, and AUA will select them based on each s Ar Assigning transfer tasks; when the number of elements in a certain AA set is greater than 1, the AGV Agent inside the AUA conducts local negotiation and uses the greedy principle to assign the process to the AGV without competition as much as possible, so that more processes are assigned to the more suitable AGVs for transfer to maximize benefits. Step S3: MA receives process information and selects processing tasks to add to strategy set s Mk MUA according to each s Mk Assigning processing tasks; when the number of elements in a certain MA set is greater than 1, the MA within the processing service unit Agent conducts local negotiation and uses the greedy principle to assign the process to a machine with a set of no competing alternative strategies containing 1 element, so that more processes are assigned to more suitable processing machines. Step S4: AUA and MUA conduct local negotiations to coordinate the selection results of AGVs and machines to ensure that the AGVs and machines are assigned to the finally selected AGVs and machines for each processing step; AUA and MUA issue transfer tasks and processing tasks to the finally selected AGVs and machines respectively, and the AGVs and machines execute the transfer tasks and processing tasks. Step S5: Repeat the above process until all processes for all workpieces are transferred and processed, obtaining the Nash equilibrium solution {s}. l } 3. The method for collaborative scheduling of AGVs in a flexible job shop based on non-cooperative evolutionary game theory as described in claim 1, characterized in that, In the non-cooperative game process, the initial population size is 50, the selection probability γ is 0.1, the diffusion probability ψ is 0.8, the innovation probability ζ is 0.1, and the maximum number of evolution iterations τ is 200. The selection operator adopts two types: elite selection and tournament selection. The diffusion operator process sequence adopts two types: POX and JBX crossover. The machine and AGV sequence adopts two-point crossover. The innovation operator adopts two types: exchange type and neighborhood type.

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