Adaptive multi-group interaction PSO flexible workshop AGVs integrated scheduling optimization method

Abstract

The invention discloses an adaptive multi-group interaction PSO flexible workshop AGVs integrated scheduling optimization method, which comprises the steps of dividing three functional populations, namely elite, exploration and development, and realizing global exploration and local mining of a solution space through multi-group interaction. A task matrix and a resource matrix are constructed to represent the correlation essence of the position of a task processing machine and AGVs transportation time, and a matrix updating mechanism based on local feature reconstruction and global trajectory avoidance is proposed and used for extracting an excellent solution gene mode and guiding search of a foreground area. The proposed method is verified on two standard data sets of FJSP and EX, and the result shows that the proposed method can effectively improve the scheduling solution quality, has relatively strong convergence capability and adaptability, has wide application potential in solving the AGVs scheduling problem of the complex flexible job shop, and has a wide application prospect. And efficient and feasible technical support can be provided for scheduling optimization of the intelligent manufacturing workshop.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent manufacturing scheduling optimization, and particularly relates to an integrated scheduling method for PSO flexible workshop AGVs with adaptive multi-group interaction. Background Art

[0002] To address the problems of high cost, low efficiency, and high risk in the traditional manufacturing mode, China's intelligent manufacturing faces huge challenges in aspects such as constructing guidelines, planning schemes, and implementing technologies. In addition, to meet the increasing personalized needs of the manufacturing industry, the large-scale standardized production mode is shifting towards the large-scale personalized customization production mode.

[0003] Flexible manufacturing systems play important roles such as improving production efficiency, reducing production costs, enhancing production flexibility, and optimizing resource utilization, and are important operation modes in intelligent manufacturing systems. Existing flexible manufacturing production modes mainly focused on personalization have many pain points, such as a wide variety of product types, complex process flows, and strong dynamics of logistics tasks. Automated Guided Vehicles (AGVs), as important equipment in intelligent manufacturing systems, with their characteristics of high efficiency, flexibility, scalability, and parallel operation, achieve precise material distribution in the production workshop, greatly reducing the intervention of manual operations, and becoming the key support for enhancing the full-process automation level of intelligent manufacturing systems. The intelligent manufacturing system constructed by multiple AGVs is becoming the norm for quickly switching production lines to meet the customized manufacturing needs of different products. Therefore, the integrated scheduling of flexible workshop AGVs is crucial for improving production efficiency.

[0004] Existing flexible workshop scheduling methods usually consider the flexible workshop operation scheduling and the AGVs logistics transportation scheduling separately. However, in essence, flexible workshop operation scheduling involves how to efficiently allocate workpieces to different processing machines and reasonably arrange the processing sequence of each workpiece on the machines. The prerequisite is to arrange AGVs to transport materials to the designated processing machines efficiently and in a timely manner, and avoid problems such as path conflicts and transportation delays. The integrated scheduling of flexible workshop AGVs is a scheduling mode that promotes the collaborative work of processing resources and transportation resources and conforms to the actual operation environment of intelligent manufacturing systems.

[0005] The core objective of the integrated scheduling of AGVs in a flexible workshop is to minimize the processing and transportation time in the production process through reasonable resource allocation and task arrangement, thereby improving the overall production efficiency. It is necessary to consider both flexible job scheduling and coordinate the path planning and task allocation of AGVs, which poses higher requirements for the solution ability of the algorithm. In view of the above problems existing in the integrated scheduling of AGVs in a flexible workshop, the present invention proposes a PSO scheduling optimization method with adaptive multi-group interaction. Considering both the processing machine resources and the AGVs resources for transporting workpieces, the two are efficiently coordinated to form an intelligent scheduling scheme with flexibility and high efficiency, providing technical support for intelligent manufacturing. Summary of the Invention

[0006] To solve the problems that the existing intelligent manufacturing flexible workshop warehousing management system, logistics transportation system, and manufacturing execution system are isolated from each other, it is difficult to efficiently coordinate the warehousing storage resources, logistics transportation resources, and manufacturing processing resources, and it is impossible to achieve the full-process digital control from manufacturing orders to product delivery, resulting in poor robustness of the intelligent manufacturing system. The present invention discloses a PSO integrated scheduling method for AGVs in a flexible workshop with adaptive multi-group interaction, with the optimization goal of minimizing the total completion time. Integrating AGVs into the flexible workshop job scheduling process, it supports the intelligent manufacturing flexible workshop to achieve efficient, flexible, and intelligent production goals, meeting the development needs of future manufacturing.

[0007] The technical solution of the present invention is as follows: A PSO integrated scheduling optimization method for AGVs in a flexible workshop with adaptive multi-group interaction, the method comprising the following steps:

[0008] Step 1. Design a hierarchical individual coding structure;

[0009] Step 2. Design an integrated scheduling statistical analysis collaborative probability matrix;

[0010] Step 3. Generate an initial integrated scheduling statistical analysis collaborative probability matrix;

[0011] Step 4. Function-driven multi-group self-customized initialization;

[0012] Step 5. PSO iterative optimization with adaptive multi-group interaction.

[0013] Further, in Step 1, the hierarchical individual coding structure adopts a three-layer coding structure, which is, from top to bottom, the operation sequence string OS, the machine selection string MS, and the AGV selection string AS. The length of each layer of coding string is the same, and is the sum of the operations of all jobs.

[0014] Further, in Step 2, the integrated scheduling statistical analysis collaborative probability matrix includes a task matrix and a resource matrix (where m is the number of machines and w is the number of trolleys). For assisting in the allocation of the operation sequence for decision-making, For assisting in the joint allocation of machines and trolleys for decision-making. The element μ in the i-th row and j-th column in ij represents the probability that the j-th job is assigned to the i-th gene position in the operation sequence string OS of the three-layer coding string. The element ρ in the i-th row and j=(k×h)-th column in i(k×h) represents the probability that the k-th machine and the h-th trolley are respectively assigned to the i-th gene position in the machine selection string MS and the AGV selection string AS of the three-layer coding string.

[0015] Furthermore, in step 3, when generating the initial integrated scheduling statistical analysis collaborative probability matrix, formula (1) is used as to initialize each element in, and formula (2) is used as to initialize each element in.

[0016]

[0017] Formula (1) indicates that for all operations, the initial processing order priorities are the same. In formula (2), MS i represents the set of optional processing machines corresponding to the operation (denoted as opr i ) at the i-th gene position in the operation sequence string OS of the three-layer coding string. Initially, if k∈MS i , then the element ρ i(k×h) represents that the probability of the operation opr i being assigned to each optional processing machine k and the h-th trolley is equal; otherwise, the probability is 0.

[0018] Furthermore, in step 4, the population is divided into three categories, namely the elite population, the exploitation population, and the exploration population. The elite population guides the search direction of the algorithm in the solution space, the exploitation population conducts in-depth excavation around the elite population, and the exploration population avoids falling into local convergence under the guidance of the elite population. Considering the different functional responsibilities of each type of population in the algorithm optimization process, a multi-type population self-customized initialization method is adopted, specifically as follows:

[0019] Step 41. For each individual in the elite population, first randomly generate the operation sequence OS and the AGV selection string AS of the three-layer coding string, and then successively select the machine with the shortest processing time for each operation in the operation sequence string OS to generate the second-layer MS string;

[0020] Step 42. For each individual in the exploration population and the exploitation population, use the initial integrated scheduling statistical analysis collaborative probability matrix and for initialization. Specifically:

[0021] For each gene position i in the individual three - layer encoded string, where i ranges from 1 to n s , based on roulette wheel sampling for and , select the job number j from the i - th row corresponding to the gene position i matrix, and select the combination of machine k and cart h from the i - th row matrix; determine whether the operation of job j has exceeded the sampling threshold (i.e., the total number of operations of job j). If so, then set all the column elements corresponding to job j in and to 0, and perform normalization processing on each row of and .

[0022] Furthermore, step 5 is the PSO iterative optimization with adaptive multi - swarm interaction, which is specifically as follows:

[0023] Step 51. Set the hyperparameters of the adaptive multi - swarm interaction PSO;

[0024] Step 52. Set the initial values and upper and lower bound thresholds of the adaptive dynamic inertia weight factors for three types of populations;

[0025] Step 53. Perform PSO multi - swarm interaction optimization based on the adaptive dynamic inertia weight factor;

[0026] Step 54. Perform individual local search based on AGVs - swap;

[0027] Step 55. Determine whether the PSO iterative optimization has ended? If yes, go to step 6; if no, go to step 3.

[0028] Step 56. Update the integrated scheduling statistical analysis collaborative probability matrix;

[0029] Step 57. Generate a new population based on the updated probability matrix;

[0030] Step 58. Determine whether to perform adaptive multi - swarm interaction optimization on the current new population? If yes, go to step 2; if no, output the optimal solution.

[0031] Furthermore, step 51 sets the hyperparameters of the adaptive multi - swarm interaction PSO, including: the maximum number of algorithm iterations maxIter, the number of PSO iterations psoIter, the population size popSize, the number of individuals in the elite population Num elite , the number of individuals in the exploration population Num exploit , the number of individuals in the exploitation population Num explore , the learning factors c1, c2, and the probability matrix update factor α.

[0032] Further, step 52 sets the initial values and upper and lower bound thresholds of the adaptive dynamic inertia weight factors for three types of populations, including: the three types of populations each perform their own functions during the algorithm optimization process, so different populations adopt different adaptive weight parameters ω elite , ω exploit , ω explore ; To enhance the search ability of the algorithm, global search is emphasized in the early stage of the iteration process and gradually transitions to local search in the later stage. Set the upper limit and the lower limit of the adaptive weight parameters for the three types of populations. Among them, to ensure the continuation of the excellent genes of the elite population and enable the exploration population and the exploitation population to effectively escape from the local optimum, set and Furthermore, to enhance population diversity, the adaptive weight parameters of the three types of populations are dynamically updated using formula (3), where iter psoCurrent is the current iteration number of PSO. The adaptive weights of the three types of populations gradually decrease with the increase of the iteration number under the control of their respective thresholds.

[0033]

[0034] Further, step 53 is the PSO multi-group interaction optimization based on the adaptive dynamic inertia weight factor, specifically as follows:

[0035] Step 531. For each type of population, generate a set of random perturbation factors respectively used to control the crossover and mutation of individuals;

[0036] Step 532. If , then apply the customized mutation operator to each layer of the three-layer coding string of the current individual in the type class;

[0037] Step 533. If , then perform customized crossover on the corresponding layers of the three-layer coding string of the current individual in the type class and the three-layer coding string of the historical optimal solution of the current individual;

[0038] Step 534. If , then perform customized crossover on the corresponding layers of the three-layer coding string of the current individual in the type class and the three-layer coding string of the global optimal solution of the multi-group;

[0039] Further, step 54 is the local search based on AGVs-swap to obtain a shorter total completion time by attempting to replace the currently selected AGV for each operation, specifically as follows:

[0040] Step 541. For each individual in the three types of populations, sequentially process the operation opr i at the i-th gene position of the first layer OS string of the three-layer coding string;

[0041] Step 542. For opr i , in the second-layer machine string MS and the third-layer AS string, determine the currently assigned machine m i and trolley a i , and calculate the

[0042] Step 543. In the set Aopr i of optional AGVs of opr i , for each trolley b ∈ Aopr i ∧ b ≠ a i , calculate the total completion time makespan i of the individual after replacing a with b b ;

[0043] Step 544. Select a trolley If then replace a with trolley b i ;

[0044] Furthermore, Step 6 integrates scheduling statistical analysis and collaborative probability matrix update, as follows:

[0045] Step 61: Construct the optimal position population p best based on the historical optimal positions of the three types of population individuals;

[0046] Step 62: Select the top X% from the three types of population individuals as the new elite population;

[0047] Step 63: Based on the optimal position population p best , use formulas (4) and (5) to update and generate the task matrix and resource matrix

[0048] Step 64: Based on the current entire population, use formulas (6) and (7) to update and generate the task matrix and resource matrix

[0049]

[0050] In formulas (4), (5), (6), and (7), N is the total number of the three types of population individuals, and α is the probability matrix update learning factor, which is used to control the dependence degree of the current probability matrix on the excellent genes of the historical population. and are decision variables, which are used to count whether the job number at the i-th gene position in the OS string of the z-th individual is the same as the job number in the j-th column of the task matrix ; used to count whether the combination of machine number and trolley number of the z-th individual MS and the i-th gene position in the AS string is the same as the combination of machine number and trolley number in the j-th column of the resource matrix

[0051] The purpose of updating the exploration population probability matrix based on formulas (4) and (5) is to, through statistical analysis of all individuals in population p best for the selection of operation sequence and resource combination, feedback the gene patterns with high frequencies to the corresponding task matrix and resource matrix In the update process, the probability matrix is used to update the learning factor α to balance the weights of the statistical characteristics of two generations of individuals, gradually strengthen the learning and retention of excellent genes, prompt the offspring individuals to gather towards the historical high-quality solutions, and improve the guiding ability and quality stability of the exploration solutions

[0052] The purpose of updating the exploitation population probability matrix based on formulas (6) and (7) is to, by statistically analyzing the operation sequences and resource combinations not selected by all individuals in the current entire population, reverse-strengthen the gene patterns not frequently selected, guide the exploitation population to jump out of the current concentrated search area, enhance the dispersion and diversity of the population, and avoid falling into local optima. In particular, for the update of the resource matrix, only when the current machine and trolley combination meets the optional machines for the operation will it participate in the calculation, ensuring the rationality and feasibility of the update, promoting the exploitation population to cover a wider solution space, and realizing the improvement of the global search ability

[0053] Advantages of the present invention

[0054] (1) Divide the population into three types of functional populations: elite, exploration, and exploitation, share information among groups through a multi-group interaction mechanism, and then widely and efficiently search the solution space, optimize the collaborative configuration of machine resources and AGVs resources, and improve resource utilization

[0055] (2) Construct an integrated scheduling statistical analysis collaborative probability matrix, deeply analyze the impact of each heterogeneous resource collaboration mode on the scheduling objective, accurately guide the search direction of the algorithm in the solution space, and at the same time improve the quality of the scheduling scheme and the search efficiency of the algorithm

[0056] (3) Design an adaptive dynamic probability update mechanism to cope with the manufacturing and processing requirements with different scales and complexities in the actual intelligent production workshop, reduce the scheduling failure caused by environmental changes, and enhance the stability of the intelligent workshop scheduling system Description of the Drawings

[0057] Figure 1 Example diagram of the integrated scheduling problem of flexible workshop AGVs in the embodiment of the present invention

[0058] Figure 2 ​Schematic diagram of the integrated scheduling optimization method for AGVs in a flexible job shop based on the self - adaptive multi - swarm interaction PSO of the present invention;

[0059] Figure 3 Example diagram of the individual three - layer coding in the embodiment of the present invention;

[0060] Figure 4 Structural diagram of the collaborative probability matrix for integrated scheduling statistical analysis in the embodiment of the present invention;

[0061] Figure 5 Example diagram of the selected crossover operator in the embodiment of the present invention;

[0062] Figure 6 Verification result diagram of the embodiment of the present invention on the standard data sets FJSP and EX;

[0063] Figure 7 Gantt chart of the optimal solution scheduling in the embodiment of the present invention, where (a) shows the Gantt chart of the scheduling corresponding to the optimal solution obtained by the embodiment of the present invention on the data instance FJSP1; (b) shows the Gantt chart of the scheduling corresponding to the optimal solution obtained by the embodiment of the present invention on the data instance EX21;

[0064] Figure 8 Algorithm convergence process diagram in the embodiment of the present invention, where (a) gives the convergence process of the algorithm optimization in the embodiment of the present invention on the data instance FJSP1; (b) gives the convergence process of the algorithm optimization in the embodiment of the present invention on the data instance EX21;

[0065] Figure 9 Analysis diagram of the self - adaptive inertia weight factor in the embodiment of the present invention;

[0066] Figure 10 Illustration diagram of the effectiveness of local search in the embodiment of the present invention;

[0067] Figure 11 Illustration diagram of the effectiveness of the collaborative probability matrix for integrated scheduling statistical analysis in the embodiment of the present invention. Detailed implementation manners

[0068] Combined with the accompanying drawings and specific implementation manners, the present invention is further clarified. It should be understood that the following specific implementation manners are only used to illustrate the present invention and not to limit the scope of the present invention. It should be noted that the terms "front", "rear", "left", "right", "up" and "down" used in the following description refer to the directions in the accompanying drawings, and the terms "inside" and "outside" respectively refer to the directions towards or away from the geometric center of a specific component.

[0069] Figure 1The flexible job shop AGVs integrated scheduling problem solved by the present invention is presented. Compared with the flexible job shop scheduling, AGVs scheduling needs to be carried out simultaneously. It can be divided into four sub-problems: allocating processing machines for each job, selecting transportation AGVs for each operation, determining the processing sequence of the previous operation on each machine, and determining the sequence of each AGVs transportation operation.

[0070] Figure 2 It is a schematic diagram of the PSO flexible job shop AGVs integrated scheduling optimization method with adaptive multi-group interaction of the present invention. This method represents individuals using a multi-layer coding structure and divides individuals into three types of populations with different functions. An integrated scheduling statistical analysis collaborative probability matrix is designed to assist the three types of populations to search extensively and deeply in the solution space. After initialization, the three types of populations conduct information sharing and interaction, co-evolve under the guidance of the integrated scheduling statistical analysis collaborative probability matrix, and use the excellent genes obtained after evolution to update the integrated scheduling statistical analysis collaborative probability matrix.

[0071] Figure 3 It is the three-layer coding structure of the individual designed by the present invention. From the first layer to the third layer, they are the operation sequence string OS, the machine selection string MS, and the AGVs selection string AS in turn. The string contains three jobs, and each job contains four operations. Therefore, the length of the three strings is 12. The numbers in the OS string represent job numbers, and the order in which the same number appears in the OS string represents the operation sequence number of the same job, that is: O 21 -O 11 -O 22 -O 31 -O 32 -O 12 -O 23 -O 33 -O 13 -O 24 -O 14 -O 34 。The indexes in the MS string and the AS string start from the first operation of the first job and gradually increase until the last operation of the last job. The element values in the string represent the processing machine number and the transportation vehicle number selected for the corresponding operation respectively. For example, O 14 is assigned to be processed on the machine m4 with the number 4, and after O 13 is completed, it is transported from the machine m2 to m4 by the vehicle agv2 with the number 2.

[0072] Figure 4 As shown, it is the structure diagram of the integrated scheduling statistical analysis collaborative probability matrix in the embodiment of the present invention. The blue part on the right is the task matrix The yellow part on the left is the resource matrix Task matrix The element in it represents job J jThe probability of being assigned to the corresponding OS string gene position i, resource matrix The element in represents the probability that machine m k and the AGV h are respectively assigned to the corresponding MS string and AS string gene positions i. Where l is used to distinguish the population category, and g represents the update of the current statistical analysis cooperation probability matrix participating in the g-th generation population.

[0073] Figure 5 Shown in the following are two mutation operators selected in the PSO multi-group interaction optimization process based on the adaptive dynamic inertia weight factor in the embodiment of the present invention, namely the operation flip mutation SIM and the machine replacement mutation MRM. The SIM operator randomly selects a cut point k (0 ≤ k ≤ n s ) in the individual, and then reverses the strings on both sides of the cut point k in turn. For example, when k = 4, the parent individual P1 is cut into two strings 2-1-2-3 and 3-1-2-3-1-2-3-1, and the two strings are respectively reversed to obtain 3-2-1-2 and 1-3-2-1-3-2-1-3, and finally merged into the child individual C1. The MRM operator randomly selects two cut points k1 and k2 in the individual and k1 < k2, and randomly permutes the machine string MS and the AGV string AS between k1 and k2 in the optional set. For example, when k1 = 2 and k2 = 5, the machine 2-4-3 between the MS string position 2 and position 5 of the parent individual P1 is replaced with other optional machines 1-3-2, and the same operation is performed on the AGV string AS, and finally it evolves into the child individual C1.

[0074] Figure 6 Shown in the following are the characteristics of the FJSP and EX data sets adopted in the embodiment of the present invention, as well as the makespan results obtained by the algorithm of the embodiment of the present invention on the two data sets. FJSP contains 10 data instances, with 8 machines and 2 AGVs in each instance, and the maximum number of jobs is 8 and the minimum is 5. EX contains 12 data instances, with 4 machines and 2 AGVs in each instance, and the maximum number of jobs is 8 and the minimum is 5. Figure 6 Two currently representative algorithms BRKGA and HDPSO are selected in

[0075] Figure 7 to compare with the embodiment of the present invention. It can be verified from the experimental results that the embodiment of the present invention is superior to HDPSO on all data instances, is on a par with BRKGA on 12 data instances, and is superior to BRKGA on the remaining 10 data instances. Thus, it can be seen that the algorithm of the present invention has good applicability and effectiveness in dealing with data instances of different scales. Figure 8(a) and (b) present the convergence process of the algorithm optimization in the embodiments of the present invention on data instances FJSP1 and EX21. From Figure 8 As can be seen from (a), for the FJSP1 instance, the inflection points of the algorithm are located near the iteration numbers of 50, 200, and 400. The reason for the significant convergence of the objective function value is that at the inflection points, the algorithm uses the integrated scheduling statistical analysis to cooperate with the probability matrix to learn the characteristics of different populations, and updates the task matrix and the resource matrix respectively. Different-quality next-generation populations are obtained through the updated matrix sampling. During other iteration processes, the population only undergoes the optimization of the particle swarm algorithm. This shows that the update and sampling of the integrated scheduling statistical analysis cooperation probability matrix have a significant impact on the reduction of the objective function. Figure 8 (b) shows the algorithm convergence process under the EX21 dataset. It can be seen that when the algorithm deals with the EX21 dataset, excellent solutions are obtained within a small number of iterations, indicating that the algorithm has an extremely fast convergence speed.

[0076] To verify the effectiveness of the adaptive dynamic inertia weight factor of the present invention, 4 data instances with different scales are selected for testing. From Figure 9 As shown, the adaptive inertia weight factor with dynamic update can effectively reduce the total completion time on the 4 selected data instances with different scales compared with the fixed inertia weight factor. Moreover, as the scale of the dataset increases, the optimization amplitude is more obvious, fully proving the effectiveness of the adaptive dynamic weight inertia factor.

[0077] Figure 10 The following shows the performance analysis of the local search in the algorithm of the embodiments of the present invention. As can be seen from the figure, for the 4 selected data instances, compared with not using local search, the total completion time obtained by the embodiments of the present invention has been greatly improved, and the improvement amplitude is the largest on the data instance FJSP10, reaching 6.45%.

[0078] Figure 11 The following shows the effectiveness analysis of the integrated scheduling statistical analysis cooperation probability matrix of the embodiments of the present invention. Compared with the independent optimization of processing resources and transportation resources, the present invention designs a resource matrix to achieve the cooperative optimization of machines and AGVs. As can be seen from the figure, for all data instances of FJSP, the integrated scheduling statistical analysis cooperation probability matrix designed by the embodiments of the present invention has an improvement effect. Particularly, due to the small scale of the FJSP5 instance and the low complexity of finding the solution space, the effectiveness of the cooperation probability matrix cannot be fully reflected. However, on the remaining data instances, the integrated scheduling statistical analysis cooperation probability matrix shows obvious optimization results, such as the optimization amplitudes of 4.83%, 4.68%, and 5.82% on the FJSP1, FJSP4, and FJSP7 datasets respectively.

[0079] The technical means disclosed in the solution of the present invention are not limited to those disclosed in the above embodiments, and also include technical solutions composed of any combination of the above technical features.

Claims

1. An integrated scheduling optimization method for AGVs in a flexible job shop with adaptive multi-group interaction in PSO, characterized in that, The method includes the following steps: Step 1. Design a hierarchical individual coding structure; Step 2. Design an integrated scheduling statistical analysis collaborative probability matrix; Step 3. Generate an initial integrated scheduling statistical analysis collaborative probability matrix; Step 4. Function-driven multi-group self-customized initialization; Step 5. Adaptive multi-group interactive PSO iterative optimization.

2. The self-adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 1, wherein: In Step 1, the hierarchical individual coding structure adopts a three-layer coding structure, which is, from top to bottom, the operation sequence string OS, the machine selection string MS, and the AGV selection string AS. The lengths of the coding strings in each layer are the same and are equal to the sum of all operations of all jobs.

3. The self-adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 1, characterized in that: The integrated scheduling statistical analysis collaborative probability matrix in step 2 includes a task matrix and a resource matrix where m is the number of machines and w is the number of trolleys; which is used to assist in the allocation of the decision-making operation sequence For the joint allocation of the decision-making assistance machine and the trolley; The element μ in the i-th row and j-th column of ij Represents the probability that the j-th job is assigned to the i-th gene position in the operation sequence string OS of the three-layer coding string; The element ρ in the i-th row and j=(k×h)-th column of i(k×h) Represents the probability that the k-th machine and the h-th trolley are respectively assigned to the i-th gene position in the machine selection string MS and the AGV selection string AS of the three-layer coding string.

4. The integrated scheduling optimization method for PSO flexible job-shop AGVs with adaptive multi-group interaction according to claim 1, wherein: In step 3, when generating the initial integrated scheduling statistical analysis collaborative probability matrix, formula (1) is used for initializing each element in and formula (2) is used for initializing each element in Formula (1) indicates that for all operations, the initial processing order priorities are the same; in Formula (2), MS i represents that the operation at the i-th gene position of the operation sequence string OS for the three-layer coding string is denoted as opr i and the corresponding set of optional processing machines. Initially, if k ∈ MS i , then the element ρ i(k×h) represents that the operation opr i is equally likely to be assigned to each optional processing machine k and the g-th trolley; Conversely, the probability is 0.

5. The integrated scheduling optimization method of PSO flexible job shop AGVs with adaptive multi-group interaction according to claim 1, characterized in that: Step 4 divides the population into three categories, namely, the elite population, the development population, and the exploration population; the elite population guides the search direction of the algorithm in the solution space, the development population conducts in-depth exploration around the elite population, and the exploration population avoids falling into local convergence under the guidance of the elite population; since the functional responsibilities of each type of population are different in the algorithm optimization process, a multi-type population self-customized initialization method is adopted, which is specifically as follows: Step 41. For each individual in the elite population, first randomly generate the operation sequence string OS and the AGV selection string AS of the three-layer coding string, and then select the machine with the shortest processing time for each operation in the operation sequence string OS in turn to generate the machine selection string MS; Step 42. For each individual in the exploration population and the exploitation population, initialize using the initial integrated scheduling statistical analysis collaborative probability matrix and Specifically, For each gene position \(i: 1\rightarrow n\) in the individual three - layer coding string s , based on roulette wheel sampling and , select the job number \(j\) from the \(i\)-th row matrix corresponding to the gene position \(i\), and select the combination of machine \(k\) and trolley \(h\) from the \(i\)-th row matrix; judge whether the operation of job \(j\) has exceeded the sampling threshold, that is, the total number of operations of job \(j\). If so, set all the column elements corresponding to job \(j\) in and to 0, and perform normalization processing on each row of and .

6. The self-adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 1, characterized in that: Step 5 Adaptive multi-group interactive PSO iterative optimization is specifically as follows: Step 51. Set the adaptive multi-group interaction PSO hyperparameters; including: the maximum number of algorithm iterations maxIter, the number of PSO iterations psoIter, the population size popSize, the number of individuals in the elite population Num elite , the number of individuals in the exploration population Num exploit , the number of individuals in the development population Num explore , the learning factors c1, c2, and the probability matrix update factor α; Step 52. Set the initial values and upper and lower bound thresholds of the adaptive dynamic inertia weight factors for three types of populations; including: the three types of populations each perform their own functions during the algorithm optimization process, so different populations adopt different adaptive weight parameters ω elite , ω exploit , ω explore ; To enhance the search ability of the algorithm, focus on global search in the early stage of the iteration process and gradually transition to local search in the later stage. Set the upper limit and the lower limit of the adaptive weight parameters of the three types of populations. Set and Dynamically update the adaptive weight parameters of the three types of populations using formula (3), where iter psoCurrent is the current iteration number of PSO. The adaptive weights of the three types of populations gradually decrease with the increase of the iteration number under the control of their respective thresholds; Step 53. PSO multi-group interactive optimization based on an adaptive dynamic inertia weight factor; Step 54. Individual local search based on AGVs-swap; Step 55. Determine whether the PSO iterative optimization ends? If yes, go to Step 56; if no, go to Step 53. Step 56. Update the integrated scheduling statistical analysis collaborative probability matrix; Step 57. Generate a new population by sampling based on the updated probability matrix; Step 58. Determine whether to perform adaptive multi-group interactive optimization on the current new population? If yes, go to Step 52; if no, output the optimal solution.

7. The self-adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 6, wherein: Step 53 PSO multi-group interactive optimization based on an adaptive dynamic inertia weight factor is specifically as follows: Step 1. For each type of population, generate a set of random perturbation factors respectively which are used to control the crossover and mutation of individuals respectively; Step 2. If then apply the customized mutation operator to each layer of the three-layer coding string of the current individual in the type class; Step 3. If perform customized crossover on the corresponding layers of the three-layer coding string of the current individual in the type class and the three-layer coding string of the historical optimal solution of the current individual; Step 4. If then perform customized crossover on the corresponding layers of the three-layer coding string of the current individual of type class and the three-layer coding string of the global optimal solution of multiple groups.

8. The self-adaptive multi-group interaction-based PSO flexible job-shop AGVs integrated scheduling optimization method according to claim 6, wherein: Step 54 The local search based on AGVs-swap obtains a shorter total completion time by attempting to replace the currently selected AGV for each operation, specifically as follows: Step 541. For each individual in the three types of populations, sequentially process the operation opr at the i-th gene position in the first layer OS string of the three-layer coding string i ; Step 542. For opr i , in the second-layer machine string MS and the third-layer AS string, determine the currently assigned machine m i and trolley a i , and calculate the current individual's Step 543. In the optional set of AGVs Aopr i for opr i calculate, for each vehicle b ∈ Aopr i ∧ b ≠ a i the total completion time makespan of the individual after replacing a with b i ; b ​ Step 544. Select the trolley If Replace a with trolley b i .

9. The adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 6, wherein: Step 56 Update the integrated scheduling statistical analysis collaborative probability matrix, specifically as follows: Step 561: Construct the optimal position population p based on the historical optimal positions of the three types of population individuals best ; Step 562: Based on the optimal position population p best Update and generate the task matrix of the exploration population using Equation (4) and Equation (5) and the resource matrix Step 563: Update and generate the task matrix and resource matrix of the development population based on the current entire population using Formula (6) and Formula (7). and the resource matrix In formulas (4), (5), (6) and (7), N is the total number of individuals in three types of populations, and α is the probability matrix update learning factor, which is used to control the dependence degree of the current probability matrix on the excellent genes of the historical population; and is a decision variable, which is used to count whether the job number at the i-th gene position in the operation sequence string OS of the z-th individual is the same as the job number in the j-th column of the task matrix ; is used to count whether the combination of the machine number and the AGV number at the i-th gene position in the machine selection string MS and the AGV selection string AS of the z-th individual is the same as the combination of the machine number and the AGV number in the j-th column of the resource matrix .

10. The self-adaptive multi-group interaction-based PSO flexible job shop AGVs integrated scheduling optimization method according to claim 6, wherein: Step 7 Generate a new population by sampling based on the updated probability matrix, specifically as follows: Step 71: Select the top X% of the individuals from the three types of populations as the new elite population; Step 72: Based on the task matrix and the resource matrix sample and generate a development population; Step 73: Based on the task matrix and the resource matrix sample to generate an exploration population.

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