Dynamic vehicle routing problem considering empty material distribution truck recovery in workshop

Abstract

This invention discloses a dynamic vehicle routing method considering the recovery of empty material delivery vehicles in a workshop, comprising the following steps: Step 1, establishing the objective function and constraints of a multi-objective material delivery route planning model; Step 2, solving the multi-objective material delivery route planning model using an improved NSGA-II algorithm to obtain a set of non-dominated solutions, and finding the optimal non-dominated solution to obtain the current material transportation route; Step 3, determining whether the vehicle has completed material delivery. If the vehicle has completed material delivery, the optimal empty tool recovery task that does not affect subsequent delivery tasks is dynamically inserted into the current material transportation route. This invention improves the efficiency of logistics delivery and resource utilization, can handle complex delivery and recovery tasks, and the step-by-step optimization strategy of the algorithm simplifies the complexity of the problem, making it easier to manage and optimize.

Description

Technical Field

[0001] This invention relates to the field of material distribution route planning methods, specifically a dynamic vehicle route planning method that takes into account the recovery of empty material distribution turnover vehicles in the workshop. Background Technology

[0002] In modern manufacturing, material distribution has a crucial impact on production efficiency and cost control. The recovery of empty material handling vehicles accounts for a significant proportion of operations, directly affecting distribution efficiency and vehicle utilization. With the rapid development of Industrial Internet of Things (IIoT) technology, the integration of advanced IoT devices with manufacturing technologies has become a new trend. New demand patterns combined with new information technologies place higher demands on material distribution in intelligent manufacturing environments. As industrialization accelerates and industrial capacity further increases, the use of material handling vehicles is also growing rapidly. Under the multiple pressures of resource utilization and economic efficiency, the 1:n material distribution model, using AGVs to pull a certain number of material handling vehicles to meet specific workstation needs, is widely used in actual production, especially for intermediate industrial products such as parts and raw materials, which have large production volumes and high consumption rates, resulting in relatively large material transportation demands.

[0003] Currently, the material distribution in traditional manufacturing workshops faces the following problems in both theoretical research and production practice:

[0004] (1) Currently, research on reverse logistics in material distribution mainly focuses on material recycling and waste disposal. However, in actual manufacturing workshops, empty material handling carts are a common and indispensable part of the process. These tools need to be effectively recycled after completing material transportation to reduce resource waste and improve overall efficiency. Existing research has neglected this point, which may lead to inefficiency and resource waste in actual workshop operations. To improve overall efficiency and reduce waste, research on the recycling of empty material handling tools should be strengthened.

[0005] (2) Since the material distribution problem has the characteristics of an NP-hard problem, the solution methods are currently mainly focused on heuristic and metaheuristic algorithms. In the process of solving multi-objective optimization problems, weighting is usually used to integrate many objectives and transform them into a single objective problem for easy solution. However, this approach may lead to subjectivity and one-sidedness in the results, and the conflicts and trade-offs between different objectives are difficult to quantify accurately.

[0006] (3) Traditional material distribution research mainly focuses on solving static problems, that is, once the distribution route is determined, it will not be adjusted during the entire distribution process. However, in actual production, there are often various uncertain factors that may cause the originally planned distribution route to be unable to adapt to the actual situation, and the distribution process may need to be adjusted dynamically in real time. At present, research on dynamic distribution mainly focuses on equipment failure and material shortage, and there is relatively little research on the problem of distribution route planning combined with the recovery of empty material distribution turnover vehicles. Summary of the Invention

[0007] This invention provides a dynamic vehicle path planning method that considers the recovery of empty material delivery turnover vehicles in the workshop, in order to solve the problems of existing material delivery path planning methods that ignore empty material delivery turnover vehicles, have subjective and one-sided solutions to material delivery problems, and cannot dynamically adjust the planned delivery paths.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A dynamic vehicle routing method for the recovery of empty material delivery vehicles in the workshop is considered, including the following steps:

[0010] Step 1: Analyze the multi-objective material distribution problem in the workshop and establish the objective function and constraints of the multi-objective material distribution path planning model;

[0011] Step 2: Solve the multi-objective material distribution route planning model established in Step 1 using the improved NSGA-II algorithm to obtain the non-dominated solution set, and find the optimal non-dominated solution to obtain the current material transportation route.

[0012] Step 3: Use IoT technology to monitor the status of the delivery point in real time and determine whether the vehicle has completed the material delivery. If the vehicle has completed the material delivery, select the optimal empty tooling recovery task that will not affect subsequent delivery tasks and dynamically insert it into the current material transportation path obtained in Step 2.

[0013] In further step 1, the objective function of the multi-objective material delivery route planning model is to minimize the total cost of delivery vehicle assignment f1, the total cost of route delivery f2, and the total cost of demand station time window penalty f3.

[0014] In further step 1, the constraints of the multi-objective material delivery path planning model include: each workstation is served only once and only one AGV performs the task; the maximum number of turnover carts that each AGV can pull is the set Wmax vehicles; the AGVs arriving at and leaving the workstation are the same; and the starting point and destination of the vehicles are both the distribution center.

[0015] In the further step 2, the fitness of all non-dominated solutions in the non-dominated solution set is calculated, and the non-dominated solution with the most ideal fitness value is selected as the optimal solution for the current material transportation route, thus obtaining the current material transportation route.

[0016] Furthermore, in step 3, a quadrant optimization strategy is used to select the optimal empty tooling recovery task that does not affect subsequent delivery tasks and dynamically insert it into the current material transportation path obtained in step 2.

[0017] Furthermore, the constraints when using the quadrant optimization strategy include: the number of tractor turnover vehicles after inserting a recycling task cannot exceed the maximum towing capacity constraint, and the inserted recycling task must not affect the normal delivery execution of subsequent delivery tasks.

[0018] This invention proposes a material delivery strategy that considers empty material delivery turnover vehicles in a workshop. First, the material delivery process combining tractor-guided vehicles (AGVs) with material delivery turnover vehicles is analyzed, taking into account the material delivery needs in a flexible workshop and the need to recover empty material delivery turnover vehicles. Combining the capacity constraints of specific material delivery containers, a multi-objective material delivery path planning model is established, with the optimization objective of minimizing the total cost of vehicle assignment, the total cost of route delivery, and the total cost of time window penalties for demand workstations during the workshop material delivery process.

[0019] To solve this model, this invention employs a heuristic step-by-step optimization algorithm. First, an improved Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used to generate a multi-objective delivery task sequence. Then, a quadrant optimization strategy is used to dynamically insert retrieval tasks into the existing delivery sequence. Compared with existing technologies, this invention has the following advantages:

[0020] 1. By comprehensively considering material distribution and empty material distribution vehicle recycling, the efficiency of logistics distribution and resource utilization has been improved.

[0021] 2. By using the improved NSGA-II algorithm and quadrant optimization strategy, an effective multi-objective optimization solution is provided, which can handle complex delivery and recycling tasks.

[0022] 3. The step-by-step optimization strategy of the algorithm simplifies the complexity of the problem, making it easier to manage and optimize. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method according to an embodiment of the present invention.

[0024] Figure 2 This is a workshop layout diagram in the experimental example of this invention.

[0025] Figure 3 This is a comparison chart of the minimum values ​​of the normalized fitness function in this practical experimental example.

[0026] Figure 4 This is a comparison chart of the minimum path cost in this practical experimental example.

[0027] Figure 5 This is a comparison of the minimum penalty cost in this practical experimental example. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] like Figure 1 As shown, this embodiment discloses a dynamic vehicle routing method that considers the recovery of empty material delivery turnover vehicles in the workshop, including the following steps:

[0030] Step 1: Analyze the multi-objective material distribution problem in the workshop and establish the objective function and constraints of the multi-objective material distribution path planning model.

[0031] In this embodiment, the multi-objective material distribution problem in the workshop is analyzed, and the following assumptions are made:

[0032] (1) There is only one distribution center in the workshop, and the starting and ending points of the traction material turnover vehicle are both the distribution center.

[0033] (2) Each detachable material cart is identical, and the starting, stopping, and collision of the carts are negligible, and the driving speed is constant.

[0034] (3) The material demand of each workstation shall not exceed the maximum loading capacity of a detachable material turnover vehicle. When the turnover vehicle is empty, a corresponding empty material delivery turnover vehicle recycling task shall be generated.

[0035] (4) Material requirements, distribution center and workstation coordinates are known, and all nodes in the path can be connected to each other.

[0036] (5) The needs of each workstation cannot be split. Each material delivery vehicle is only responsible for the material delivery needs of one workstation.

[0037] (6) Empty material delivery turnover vehicle recycling tasks are collected and uploaded through the logic controller of the workstation, and the material system can receive the generated recycling tasks in a timely and stable manner.

[0038] In this embodiment, the parameters and decision variables involved in the multi-objective material delivery route planning model to be constructed are shown in Table 1:

[0039] Table 1. Parameters and Decision Variables

[0040]

[0041]

[0042] Based on the above assumptions, the objective function of the multi-objective material delivery route planning model established in this embodiment aims to minimize the total cost of delivery vehicle assignment f1, the total cost of route delivery f2, and the total cost of demand station time window penalty f3, where:

[0043] The total cost of dispatching delivery vehicles, f1, is the sum of the number of AGV deliveries multiplied by the fixed cost per delivery, as shown in formula (1):

[0044]

[0045] The total route delivery cost f2 is the total travel distance of the AGV during the delivery process multiplied by the route cost per unit length, as shown in formula (2):

[0046]

[0047] The total penalty cost f3 for the time window of the demand station is the sum of the penalty costs for each demand station, as shown in formula (3):

[0048]

[0049] Therefore, the objective function of the multi-objective material distribution route planning model established in this embodiment is shown in formula (4):

[0050] F={minf1∪minf2∪minf3} (4)

[0051] Furthermore, based on the above assumptions, this embodiment also establishes the constraints, penalty factors, and decision variable attributes of the objective function of the multi-objective material distribution route planning model, as shown in formulas (5)-(11):

[0052]

[0053]

[0054] In formulas (5)-(11), formula (5) indicates that each workstation is served only once and only one AGV performs the task; formula (6) indicates that the maximum number of turnover carts that each AGV can tow is W. max Each vehicle departs from the distribution center and can respond to a maximum of W vehicles per trip. max One delivery demand; Formula (7) indicates that the trolleys arriving at and leaving the workstation are the same; Formula (8) indicates that the vehicle's starting point and destination are both the distribution center; Formula (9) indicates that the materials are in LT i Arriving at the workstation after a certain time, the penalty factor is β. Formulas (10) and (11) are the attributes of the decision variables.

[0055] In this embodiment, the constraints of the multi-objective material delivery path planning model include: each workstation is served only once and only one AGV performs the task; the maximum number of turnover AGVs that each AGV can pull is the set Wmax vehicles; the AGVs arriving at and leaving the workstation are the same; and the starting point and destination of the vehicles are both the distribution center.

[0056] Step 2: Solve the multi-objective material distribution route planning model established in Step 1 using the improved NSGA-II algorithm to obtain the non-dominated solution set, and find the optimal non-dominated solution to obtain the current material transportation route.

[0057] In this embodiment, the improved NSGA-II algorithm process is as follows:

[0058] a. Encoding and Decoding: The encoding process is a crucial step in solving the algorithm. The final output of the model is the material delivery sequence of different AGVs. Because it is necessary to consider the situation of multiple vehicles delivering simultaneously, as well as the constraint of the number of service stations for each delivery vehicle, natural number encoding was chosen. The chromosome encoding structure is as follows:

[0059] 0,N i1 N i2 ,...N io ,0,N j1 N j2 ,...N jp ,0,...0

[0060] Where, N jp —The p-th delivery task of the j-th vehicle is to deliver to work site N. jp Perform material distribution tasks; 0—Distribution Center.

[0061] b. Population Initialization: An initial population is determined using a random generation strategy. Due to the constraint on the number of traction vehicles, each chromosome in the initial population must be assigned a workstation to a vehicle. The purpose of this step is to ensure that each chromosome clearly reflects the required workstations and their respective delivery order, while satisfying the vehicle allocation constraints. This method provides a diverse and problem-constrained starting point for subsequent iterations of the algorithm. The vehicle allocation steps for the initial population chromosomes are as follows:

[0062] b1): Randomly generate a chromosome individual containing all required workstations.

[0063] b2): Considering the constraint of the maximum number of traction turnover vehicles, workstations on the chromosome are allocated to AGVs using different probability selection methods. The probability selection strategy here is to increase the probability of each vehicle being assigned to more demand workstations. That is, when the maximum number of traction turnover vehicles is set to 4, each AGV can traction a maximum of 4 material turnover vehicles to different demand workstations to respond to demand tasks. A roulette wheel strategy is used to select the number of demand workstations assigned to each vehicle: the probability of being assigned to 1 workstation is 1 / 10, 2 workstations is 2 / 10, 3 workstations is 3 / 10, and 4 workstations is 4 / 10. After the demand workstations for the first vehicle are allocated, the remaining workstations are allocated.

[0064] b3): Repeat the above operation until the initial population size is reached.

[0065] c. Crossover Strategy: A novel uneven crossover strategy was designed to preserve the superior sub-path information of the parents and generate differentiated individuals in the population. The specific operation is as follows:

[0066] c1): Randomly select a sub-path on the parent individual.

[0067] c2): The selected sub-segments are moved forward, thereby generating some differentiated individuals in the population. This helps prevent the algorithm from getting stuck in local optima and may allow it to find better solutions in the search space.

[0068] c3): For offspring chromosome 1, firstly, subpath A from parent chromosome 1 is selected as a component of offspring chromosome 1. Next, codes not in subpath A are selected from parent chromosome 2 and added to the end of subpath A in the original order of parent chromosome 2. Finally, code 0 is appended to the tail of the offspring chromosome.

[0069] c4): For chromosome 1, considering the constraint of the number of turnover vehicles in the positions following sub-path A, fill the code 0 twice using a roulette wheel workstation allocation strategy to obtain 2 offspring chromosomes. Calculate the dominance of the two individuals obtained, select the better solution to enter the offspring population, and randomly select an individual to enter the offspring population when no choice can be made in the non-dominance case. Similarly, offspring chromosome 2 is obtained.

[0070] d. Mutation Strategy: To enhance the search capability of individuals, a two-point exchange mutation strategy is implemented on chromosomes. A random number is generated, and it is checked whether the number is lower than the preset mutation probability. If the condition is met, the mutation operation is performed. Simultaneously, the validity of the mutated chromosome individual must be guaranteed. If the mutated chromosome is an infeasible solution, the mutation is repeated until two valid chromosomes are generated. From the two generated mutated chromosomes and the original individual, an elite retention strategy is used to select one as the offspring individual.

[0071] e. Selection Strategy: A combination of hierarchical selection and elite retention strategies is used to prevent premature convergence and improve the quality of the global search. Hierarchical selection, through proportional selection based on fitness values, effectively prevents premature convergence. Elite retention, by directly selecting the best individuals from the current population for the next generation, ensures the algorithm maintains efficient optimization capabilities. In the early stages of iteration, hierarchical selection is primarily used to promote population diversity and avoid premature convergence, selecting the best-performing individuals from each non-dominated level for the next generation. In the later stages of iteration, the elite retention strategy is adopted. This not only helps expand the search space and accelerate the search speed but also continuously improves the quality of the global search during iteration. Through this dynamic adjustment of the strategy, the algorithm can effectively balance local and global searches while maintaining solution diversity, thereby increasing the probability of finding the global optimum.

[0072] In this embodiment, after obtaining all non-dominated solutions, the fitness of all non-dominated solutions in the non-dominated solution set is calculated, and the non-dominated solution with the most ideal fitness value is selected as the optimal solution for the current material transportation route, that is, the current material transportation route is obtained. The fitness function is shown in formula (12):

[0073] F(x)=n1f1(x)+n2f2(x)+n3f3(x) (12)

[0074] In formula (12), n i The corresponding weighting coefficients for the objective function, f i (x) represents the objective function value corresponding to the current solution.

[0075] Step 3: Utilize IoT technology to monitor the status of the delivery point in real time and determine whether the vehicle has completed material delivery. If the vehicle has completed material delivery, use a quadrant optimization strategy to select the optimal empty tooling recovery task t that will not affect subsequent delivery tasks and dynamically insert it into the current material transportation path obtained in Step 2. The constraints of the quadrant optimization strategy include that the number of tractor turnover vehicles after inserting the recovery task cannot exceed the maximum tractable number constraint, and the inserted recovery task must not affect the normal delivery execution of subsequent delivery tasks, as shown in formulas (13)-(15):

[0076] w i ≤w max -1 (13)

[0077] T i-1 +T pt ≤min{T i ,LT i} (14)

[0078] T pt =[(di-1,t +d t,i )-d i-1,i ] / v (15)

[0079] Formula (13) indicates that the number of tractor turnover vehicles after inserting a recycling task cannot exceed the maximum towing quantity constraint; Formulas (14) and (15) indicate that the inserted recycling task shall not affect the normal delivery execution of subsequent delivery tasks.

[0080] In this embodiment, the quadrant optimization strategy aims to find an ideal time and location to insert a real-time generated recycling task without affecting the AGV's current delivery task. This embodiment divides the material delivery area into several quadrants, each evaluated based on its geographical location and the remaining material demand to be delivered. Through this method, this embodiment can determine which recycling task is most suitable to insert into the current AGV's delivery path after the delivery task is completed. The application of this path adjustment strategy helps this embodiment maximize the efficiency of empty material delivery trolley recycling while ensuring the delivery task is completed.

[0081] The performance of the method in this embodiment is illustrated by the following experiments.

[0082] To verify the effectiveness of the method described in this embodiment of the invention, this experimental example conducted a simulation experiment using a real-world example of a digital workshop in a manufacturing enterprise.

[0083] The experiment included a control group that combined the standard NSGA-II algorithm with the current pickup and delivery strategy. Specifically, after a certain number of retrieval tasks accumulated, a dedicated AGV was dispatched from the distribution center to perform empty AGV retrieval tasks. The standard NSGA-II algorithm was used with the same population size and number of iterations as the improved algorithm. Experimental data demonstrates the effectiveness of this invention in improving delivery efficiency, reducing costs, increasing AGV utilization, and adapting to dynamic changes.

[0084] like Figure 2 As shown, the workshop is 165m long and 85m wide, with a total area of ​​14025m². 2The delivery needs and time windows within the workshop are known from the upper-level factory MOM system. The material distribution center within the workshop is located in the southwest direction. Starting from the distribution center, AGVs (Automated Guided Vehicles) tow a certain number of turnover carts to deliver materials to the 25 workstations within the workshop. When a cart reaches a corresponding workstation, it leaves the turnover cart containing the required materials beside that workstation, and the cart tows other turnover carts to continue performing other material delivery tasks. After a workstation finishes loading materials, an empty cart retrieval task is generated for that workstation, requiring AGVs to tow the empty cart back to the material distribution center. The coordinates of the distribution center and workstations are shown in Table 2. Based on the company's actual situation, the following values ​​are assigned to each delivery parameter: C1 = 10 yuan / trip, C2 = 1 yuan / meter, C3 = 100 yuan / minute, v = 40 meters / minute, W = 4 carts.

[0085] like Figures 3-5 As shown, during the entire iterative process of generating the initial demand delivery path, the improved strategy converged to a local optimum around generation 50. Then, it escaped the local optimum during generations 50-100, and began to converge rapidly from generation 150, gradually converging to the optimum between generations 200-300. The large fluctuations in the early stages of the improved strategy are because the first 150 generations used hierarchical selection to choose offspring individuals, increasing population diversity for better global search. As iterations progressed, the tendency to select offspring individuals became more greedy, accelerating the convergence speed.

[0086] As shown in Table 2, the planar coordinates of each workstation and distribution center, along with the latest delivery time, serve as the initial conditions for the solution. Table 2 is as follows:

[0087] Table 2 Distribution Center and Workstation Information

[0088]

[0089]

[0090] The solution results are shown in Table 3, where 0 represents a material distribution center and * represents a recycling task. Clearly, the improved strategy algorithm yields better results and higher quality, effectively addressing the workshop material distribution optimization problem that considers the recycling of material transport tools. This result not only demonstrates the adaptability and flexibility of the step-by-step multi-objective optimization solution method based on the improved NSGA-II algorithm for dynamic task processing but also reveals the effectiveness of the improved strategy in cost control and resource allocation, thus providing decision-makers with more options. Table 3 is as follows:

[0091] Table 3 Summary of Solution Results

[0092]

[0093]

[0094] Table 4 shows the comparison before and after optimization. Considering the reduction in vehicle travel path cost and the number of vehicles dispatched, the number of vehicles dispatched to complete all delivery and retrieval tasks decreased from 15 to 8, a reduction of 46.7%; the average number of tasks handled by each towing AGV increased from 3.3 to 6.2; and the vehicle travel path cost decreased from 4309.05 to 3541.86, a reduction of 17.8%. This effectively controlled material delivery costs and delivery time, reduced the investment in towing AGVs, and greatly improved vehicle utilization. The optimized late-arrival penalty cost for workstations was 59.74, a reduction of 69% compared to the previous late-arrival penalty cost of 197.73. This effectively ensured timely response to material needs while balancing the total cost. Table 4 is as follows:

[0095] Table 4 Comparison of results before and after improvement

[0096]

[0097] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0098] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A dynamic vehicle routing method considering the recovery of empty material delivery vehicles in the workshop, characterized in that, Includes the following steps: Step 1: Analyze the multi-objective material distribution problem in the workshop and establish the objective function and constraints of the multi-objective material distribution path planning model; Step 2: Solve the multi-objective material distribution route planning model established in Step 1 using the improved NSGA-II algorithm to obtain the non-dominated solution set, and find the optimal non-dominated solution to obtain the current material transportation route. Step 3: Use IoT technology to monitor the status of the delivery point in real time and determine whether the vehicle has completed the material delivery. If the vehicle has completed the material delivery, select the optimal empty tooling recovery task that will not affect the subsequent delivery tasks and dynamically insert it into the current material transportation path obtained in Step 2. The improved NSGA-II algorithm process is as follows: a. Encoding and Decoding: The encoding process is a crucial step in solving the algorithm. The final output of the model is the material delivery sequence of different AGVs. Because it is necessary to consider the situation of multiple vehicles delivering simultaneously, as well as the constraint of the number of service stations for the delivery vehicles, natural number encoding was chosen. The chromosome encoding structure is as follows: 0,N i1 ,N i2 ,...N io ,0,N j1 ,N j2 ,...N jp ,0,...0 Where, N jp —The p-th delivery task of the j-th vehicle is to deliver to work site N. jp Perform material distribution tasks; 0—Distribution Center; b. Population Initialization: An initial population is determined using a random generation strategy. Due to the constraint on the number of traction vehicles, each chromosome in the initial population must be assigned a workstation to a vehicle. The purpose of this step is to ensure that each chromosome clearly reflects the required workstations and their respective delivery order, while satisfying the vehicle allocation constraints. This method provides a diverse and problem-constrained starting point for subsequent iterations of the algorithm. The vehicle allocation steps for the initial population chromosomes are as follows: b1): Randomly generate a chromosome containing all required workstations; b2): Considering the constraint of the maximum number of traction turnover vehicles, the workstations on the chromosome are allocated to AGVs through different probability selections. The probability selection strategy is to make the vehicle have a higher probability of being allocated to more demand workstations. That is, when the maximum number of traction turnover vehicles is set to 4, each AGV can pull up to 4 material turnover vehicles to different demand workstations to respond to demand tasks. The number of demand workstations allocated to the vehicle is selected by a roulette wheel strategy. The probability of being allocated to 1 workstation is 1 / 10, the probability of 2 workstations is 2 / 10, the probability of 3 workstations is 3 / 10, and the probability of 4 workstations is 4 / 10. After the demand workstations of the first vehicle are allocated, all the remaining workstations are allocated. b3): Repeat the above operation until the initial population size is reached; c. Crossover Strategy: A novel uneven crossover strategy was designed to preserve the superior sub-path information of the parents and generate differentiated individuals in the population. The specific operation is as follows: c1): Randomly select a sub-path on the parent individual; c2): The selected sub-segments are moved forward, thereby generating some differentiated individuals in the population. This helps prevent the algorithm from getting stuck in local optima and may find a better solution in the search space. c3): For offspring chromosome 1, firstly select subpath A from parent chromosome 1 as a component of offspring chromosome 1. Then, select those codes from parent chromosome 2 that are not in subpath A and add them to the end of subpath A in the original order of parent chromosome 2. Finally, append code 0 to the tail of the offspring chromosome. c4): For chromosome 1, in the position after sub-path A, considering the constraint of the number of turnover vehicles, fill the code 0 twice through the work station allocation strategy of roulette wheel to obtain 2 offspring chromosomes. Calculate the dominance of the two individuals obtained, select the better solution to enter the offspring population, and randomly select an individual to enter the offspring population when the non-dominance situation cannot make a choice. Similarly, offspring chromosome 2 is obtained. d. Mutation Strategy: To enhance the search ability of individuals, a two-point exchange mutation strategy is implemented on chromosomes. A random number is generated and checked whether the number is lower than the preset mutation probability. If the condition is met, the mutation operation is performed. At the same time, it is necessary to ensure the legality of the individual after mutation. If the mutated chromosome is an infeasible solution, the mutation is performed on the chromosome again until two valid chromosomes are generated. From the two generated mutated chromosomes and the original individual, an elite retention strategy is used to select one as the offspring individual. e. Selection Strategy: Combining hierarchical selection and elite retention strategies to prevent premature convergence and improve the quality of global search. Hierarchical selection, by selecting individuals based on fitness values, effectively prevents premature convergence. Elite retention, by directly selecting the best individuals from the current population for the next generation, ensures the algorithm maintains efficient optimization capabilities. In the early stages of iteration, hierarchical selection is primarily used to promote population diversity and avoid premature convergence. In each non-dominated level, the best-performing individuals are selected for the next generation. In the later stages of iteration, elite retention is adopted. This not only helps to expand the search space and accelerate the search speed but also continuously improves the quality of global search during iteration. Through this dynamic adjustment of the strategy, the algorithm can effectively balance local and global searches while maintaining solution diversity, thereby increasing the probability of finding the global optimum. In step 3, a quadrant optimization strategy is used to select the optimal empty tooling recovery task t that does not affect subsequent delivery tasks and dynamically insert it into the current material transportation path obtained in step 2.

2. The dynamic vehicle routing planning method considering the recovery of empty material delivery vehicles in the workshop according to claim 1, characterized in that, In step 1, the objective function of the multi-objective material delivery route planning model is to minimize the total cost of delivery vehicle assignment f1, the total cost of route delivery f2, and the total cost of demand station time window penalty f3.

3. The dynamic vehicle routing method considering the recovery of empty material delivery vehicles in the workshop according to claim 1, characterized in that, In step 1, the constraints of the multi-objective material delivery path planning model include: each workstation is served only once and only one AGV performs the task; the maximum number of turnover carts that each AGV can pull is the set Wmax vehicles; the AGVs arriving at and leaving the workstation are the same; and the starting point and destination of the vehicles are both the distribution center.

4. The dynamic vehicle routing method considering the recovery of empty material delivery vehicles in the workshop according to claim 1, characterized in that, In step 2, the fitness of all non-dominated solutions in the non-dominated solution set is calculated, and the non-dominated solution with the most ideal fitness value is selected as the optimal solution for the current material transportation route, thus obtaining the current material transportation route.

5. The dynamic vehicle routing method considering the recovery of empty material delivery vehicles in the workshop according to claim 1, characterized in that, The constraints of the quadrant optimization strategy include that the number of tractor turnover vehicles after inserting a recycling task cannot exceed the maximum towing capacity, and the inserted recycling task must not affect the normal delivery execution of subsequent delivery tasks, as shown in formulas (13)-(15): (13) (14) (15) Formula (13) indicates that the number of tractor turnover vehicles after inserting a recycling task cannot exceed the maximum towing limit; Formulas (14) and (15) indicate that the inserted recycling task must not affect the normal delivery execution of subsequent delivery tasks; where: This indicates the maximum number of transfer vehicles that each AGV can tow. This indicates the maximum number of transfer vehicles that each AGV can tow. This indicates the material delivery time at workstation i. This indicates the latest material requirement time for workstation i. This represents the additional transport time if a tooling recycling task t is inserted between workstation i-1 and workstation i. This represents the distance between workstation i-1 and the workstation where the tooling recycling task t is located if a tooling recycling task t is inserted between workstation i-1 and workstation i. This represents the distance between the workstation where the tooling recycling task t is located and workstation i if a tooling recycling task t is inserted between workstation i-1 and workstation i. This indicates the speed at which the delivery vehicle is traveling.

Images