Robust vehicle path planning method with uncertain travel time based on multi-population evolutionary algorithm

Abstract

The invention discloses a robust vehicle path planning method with uncertain travel time based on a multi-population evolutionary algorithm. The method comprises the following steps: 1, constructing a multi-objective optimization model for vehicle path planning; 2, randomly initializing a population and carrying out clustering grouping to divide the population into a plurality of sub-populations; 3, iteratively optimizing a plurality of sub-populations based on a multi-population coevolution framework, and executing local search operation on the sub-populations until a stop condition is met, so as to obtain a path planning optimal scheme set and a robust scheme set; and 4, executing a crossover operator on the optimal path planning scheme set and the robust scheme set, and outputting a final path planning scheme with both robustness and optimality. According to the method, the problem of vehicle path planning with uncertain travel time can be solved, and shorter total travel time can be obtained while the minimum number of used vehicles is found, so that the transportation efficiency can be improved, and the transportation cost can be reduced.

Description

Technical Field

[0001] The invention belongs to the field of transportation, and in particular is a robust vehicle path planning method with uncertain travel time based on a multi-population evolutionary algorithm. Background Art

[0002] The vehicle routing problem refers to a group of vehicles that need to find a set of economical and efficient routes to meet the needs of different customers. It is a well-known NP-hard combinatorial problem in logistics management, vehicle scheduling, and transportation. The travel time between two customers in the vehicle service route is often uncertain, so the vehicle routing problem is transformed into a vehicle routing planning problem with uncertain travel time.

[0003] Among existing technologies, evolutionary algorithms are widely used to solve vehicle path planning problems. Due to their slow speed, evolutionary algorithms are usually combined with local search to accelerate convergence. However, the running time is still long, and it is not possible to quickly and efficiently search for the optimal path planning solution. In addition, the research on robust vehicle path planning considering uncertain travel time is relatively limited. In the real world, travel time is usually uncertain and easily affected by weather, traffic congestion, etc., resulting in the vehicle path planning solution finally obtained cannot be applied in practice. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a robust vehicle path planning method with uncertain travel time based on a multi-population evolutionary algorithm, in order to find the minimum number of vehicles used and a shorter total driving time, thereby improving transportation efficiency and reducing transportation costs.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The invention discloses a robust vehicle path planning method with uncertain travel time based on a multi-population evolutionary algorithm, which is applied to a single central warehouse, client nodes and In the distribution service area, a central warehouse node is defined as and The node set consists of client nodes , Indicates nodes; the path set between each node is recorded as ;in, Indicates any Nodes and Nodes The path between the vehicles Nodes Arrive at Nodes The travel time between ; Assume that all vehicles are based on warehouse nodes The vehicle path planning method is performed in the following steps:

[0007] Step 1: Create A vehicle path planning model for a discrete scenario, including objective functions and constraints;

[0008] Step 1.1: Use equations (1) and (2) to establish the objective function of vehicle path planning with uncertain travel time: :

[0009] (1)

[0010] st , (2)

[0011] In formula (1), represents the upper limit of all travel times, Indicates the number of vehicles;

[0012] In formula (2), Indicates The travel time of the path for each discrete scenario, Represents all paths, Represents the total number of discrete scenarios;

[0013] Step 1.2: Use equations (3) to (9) to construct the constraints of the vehicle path planning model:

[0014] (3)

[0015] (4)

[0016] (5)

[0017] (6)

[0018] (7)

[0019] (8)

[0020] (9)

[0021] In formula (3) to formula (9), Indicates that the vehicle passes through the warehouse node To Nodes The path between Indicates that the vehicle passes through Nodes To the warehouse node The path between Indicates that the vehicle passes through Nodes To Nodes The path between Indicates that the vehicle passes through Nodes To Nodes The path between and Respectively indicate that the vehicle arrives at Nodes and Nodes Vehicle load at the time; Indicates the maximum capacity of each transport vehicle; Indicates Nodes the quantity of goods delivered or demanded; Indicates Nodes the quantity of goods delivered or demanded; Indicates whether the vehicle has passed the Nodes To Nodes If the path between , then let , otherwise, let ; Represents an integer;

[0022] Step 2: Initialize the size Population ; Each individual in the population consists of the subscript codes of the customer nodes and warehouse nodes visited and served by the vehicle; and according to the maximum load of the transport vehicle, when the customer's demand reaches the maximum load, 0 is inserted in the subscript sequence as a separator for different routes;

[0023] Step 2.1: According to the travel time of each individual, Perform clustering and obtain Subpopulation ,in represents the sth subpopulation, let The size is ;

[0024] Step 2.2, Initialization ;

[0025] Step 2.3: Define the current number of iterations , and initialize ; Set the maximum number of iterations to ;

[0026] Step 2.4: Calculate Daidi Subpopulation middle The objective function value of each individual in the vehicle path planning model;

[0027] Step 2.5: According to Daidi Subpopulation The upper limit of all travel times for each individual and the number of vehicles in the calculation Daidi Subpopulation The non-dominated ranking and crowding distance of each individual in the ; thus, the binary tournament selection mechanism is used to select an individual with a better ranking from any two individuals as a parent individual, thereby constructing The first generation consists of Daidi A mating pool;

[0028] Step 2.6: Daidi Each mating pool selects two parent individuals in turn and executes the crossover operator and mutation operator to generate the first Daidi Subpopulation The two diversity offspring individuals of The first generation of diverse offspring individuals Daidi Diversity population ;

[0029] Step 2.7: Perform a local search to obtain The first generation of convergent offspring individuals Generation Convergence Population ;

[0030] Step 2.8: and Combined, the size is No. Daidi Temporary population ;

[0031] Step 2.9: Calculate Daidi Temporary population The objective function value of each individual in the vehicle path planning model;

[0032] Step 2.10: After each individual in the non-dominated order is sorted, the individuals of each level are selected in order from high to low non-dominated levels until the total number of individuals in all levels selected reaches Until the total number of individuals exceeds , then the crowding distance of the individuals in the selected current level is calculated, and the individuals with the smallest crowding distance are deleted, so that the total number of individuals in all levels is , and constitute the Daidi Subpopulation ;

[0033] Step 2.11: When The individuals that are the optimal path planning solutions in all scenarios constitute the path robust solution set Otherwise, execute step 2.12; where, represents crossing algebra;

[0034] Step 2.12: Assign to ,judge Is it established? If established, then Daidi Subpopulation The individual with the highest dominance rank in the non-dominant group is the Subpopulation The optimal path planning solution ; Otherwise, return to step 2.4 and execute sequentially;

[0035] Step 2.13: Assign to Then return to step 2.3 and execute sequentially until So far, we get Subpopulation The optimal path planning solution ;

[0036] Step 2.14: From Delete the same optimal path planning solutions from the set to obtain the optimal path planning solution set ;right and After executing the crossover operator, the balanced final path planning solution is obtained .

[0037] The robust vehicle path planning method with uncertain travel time based on multi-population evolutionary algorithm of the present invention is also characterized in that the local search in step 2.7 is performed according to the following process:

[0038] Initialize a random integer ;

[0039] like , then middle Individuals perform a double-line neighborhood exchange operation to obtain convergent offspring individuals:

[0040] Any individual randomly selects two routes from its own customer nodes, and then judges in turn whether the current customer node on the first route is a neighboring customer node with the customer node on the second route. If so, the two customer nodes are exchanged under the condition of satisfying the maximum capacity of the vehicle, and the total driving time after the exchange is calculated to be less than the total driving time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next customer on the first route is judged and calculated until all customer nodes on the first route are traversed, thereby obtaining a convergent child individual;

[0041] like , then middle Individuals perform adjacent node exchange operations to obtain convergent offspring individuals:

[0042] Any individual in the algorithm randomly selects a route from its own customer nodes, then exchanges the positions of two adjacent customer nodes on the selected route, and calculates whether the total travel time after the exchange is shorter than the total travel time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next pair of adjacent customer nodes on the first route is judged until all customer nodes on the selected route are traversed, thereby obtaining a convergent child individual;

[0043] like , then middle Individuals perform neighborhood insertion operations to obtain convergent offspring individuals:

[0044] Any individual randomly selects two routes from its own client node, and then determines the first route in turn. Is the first customer node a neighboring customer node of the second route? If so, insert the first customer node after the neighboring customer node while satisfying the maximum vehicle capacity. customer nodes, and calculate whether the total travel time after insertion is shorter than the total travel time without insertion. If so, the inserted individual is taken as a convergent child individual; otherwise, the first individual on the first route is The process continues until all customer nodes on the first route are traversed, thereby obtaining convergent child individuals.

[0045] like , then middle Individuals perform non-neighbor node exchange operations to obtain convergent offspring individuals:

[0046] Any individual in the network randomly selects a route from its own client node, and then The customer nodes are connected to the The positions of the first customer node to the last customer node are exchanged respectively, and the minimum value of the total travel time after each exchange is calculated to be shorter than the total travel time without exchange. If the exchange individual corresponding to the minimum value of the total travel time is used as a convergent child individual; otherwise, continue to exchange the first customer node on the first route. The process continues until all customer nodes on the selected route are traversed, thereby obtaining convergent offspring individuals.

[0047] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the robust vehicle path planning method, and the processor is configured to execute the program stored in the memory.

[0048] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the robust vehicle path planning method when the computer program is run by a processor.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. The present invention divides the population into multiple sub-populations through a clustering method, and each sub-population has a different distribution in the decision space. This multi-population strategy enhances diversity, avoids the limitations of a single optimization direction, and can explore the solution space more comprehensively. This effectively improves the search efficiency and can find multiple potential optimal solutions in a shorter time. At the same time, since each sub-population focuses on different travel time scenarios and can be optimized for specific time periods or traffic conditions, the robustness of the algorithm under uncertainty conditions is significantly improved, making the final path planning solution more practical.

[0051] 2. In the late stage of evolution, the present invention introduces the search process of robust solutions, and finally obtains the optimal solution set and the robust solution set, and balances them under uncertainty. This method can maintain the optimality and robustness of path planning in all scenarios. This balancing mechanism not only ensures the reliability of the solution in the worst scenario, but also minimizes the total driving time and cost, and improves the practical application value of the algorithm, especially in the face of uncontrollable factors such as traffic congestion and weather changes.

[0052] 3. The present invention proposes four local search operators in the multi-population evolutionary algorithm. Although the prior art has combined the evolutionary algorithm with the local search, the present invention makes the local search more coordinated with the global optimization process by introducing the multi-population strategy and the robust solution balancing mechanism. The local search accelerates the convergence of the algorithm, while the multi-population strategy ensures that the path planning method will not fall into the local optimum. This combination overcomes the computational bottleneck of the traditional evolutionary algorithm in large-scale complex problems, significantly shortens the computational time of path planning, and ensures the global optimality and robustness of the final solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a local search strategy diagram of the method of the present invention;

[0054] Figure 2 is a flow chart of the method of the present invention;

[0055] Figure 3 This is an example of coding of the method of the present invention. DETAILED DESCRIPTION

[0056] In this embodiment, a robust vehicle path planning method based on a multi-population evolutionary algorithm with uncertain travel time is applied to a single central warehouse, client nodes and The distribution service area consists of transport vehicles with capacity characteristics. In the distribution service area, a central warehouse node is defined. and The node set consists of client nodes , Indicates nodes; the path set between each node is recorded as ;in, Indicates any Nodes and Nodes The path between the vehicles Nodes Arrive at Nodes The travel time between ; Assume that all vehicles are based on warehouse nodes As the starting point and end point; Figure 2 As shown, the vehicle path planning method is carried out in the following steps:

[0057] Step 1: Create A vehicle path planning model for a discrete scenario, including objective functions and constraints;

[0058] Step 1.1: Use equations (1) and (2) to establish the objective function of vehicle path planning with uncertain travel time: :

[0059] (1)

[0060] st , (2)

[0061] In formula (1), represents the upper limit of all travel times, Indicates the number of vehicles;

[0062] In formula (2), Indicates The travel time of the path for each discrete scenario, Represents all paths, Represents the total number of discrete scenarios;

[0063] Scenarios can be understood as "different possible situations" or "various possible situations". The travel time between each pair of customer nodes is different in different scenarios; for example, in one scenario, referring to Table 1, there may be smooth traffic and a short travel time; while in another scenario, referring to Table 2, there may be traffic jams and a long travel time. The algorithm takes these different scenarios into consideration to ensure that the final path planning solution performs as well as possible in all possible situations.

[0064] Tables 1 and 2 record the travel time between customers in two different scenarios. .

[0065] Table 1 Scenario a

[0066]

[0067] Table 2 Scenario b

[0068]

[0069] Step 1.2: Use equations (3) to (9) to construct the constraints of the vehicle path planning model:

[0070] (3)

[0071] (4)

[0072] (5)

[0073] (6)

[0074] (7)

[0075] (8)

[0076] (9)

[0077] In formula (3) to formula (9), Indicates that the vehicle passes through the warehouse node To Nodes The path between Indicates that the vehicle passes through Nodes To the warehouse node The path between Indicates that the vehicle passes through Nodes To Nodes The path between Indicates that the vehicle passes through Nodes To Nodes The path between and Respectively indicate that the vehicle arrives at Nodes and Nodes Vehicle load at the time; Indicates the maximum capacity of each transport vehicle; Indicates Nodes the quantity of goods delivered or demanded; Indicates Nodes the quantity of goods delivered or demanded; Indicates whether the vehicle has passed Nodes To Nodes If the path between , then let , otherwise, let ; Represents an integer;

[0078] Formula (3) is related to the depot node, ensuring that the node leaves or returns to the warehouse The number of vehicles cannot exceed the total number of vehicles ;

[0079] Equations (4) and (5) prevent each route from looping; vehicles depart from and return to the same warehouse node ;

[0080] The inequality in (6) is used to eliminate subroutes;

[0081] Formula (7) ensures the feasibility of the solution according to the capacity of each vehicle; Nodes The quantity of goods delivered or required No more than the vehicle reaches Nodes Vehicle load at ; and vehicle load Cannot be more than the maximum capacity of the transport vehicle ;

[0082] Formula (8) and Formula (9) ensure the integrity of decision variables;

[0083] Step 2: Initialize the size Population ; Each individual in the population consists of the subscript codes of the customer nodes and warehouse nodes visited and served by the vehicle; and according to the maximum load of the transport vehicle, when the customer's demand reaches the maximum load, 0 is inserted in the subscript sequence as a separator for different routes;

[0084] For example, the decision variables of the three individuals are initialized as [1,4,2,5,3,6], [4,3,2,5,1,6], [1,2,3,4,5,6], and then 0 is inserted according to the maximum load of the vehicle. In the first individual, the vehicle cannot continue to carry the customer's needs after carrying the customer, so 0 is inserted after 2 as a path separator. After inserting 0, the final decision variables of the five individuals are [1,4,2,0,5,3,6], [4,3,0,2,5,0,1,6], [1,2,3,0,4,5,6].

[0085] An individual can be represented by a chromosome, representing a complete solution, such as Figure 3 As shown in Figure 1. The solution consists of many vehicles and routes, allowing each vehicle to visit some customer nodes starting from and ending at the parking lot. Each gene represents a route, containing the customer nodes visited and served by the corresponding vehicle. The number of genes is equal to the number of vehicles.

[0086] Step 2.1: According to the travel time of each individual, Perform clustering and obtain Subpopulation ,in represents the sth subpopulation, let The size is ;

[0087] Step 2.2, Initialization ;

[0088] Step 2.3: Define the current number of iterations , and initialize ; Set the maximum number of iterations to ;

[0089] Step 2.4: Calculate Daidi Subpopulation middle The objective function value of each individual in the vehicle path planning model;

[0090] Step 2.5: According to Daidi Subpopulation The upper limit of all travel times for each individual and the number of vehicles in the calculation Daidi Subpopulation The non-dominated ranking and crowding distance of each individual in the ; thus, the binary tournament selection mechanism is used to select an individual with a better ranking from any two individuals as a parent individual, thereby constructing The first generation consists of Daidi A mating pool;

[0091] Step 2.6: Daidi Each mating pool selects two parent individuals in turn and executes the crossover operator and mutation operator to generate the first Daidi Subpopulation The two diversity offspring individuals of The first generation of diverse offspring individuals Daidi Diversity population .

[0092] Step 2.7, if Figure 1 As shown, Perform a local search to obtain The first generation of convergent offspring individuals Generation Convergence Population ;

[0093] Initialize a random integer ;

[0094] like , then middle Individuals perform a double-line neighborhood exchange operation to obtain convergent offspring individuals:

[0095] Any individual randomly selects two routes from its own customer nodes, and then judges in turn whether the current customer node on the first route is a neighboring customer node with the customer node on the second route. If so, the two customer nodes are exchanged under the condition of satisfying the maximum capacity of the vehicle, and the total driving time after the exchange is calculated to be less than the total driving time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next customer on the first route is judged and calculated until all customer nodes on the first route are traversed, thereby obtaining a convergent child individual;

[0096] like , then middle Individuals perform adjacent node exchange operations to obtain convergent offspring individuals:

[0097] Any individual in the algorithm randomly selects a route from its own customer nodes, then exchanges the positions of two adjacent customer nodes on the selected route, and calculates whether the total travel time after the exchange is shorter than the total travel time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next pair of adjacent customer nodes on the first route is judged until all customer nodes on the selected route are traversed, thereby obtaining a convergent child individual;

[0098] like , then middle Individuals perform neighborhood insertion operations to obtain convergent offspring individuals:

[0099] Any individual randomly selects two routes from its own client node, and then determines the first route in turn. Is the first customer node a neighboring customer node of the customer node on the second route? If so, insert the first customer node after the neighboring customer node while satisfying the maximum capacity of the vehicle. customer nodes, and calculate whether the total travel time after insertion is shorter than the total travel time without insertion. If so, the inserted individual is taken as a convergent child individual; otherwise, the first individual on the first route is The process continues until all customer nodes on the first route are traversed, thereby obtaining convergent child individuals.

[0100] like , then middle Individuals perform non-neighbor node exchange operations to obtain convergent offspring individuals:

[0101] Any individual in the network randomly selects a route from its own client node, and then The customer nodes are connected to the The positions of the first customer node to the last customer node are exchanged respectively, and the minimum value of the total travel time after each exchange is calculated to be shorter than the total travel time without exchange. If the exchange individual corresponding to the minimum value of the total travel time is used as a convergent child individual; otherwise, continue to exchange the first customer node on the first route. The process continues until all customer nodes on the selected route are traversed, thereby obtaining convergent offspring individuals.

[0102] Step 2.8: and Combined, the size is No. Daidi Temporary population ;

[0103] Step 2.9: Calculate Daidi Temporary population The objective function value of each individual in the vehicle path planning model;

[0104] Step 2.10: After each individual in the non-dominated order is sorted, the individuals of each level are selected in order from high to low non-dominated levels until the total number of individuals in all levels selected reaches Until the total number of individuals exceeds , then the crowding distance of the individuals in the selected current level is calculated, and the individuals with the smallest crowding distance are deleted, so that the total number of individuals in all levels is , and constitute the Daidi Subpopulation .

[0105] Step 2.11: When The individuals that are the optimal path planning solutions in all scenarios constitute the path robust solution set Otherwise, execute step 2.12; where, The algebra representing the intersection of the robust solution set and the optimal solution set;

[0106] Step 2.12: Assign to ,judge Is it established? If established, then Daidi Subpopulation The individual with the highest dominance rank in the non-dominant group is the Subpopulation The optimal path planning solution ; Otherwise, return to step 2.4 and execute sequentially;

[0107] Step 2.13: Assign to Then return to step 2.3 and execute sequentially until So far, we get Subpopulation The optimal path planning solution ;

[0108] Step 2.14: From Delete the same optimal path planning solutions from the set to obtain the optimal path planning solution set ;right and After executing the crossover operator, the balanced final path planning solution is obtained .

[0109] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0110] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A robust vehicle path planning method with uncertain travel time based on a multi-population evolutionary algorithm, characterized in that: It is applied to a single central warehouse, client nodes and In the distribution service area, a central warehouse node is defined as and The node set consists of client nodes , Indicates nodes; the path set between each node is recorded as ;in, Indicates any Nodes and Nodes The path between the vehicles Nodes Arrive at Nodes The travel time between ; Assume that all vehicles are based on warehouse nodes The vehicle path planning method is performed in the following steps: Step 1: Create A vehicle path planning model for a discrete scenario, including objective functions and constraints; Step 1.1: Use equations (1) and (2) to establish the objective function of vehicle path planning with uncertain travel time: : (1) s.t. , (2) In formula (1), represents the upper limit of all travel times, Indicates the number of vehicles; In formula (2), Indicates The travel time of the path for each discrete scenario, Represents all paths, Represents the total number of discrete scenarios; Step 1.2: Use equations (3) to (9) to construct the constraints of the vehicle path planning model: (3) (4) (5) (6) (7) (8) (9) In formula (3) to formula (9), Indicates that the vehicle passes through the warehouse node To Nodes The path between Indicates that the vehicle passes through Nodes To the warehouse node The path between Indicates that the vehicle passes through Nodes To Nodes The path between Indicates that the vehicle passes through Nodes To Nodes The path between and Respectively indicate that the vehicle arrives at Nodes and Nodes Vehicle load at the time; Indicates the maximum capacity of each transport vehicle; Indicates Nodes the quantity of goods delivered or demanded; Indicates Nodes the quantity of goods delivered or demanded; Indicates whether the vehicle has passed the Nodes To Nodes If the path between , then let , otherwise, let ; Represents an integer; Step 2: Initialize the size Population ; Each individual in the population consists of the subscript codes of the customer nodes and warehouse nodes visited and served by the vehicle; and according to the maximum load of the transport vehicle, when the customer's demand reaches the maximum load, 0 is inserted in the subscript sequence as a separator for different routes; Step 2.1: According to the travel time of each individual, Perform clustering and obtain Subpopulation ,in represents the sth subpopulation, let The size is ; Step 2.2, Initialization ; Step 2.3: Define the current number of iterations , and initialize ; Set the maximum number of iterations to ; Step 2.4: Calculate Daidi Subpopulation middle The objective function value of each individual in the vehicle path planning model; Step 2.5: According to Daidi Subpopulation The upper limit of all travel times for each individual and the number of vehicles in the calculation Daidi Subpopulation The non-dominated ranking and crowding distance of each individual in the ; thus, the binary tournament selection mechanism is used to select an individual with a better ranking from any two individuals as a parent individual, thereby constructing The first generation consists of Daidi A mating pool; Step 2.6: Daidi Each mating pool selects two parent individuals in turn and executes the crossover operator and mutation operator to generate the first Daidi Subpopulation The two diversity offspring individuals of The first generation of diverse offspring individuals Daidi Diversity population ; Step 2.7: Perform a local search to obtain The first generation of convergent offspring individuals Generation Convergence Population ; Step 2.8: and Combined, the size is No. Daidi Temporary population ; Step 2.9: Calculate Daidi Temporary population The objective function value of each individual in the vehicle path planning model; Step 2.10: After each individual in the non-dominated order is sorted, the individuals of each level are selected in order from high to low non-dominated levels until the total number of individuals in all levels selected reaches Until the total number of individuals exceeds , then the crowding distance of the individuals in the selected current level is calculated, and the individuals with the smallest crowding distance are deleted, so that the total number of individuals in all levels is , and constitute the Daidi Subpopulation ; Step 2.11: When The individuals that are the optimal path planning solutions in all scenarios constitute the path robust solution set Otherwise, execute step 2.12; where, represents crossing algebra; Step 2.12: Assign to ,judge Is it established? If established, then Daidi Subpopulation The individual with the highest dominance rank in the non-dominant group is the Subpopulation The optimal path planning solution ; Otherwise, return to step 2.4 and execute sequentially; Step 2.13: Assign to Then return to step 2.3 and execute sequentially until So far, we get Subpopulation The optimal path planning solution ; Step 2.14, from Delete the same optimal path planning solutions from the set to obtain the optimal path planning solution set ;right and After executing the crossover operator, the balanced final path planning solution is obtained .

2. The robust vehicle path planning method with uncertain travel time based on multi-population evolutionary algorithm according to claim 1 is characterized in that: The local search in step 2.7 is performed as follows: Initialize a random integer ; like , then middle Individuals perform a double-line neighborhood exchange operation to obtain convergent offspring individuals: Any individual randomly selects two routes from its own customer nodes, and then judges in turn whether the current customer node on the first route is a neighboring customer node with the customer node on the second route. If so, the two customer nodes are exchanged under the condition of satisfying the maximum capacity of the vehicle, and the total driving time after the exchange is calculated to be less than the total driving time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next customer on the first route is judged and calculated until all customer nodes on the first route are traversed, thereby obtaining a convergent child individual; like , then middle Individuals perform adjacent node exchange operations to obtain convergent offspring individuals: Any individual in the algorithm randomly selects a route from its own customer nodes, then exchanges the positions of two adjacent customer nodes on the selected route, and calculates whether the total travel time after the exchange is shorter than the total travel time without the exchange. If so, the individual after the exchange of customer nodes is taken as a convergent child individual; otherwise, the next pair of adjacent customer nodes on the first route is judged until all customer nodes on the selected route are traversed, thereby obtaining a convergent child individual; like , then middle Individuals perform neighborhood insertion operations to obtain convergent offspring individuals: Any individual randomly selects two routes from its own client node, and then determines the first route in turn. Is the first customer node a neighboring customer node of the second route? If so, insert the first customer node after the neighboring customer node while satisfying the maximum vehicle capacity. customer nodes, and calculate whether the total travel time after insertion is shorter than the total travel time without insertion. If so, the inserted individual is taken as a convergent child individual; otherwise, the first individual on the first route is The process continues until all customer nodes on the first route are traversed, thereby obtaining convergent offspring individuals. like , then middle Individuals perform non-neighbor node exchange operations to obtain convergent offspring individuals: Any individual in the network randomly selects a route from its own client node, and then The customer nodes are connected to the The positions of the first customer node to the last customer node are exchanged respectively, and the minimum value of the total travel time after each exchange is calculated to be shorter than the total travel time without exchange. If the exchange individual corresponding to the minimum value of the total travel time is used as a convergent child individual; otherwise, continue to exchange the first customer node on the first route. The process continues until all customer nodes on the selected route are traversed, thereby obtaining convergent offspring individuals.

3. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the robust vehicle path planning method according to claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the robust vehicle path planning method according to claim 1 or 2 are executed.

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