Multi-task multi-target vehicle path planning method and device based on auxiliary task

Abstract

The invention provides a multi-task multi-target vehicle path planning method and device based on auxiliary tasks, and relates to the field of multi-target vehicle path optimization. The method comprises the following steps: respectively constructing objective functions and constraint conditions of a main task F and a dynamic auxiliary task S; generating an initial scheme solution according to an obtained customer set consisting of a plurality of customers, storing the initial scheme solution to an archive # imgabs0 #, and initializing an auxiliary archive # imgabs1 #; f, executing a task collaboration mechanism, and dynamically starting S; when the diversity of the solution in the # imgabs2 # is insufficient, S is started; otherwise, the S is not started; after the F is started, one solution is selected from # imgabs3 # for local search, and the contract solution is updated to # imgabs4 #; when S is started, if # imgabs5 # is empty, one solution is selected from # imgabs6 # for local search, otherwise, a contract scheme solution is selected from # imgabs7 # and updated to # imgabs8 #, a non-contract scheme solution is updated to # imgabs9 #, and all schemes in # imgabs10 # are output until a stop condition is met; otherwise, continuing to execute the task collaboration mechanism. According to the invention, the problem that a feasible scheme solution falls into local optimum is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-objective vehicle path optimization, and in particular to a multi-task and multi-objective vehicle path planning method and device based on auxiliary tasks. Background Art

[0002] The Multi-Objective Vehicle Routing Problem (MOVRPTW) with Time Windows (MOVRPTW) is a core challenge in logistics management and transportation organization optimization, attracting considerable attention. MOVRPTW aims to achieve multiple optimization objectives, including minimizing the number of delivery vehicles, minimizing delivery time, minimizing delivery costs, and minimizing delivery distances, by rationally arranging routes while meeting constraints such as time constraints, vehicle capacity limits, and traffic restrictions.

[0003] Local search techniques play a crucial role in solving MOVRPTW problems. By finding near-optimal solutions within the solution space, they provide efficient solutions to practical problems. Common local search methods include nearest neighbor insertion, 2-opt, 3-opt, local search, hill climbing, simulated annealing, tabu search, and hybrid local search, which combines genetic algorithms with local search. These methods each have their own unique characteristics and offer flexible optimization strategies tailored to specific needs.

[0004] However, current local search techniques primarily focus on finding better feasible solutions, often discarding infeasible solutions found during the search process. In reality, some infeasible solutions may be located near better feasible regions. Retaining these solutions and continuing the search based on them can help expand the feasible region, thereby improving the quality of the archive of feasible solutions and the overall performance of the algorithm.

[0005] In view of this, the applicant filed this application after studying the prior art. Summary of the Invention

[0006] The present invention aims to provide a multi-task and multi-objective vehicle path planning method, device, equipment and medium based on auxiliary tasks to solve the problems in existing methods that the distribution of feasible solutions is relatively concentrated, they fall into local optimality, and their performance in solving multi-objective vehicle paths with time windows is low.

[0007] In order to solve the above technical problems, the present invention is implemented through the following technical solutions: A multi-task and multi-objective vehicle path planning method based on auxiliary tasks, comprising: S1, construct the objective function and constraints of the main task F of vehicle routing optimization based on time window; S2, dynamically constructing the objective function and constraints of a dynamic auxiliary task S based on a step-by-step constraint relaxation strategy; wherein the objective function of the auxiliary task S is consistent with the objective function of the main task F; the dynamic auxiliary task S based on the step-by-step constraint relaxation strategy is: by gradually reducing the constraint relaxation variables during the local search process, allowing for the generation of temporary non-contract routes after the insertion of customers, and obtaining a non-contract solution, thereby effectively breaking through the limitations of the infeasible region and searching for more discontinuous feasible solution regions; S3, based on the obtained customer set consisting of several customers, generates an initial solution and saves it to the archive , initialize auxiliary archive ; S4, start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; S5, after the main task F is opened, from the archive Select a solution from the set to perform a target-driven local search, and update the dominant planning solution that meets the main task constraints, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; S6, when it is determined that the current optimization task has reached the stop condition, the search is terminated and the output is archived. All the solutions in the are the multi-task and multi-objective vehicle path planning solutions; otherwise, the task coordination mechanism is continued to be executed.

[0008] Preferably, the objective function includes the number of vehicles used in the dispatch , total driving distance , the maximum travel time of the route , the total waiting time of all vehicles And the sum of delay times for all customer points , the formulas are: ; ; ; ; ; Where R represents the path set of the solution; M represents the dimension of R, that is, the total number of solution; Represents the distance of the i-th driving path, and the expression is: ; in, Indicates customer point To customer point The driving distance between them; j represents the customer variable; represents the number of customer points on path i; It represents the travel time of the i-th path, and the expression is: ; in, Indicates that the vehicle is at the customer point to The travel time between Indicates that the vehicle has arrived at the customer point Time The earliest service time earlier than the customer point When , the waiting time generated is expressed as: ; ; in, Indicates leaving the customer point time; Indicates customer point Required service time; It represents the sum of waiting time of all customer points on the i-th path, and the expression is: ; in, Indicates that the vehicle has arrived at the customer point Waiting time generated when It represents the sum of the delay times of all customer points on the i-th path, and its expression is: ; ; in, Indicates customer point the latest service time; Indicates that the vehicle has arrived at the customer point delay time.

[0009] Preferably, the constraints include demand constraints, travel time limit constraints and return time constraints; wherein the constraints of the main task F are: Demand constraints for F , which means that the total passenger demand for each route should not exceed the vehicle capacity, and the expression is: ; The travel time constraint of F , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ; Return time constraint of F , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ; in, Indicates customer point the number of passengers; Indicates vehicle capacity; Indicates customer point Delay time; Indicates the maximum allowed delay time set; Indicates that the vehicle is returning to the parking lot Time of hour; Indicates the set parking lot closing time; The constraints of the auxiliary task S are: Demand constraints for S Demand constraints with F consistent; S's travel time constraint , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ; Return time constraint of S , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ; in, Represents the constraint slack variable, used to reinsert a customer into a route when the route temporarily violates the constraint and , The definition is as follows: ; in, Indicates the maximum search depth of the target-driven local search; The current search depth.

[0010] Preferably, all paths in the initial solution start from and end at the parking lot; S3 is specifically: Randomly select two customers A and B from the customer set, create a path for customer A, build an initial solution, and add the created path to the initial solution; Without violating the constraints of F, insert customer B to the next position of the path created by customer A. If inserting customer B causes a violation of the constraints of F, do not insert the customer, traverse other paths in the initial solution, and iterate to see if the customer can be inserted without violating the constraints of F. If no insertion position that meets the constraints is found after traversing all paths in the initial solution, then customer B creates a new path. The initial solution is added until all customers in the customer set are inserted into the path of the initial solution, completing the construction of the initial solution.

[0011] Preferably, the task coordination mechanism is specifically as follows: From the archive Choose a solution ,exclude , from the remaining archive Choose two solutions from , ; Get the archive at the same time Boundary solution in ; Wherein, the boundary solution is located in the extreme area of the solution space, that is, the solution where the objective function value reaches the minimum or maximum; Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; Calculate boundary solutions reconciliation The sum of the Euclidean distances between each target value in is recorded as ; like + When the current archive The solution aggregation is relatively concentrated and falls into the local optimum, so it is necessary to enhance the archiving If the solution of the current archive is evenly distributed, the auxiliary task S is started; otherwise, the auxiliary task S does not need to be started, and the computing resources are concentrated on the search of the main task to further converge the archive. .

[0012] Preferably, the single task optimization is specifically as follows: only run the main task F, optimize the objective function of the main task F while satisfying the constraints of the main task F, perform local search with the goal drive to obtain a new solution, and update it to the archive ; The multi-task optimization is as follows: optimizing the main task F and the auxiliary task S simultaneously; the optimization process of the main task F is the same as the single-task optimization; when optimizing the auxiliary task S, while satisfying the constraints of the auxiliary task S, optimizing the objective function of the auxiliary task S, performing a local search driven by the goal, and gradually relaxing the constraints of the auxiliary task S according to the constraint relaxation variables, exploring a wider solution space, obtaining a new solution and adding it to the set in; general The solution that satisfies the constraints of F is updated to the archive Otherwise, it is a non-contract solution and updated to the archive .

[0013] Preferably, when optimizing the main task F and the auxiliary task S, each of them actively initiates knowledge transfer with the other task, and the knowledge transfer is indirectly performed through archiving; wherein, the knowledge transfer initiated by the main task F is specifically: When the main task F is searched and optimized, a new solution with better convergence is obtained and saved to the archive middle; At this time, the new solution is selected for local search in the auxiliary task S; The auxiliary task S destroys and reconstructs the new solution, breaks through the obstacles around the original solution, and searches for a solution in the new feasible area; The main task F completes the knowledge transfer to the auxiliary task S; The knowledge transfer initiated by the auxiliary task S is specifically: The auxiliary task S obtains the solution of the new feasible area during the search process and updates it to the archive middle; The solution of this new feasible region is selected during the search of the main task F; The main task F selects the solution of the new feasible region for search, thereby obtaining more feasible and high-quality solutions in the feasible region; The auxiliary tasks complete the knowledge transfer to the main task.

[0014] Preferably, when updating the archive, the archive update strategy is executed, specifically: Suppose the solution to be updated to the archive is ; Solve the solution Update to archive If the current archive If it is empty, Save to Archive ; Otherwise, traverse the archive All solutions in the The dominant solution is if Than Archive If any of the solutions is worse, it will not be added; if Than Archive If any of the solutions is better, Add to Archive In, end the update; Solve the solution Update to archive If the current archive If it is empty, Add to Archive ; Traverse archive Delete all solutions in Dominant and constraint violation less severe than Solution of the solution; if Than Archive If any of the solutions is worse, it will not be added; if Than Archive Any one of the solutions is better and The constraint violation degree of Add to Archive , end the update.

[0015] Preferably, when performing a target-driven local search operation, different strategies are applied according to the target to be optimized, specifically: When the optimization goal is the number of vehicles used for scheduling When: Select the path with the least number of vehicles in the corresponding archived solution, that is, the minimum vehicle path, and add the customers of the minimum vehicle path to the best positions of the remaining paths in turn. Then evaluate whether the solution meets the existing constraints and is better than the solution before the search. If it meets the constraints, the optimization goal is Success; otherwise, the optimization fails and the solution is restored; When the optimization goal is Other goals to Time: Randomly select a path in the corresponding archive solution, use a large neighborhood operator to disrupt and reconstruct this path, and evaluate whether it meets the constraint conditions and is better than the solution before the search. If it meets the conditions, the optimization is successful; otherwise, the optimization fails and the solution is restored. In the target-driven local search, according to the search depth , find a solution x that is better than the previous target, and determine whether the maximum search depth has been reached; if not, continue the search on the optimized target with the solution x; otherwise, return the solution at the maximum search depth. Among them, the large neighborhood operator includes , and three ways, specifically: : Use the roulette selection strategy to randomly select a path i in the corresponding archive solution; select a customer point from path i , exclude the customer point , and then select another customer point ; Reverse the customer order between customer point and customer point . : Use the roulette selection strategy to randomly select two paths in the corresponding archive solution; randomly remove p customers from these two paths. If the number of customers in these two paths is k, then 1 < p < k; insert the removed p customers into the best position of the solution in the archive . : Randomly select two paths in the corresponding archive solution, find the adjacent customers in these two paths, and check whether these two paths can be merged, while adjusting the customer order to optimize the path.

[0016] The present invention also provides a multi-task multi-objective vehicle routing planning device based on an auxiliary task, including: A main task construction unit, used to construct the objective function and constraint conditions of the main task F for vehicle routing optimization based on time windows; An auxiliary task construction unit, used to dynamically construct the objective function and constraint conditions of the dynamic auxiliary task S based on the stepwise constraint relaxation strategy; among them, the objective function of the auxiliary task S is the same as the objective function of the main task F; the dynamic auxiliary task S based on the stepwise constraint relaxation strategy is: by gradually reducing the constraint relaxation variable during the local search process, allowing the generation of a temporarily non-compliant route after inserting a customer, obtaining a non-compliant solution, so as to effectively break through the limitation of the infeasible region and search for more discontinuous feasible solution regions; An initial solution generation unit, used to generate an initial solution according to the obtained customer set composed of several customers, and save it to the archive , initialize auxiliary archive ; The task coordination mechanism unit is used to start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; Local search unit, used to search from archive files after the main task F is opened Select a solution for target-driven local search and update the planning solution that meets the main task constraints and is dominant, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; Output unit, used to terminate the search and output the archive when it is determined that the current optimization task has reached the stop condition If all the solutions in the , then they are the multi-task and multi-objective vehicle path planning solutions; otherwise, continue to execute the task coordination mechanism.

[0017] The present invention also provides a multi-task and multi-objective vehicle path planning device based on auxiliary tasks, including a processor and a memory, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement the multi-task and multi-objective vehicle path planning method based on auxiliary tasks as described above.

[0018] The present invention also provides a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by the processor of the device where the computer-readable storage medium is located, the multi-task and multi-objective vehicle path planning method based on auxiliary tasks as described above is implemented.

[0019] In summary, compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a multi-task and multi-objective vehicle path planning method based on dynamic auxiliary tasks. The method combines local search, multi-objective task processing and constraint processing based on constraint relaxation variables to solve the multi-objective vehicle path planning problem with time windows.

[0020] In the method of the present invention, a multi-archive multi-task mechanism is introduced, and the current archive solution is considered. The distribution of tasks is used to execute the task coordination mechanism. During the optimization of the target task, the main task is always kept open, and the opening or closing of the auxiliary task is determined by the archive. The algorithm adjusts the distance between the solution in the archive and the boundary solution for each target. When the solution in the archive is concentrated and trapped in a local optimum, the system activates auxiliary tasks to enhance the diversity of the solutions. When the solution is evenly distributed, auxiliary tasks are not required, thus saving computing resources. This strategy significantly improves the algorithm's performance in solving multi-target vehicle routing problems with time windows and obtains high-quality solutions. Testing on real-world examples has verified that the proposed method can efficiently solve multi-target vehicle routing problems with time windows. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 A schematic diagram of a multi-task and multi-objective vehicle path planning method based on auxiliary tasks provided in Example 1.

[0023] Figure 2 This is a flowchart of a multi-task and multi-objective vehicle path planning method based on auxiliary tasks provided in Example 1.

[0024] Figure 3 The example structure diagram of the solution provided for the first embodiment is shown.

[0025] Figure 4 This is a schematic diagram of a multi-task and multi-objective vehicle path planning device based on auxiliary tasks provided in Example 2.

[0026] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention for which protection is sought, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0028] Example 1 Embodiment 1 of the present invention provides a multi-task and multi-objective vehicle path planning method based on auxiliary tasks, which can be implemented by a multi-task and multi-objective vehicle path planning device based on auxiliary tasks (hereinafter referred to as the path planning device), and in particular, executed by one or more processors in the path planning device.

[0029] In this embodiment, the path planning device may be an electronic device equipped with a processor, which carries a computer program of the multi-task and multi-objective vehicle path planning method based on auxiliary tasks and the computer program can be executed, such as a computer, a smart phone, a smart tablet, a workstation, etc., which is not limited here.

[0030] like Figures 1 to 2 As shown, a multi-task and multi-objective vehicle path planning method based on auxiliary tasks includes steps S1 to S6.

[0031] S1, construct the objective function and constraints of the main task F of vehicle routing optimization based on time window; S2, dynamically constructing the objective function and constraints of a dynamic auxiliary task S based on a step-by-step constraint relaxation strategy; wherein the objective function of the auxiliary task S is consistent with the objective function of the main task F; the dynamic auxiliary task S based on the step-by-step constraint relaxation strategy is: by gradually reducing the constraint relaxation variables during the local search process, allowing for the generation of temporary non-contract routes after the insertion of customers, and obtaining a non-contract solution, thereby effectively breaking through the limitations of the infeasible region and searching for more discontinuous feasible solution regions; S3, based on the obtained customer set consisting of several customers, generates an initial solution and saves it to the archive , initialize auxiliary archive ; S4, start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; S5, after the main task F is opened, from the archive Select a solution for target-driven local search and update the planning solution that meets the main task constraints and is dominant, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; S6, when it is determined that the current optimization task has reached the stop condition, the search is terminated and the output is archived. If all the solutions in the , then they are the multi-task and multi-objective vehicle path planning solutions; otherwise, continue to execute the task coordination mechanism.

[0032] The embodiment of the present invention is divided into nine parts in total: definition of the problem (main task), construction of dynamic auxiliary tasks, representation of solutions and generation of initial solutions, task coordination mechanism, single-task optimization stage, multi-task optimization stage, archive update mechanism, target-driven local search operation and test experimental results.

[0033] 1. Definition of the problem (main task) The main task optimization problem is the multi-objective vehicle routing problem with time windows (MOVRPTW), which includes five objective functions: the number of vehicles used in scheduling , total driving distance , the maximum travel time of the route , the total waiting time of all vehicles And the sum of delay times for all customer points , defined as follows: ; ; ; ; ; Among them, R represents the path set of the solution; M represents the dimension of R, that is, the total number of solution solutions, which is also the total number of vehicles; Represents the distance of the i-th driving path, and the expression is: ; in, Indicates customer point to The driving distance between them; j represents the customer's variable; represents the number of customer points on path i; It represents the travel time of the i-th path, and the expression is: ; in, Indicates that the vehicle is at the customer point to The travel time between Indicates that the vehicle has arrived at the customer point Time The earliest service time earlier than the customer point When , the waiting time generated is expressed as: ; ; in, Indicates leaving the customer point time; Indicates customer point Required service time; It represents the sum of waiting time of all customer points on the i-th path, and the expression is: ; in, Indicates that the vehicle has arrived at the customer point Waiting time generated when It represents the sum of the delay times of all customer points on the i-th path, and its expression is: ; ; in, Indicates customer point the latest service time; Indicates that the vehicle has arrived at the customer point delay time.

[0034] The constraints include demand constraints, travel time constraints, and return time constraints. The constraints for the main task F are: Demand constraints for F , which means that the total passenger demand for each route should not exceed the vehicle capacity, and the expression is: ; The travel time constraint of F , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ; Return time constraint of F , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ; in, Indicates customer point the number of passengers; Indicates vehicle capacity; Indicates customer point Delay time; Indicates the maximum allowed delay time set; Indicates that the vehicle is returning to the parking lot Time of hour; Indicates the set parking lot closing time 2. Dynamic auxiliary task construction The objective function optimized by the dynamic auxiliary task based on the step-by-step constraint relaxation strategy is the same as that of the main task, the difference lies in the definition of the constraints. The specific definitions of the optimization objectives and constraints of the auxiliary task are as follows: The five objective functions optimized by the auxiliary tasks are the same as those of the main task.

[0035] The constraints of the auxiliary tasks are dynamically set based on a step-by-step constraint relaxation strategy, which is defined as follows: Demand constraints for S Demand constraints with F Consistent: ; S's travel time constraint , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ; Return time constraint of S , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ; in, Represents the constraint slack variable, acting on the two constraints of travel time limit and return time constraint, and is used to reinsert the customer into the route when the route temporarily violates the constraints and , which is defined as follows: ; in, Indicates the maximum search depth of the target-driven local search. In this embodiment, the value is set to 5. Of course, other values can be set according to actual conditions and are not limited here. The current search depth.

[0036] According to the above auxiliary task construction, we can know: 1) The auxiliary task is to relax the variables according to the step-by-step constraint in the local search operation. Dynamic construction is performed, that is, the auxiliary tasks optimized by the local search process are dynamic, and the local search optimizes auxiliary tasks with different constraint relaxation variables at different depths.

[0037] 2) The auxiliary task based on the step-wise constraint slack variable allows the route constraint to be violated by ε when inserting customers in the early search phase, so that illegal solutions can be searched and retained. 3. Solution representation and generation of initial solution A solution X is a set of k paths To express, among which It is a line The path consists of a sequence of visits to vertices. represents the j-th vertex (i.e., customer) of the i-th path, represents the number of customer points on path i. In addition, for the convenience of calculation, let , means that all paths start from the parking lot and return to the parking lot. In a solution, except for the parking lot, any customer will only appear in one path.

[0038] like Figure 3 As shown, an example of a solution is shown. The solution is composed of a set of paths constituted, that is ,in , , .

[0039] In this embodiment, according to the number of objectives to be optimized, a heuristic method is used to construct the initial solution and update it to the archive. The steps are as follows: (1) Randomly select two customers A and B from the customer set, create a path for customer A, build an initial solution, and add the created path to the initial solution; (2) Without violating the constraint of F, insert customer B to the next position of the path created by customer A. If inserting customer B causes a violation of the constraint of F, do not perform the insertion operation, traverse other paths in the initial solution, and iterate to check whether the customer can be inserted without violating the constraint of F.

[0040] For example, suppose The path created for customer A, Represents the parking lot, and let population P be the current solution set If customer B inserts If the constraint is violated when the position is to Is there a possible insertion position in the without violating the constraints?

[0041] If no insertion position that satisfies the constraints is found after traversing all paths in the initial solution, Client B creates a new path. The initial solution is added until all customers in the customer set are inserted into the path of the initial solution, completing the construction of the initial solution.

[0042] 4. Task coordination mechanism During the optimization process, the main task F remains open, and the auxiliary task S is opened or closed by the archive. The distribution of the solutions is determined dynamically. Figure 2 As shown in Figure 2, the specific process of the task coordination mechanism is as follows: (1) From the archive Choose a solution ,exclude , from the remaining archive Choose two solutions from , ; Get the archive at the same time Boundary solution in ; Wherein, the boundary solution is located in the extreme area of the solution space, that is, the solution where the objective function value reaches the minimum or maximum; (2) Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; (3) Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; (4) Calculate boundary solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; (5) If + When the current archive The solution aggregation is relatively concentrated and falls into the local optimum, so it is necessary to enhance the archiving If the solution of the current archive is evenly distributed, the auxiliary task S is started; otherwise, the auxiliary task S does not need to be started, and the computing resources are concentrated on the search of the main task to further converge the archive. , saving computing resources.

[0043] 5. Single task optimization stage In this embodiment, after the task coordination mechanism determines that there is no need to supplement the archive If the diversity is too high, the auxiliary tasks will not be enabled. The single-task optimization phase will be entered. The single-target optimization phase builds a single-task optimization environment. In the single-task optimization environment: Only the main task is run to optimize the multi-objective vehicle routing problem with time windows, that is, the five objective functions of the main task F, and under the constraints, the target-driven local search operation is used to search, and only the solutions that meet the constraints in the search process are retained, that is, the contract solution. The main task searches and obtains only legal solutions and updates them to the archive. , for archiving Brings more knowledge about feasible regions and convergence to better improve archiving Then, the solution obtained during the search is updated to the archive middle.

[0044] 6. Multi-task optimization stage In this embodiment, the multi-task optimization stage includes the construction of a multi-task optimization environment and a knowledge transfer strategy, which helps archive convergence and diversity distribution based on knowledge transfer between tasks.

[0045] (1) Multi-task optimization environment construction: optimize the main task and auxiliary tasks at the same time.

[0046] Main task: This search process is similar to the single-task optimization stage.

[0047] Auxiliary task: Optimize the multi-objective vehicle routing problem with time windows (MOVRPTW), that is, multiple objective functions, to meet the constraints of the auxiliary task. Use a goal-driven local search operation, retain the planning scheme during the search process, and save it to a collection ,gather The contract solution and the non-contract solution are included. Update the contract solution to the archive. ,for It brings the relevant knowledge information about whether it is possible to cross the obstacle area and reach the feasible area; at the same time, the non-contract solution is updated to the archive , for archiving This brings higher quality illegal solution and provides better search candidate solution for the next auxiliary task search.

[0048] Determine whether the current running time has reached the stopping condition (for example, the maximum allowed running time has been reached). If so, terminate the algorithm search process and output the archive. If all the solutions in the , then they are the multi-task and multi-objective vehicle path planning solutions; otherwise, continue to execute the task coordination mechanism.

[0049] (2) Knowledge transfer strategy During the optimization process, the main and auxiliary tasks each actively initiate knowledge transfer with the other task. This mechanism enables the two tasks to indirectly transfer knowledge through archiving. The specific mechanism operates as follows: Specific steps of knowledge transfer initiated by the main task: 1) The main task searches for a solution with better convergence and saves it to the archive.

[0050] 2) The solution is selected for local search during the auxiliary task search.

[0051] 3) The auxiliary task destroys and reconstructs the solution, breaks through the obstacles around the original solution, and searches for a solution in a new feasible area.

[0052] 4) The main task completes the knowledge transfer to the auxiliary task.

[0053] Specific steps for knowledge transfer initiated by auxiliary tasks: 1) The auxiliary task obtains the solution of the new feasible region during the search process and updates it to the archive.

[0054] 2) This solution is selected during the main task search.

[0055] 3) The main task selects this solution for search, thereby obtaining more feasible and high-quality solutions in the feasible region.

[0056] 4) The auxiliary task completes the knowledge transfer to the main task.

[0057] 7. Archive update mechanism The method of the present invention uses a multi-archive mechanism to assist the search process of local search. The definition of multi-archive is as follows: Archive : Mainly responsible for storing planning schemes that meet the constraints and are dominant. The solutions for the local search operation of the main task are selected from here.

[0058] Auxiliary archive : Mainly responsible for storing the non-contract solutions obtained during the search process, and serving as an auxiliary archive When not empty, the solution for the local search of the dynamic auxiliary task is selected from here.

[0059] Therefore, according to the archive and auxiliary archives Different archive update strategies are adopted.

[0060] Archive Update strategy: When a solution Need to update to archive The specific steps are as follows: 1) If the current archive If it is empty, Add to Archive , and returns.

[0061] 2) Traverse the archive Delete all solutions in The dominant solution.

[0062] 3) If Archived If any of the solutions is dominant, return it.

[0063] 4) If Not archived If any one of the solutions is dominant, Add to Archive , return and end the update.

[0064] Archive Update strategy: When a solution Need to update to archive The specific steps are as follows: 1) If the current archive If it is empty, Add to Archive , and returns.

[0065] 2) Traverse the archive Delete all solutions in The solution that is dominant and has a constraint violation degree worse than .

[0066] 3) If Archived If any of the solutions is dominant, return it.

[0067] 4) If Not archived Any solution in the solution is dominant and the constraint violation degree is better than Add to Archive , return and end the update.

[0068] 8. Goal-driven local search operation The goal-driven local search operation mainly applies different strategies based on the current optimization goal. The specific process is as follows: 1) When the optimization goal is to dispatch the number of vehicles hour: Select a route with the least number of vehicles in the planning scheme, and add the customers on this route to the best position of the remaining routes in turn. After adding, evaluate whether the planning scheme meets the constraints and is better than the scheme before the search. If it meets the constraints, optimize the target. Success; otherwise, the optimization fails and the planning scheme is restored.

[0069] 2) When the optimization target is the remaining items, that is, hour: Randomly select a path in the planning scheme and apply the large neighborhood operator ( ) The path is destroyed and reconstructed, and the planning scheme after the search is evaluated to see whether it meets the constraints and is better than the scheme before the search. If so, the optimization is successful; otherwise, the optimization fails and the planning scheme is restored.

[0070] In target-driven local search, a threshold is set for the depth of exploration of the solution space in each target direction, that is, the maximum search depth , in this embodiment, the value is set to 5. The main process is: 1) Find a solution x that is better than the previous goal when optimizing the current goal, and keep that solution.

[0071] 2) Determine whether the current search depth has reached the maximum search depth If not, continue searching on this target with the solution x; otherwise, return the solution at the maximum search depth.

[0072] This method can find the optimal value in the target direction during the search process, making good use of computing resources. At the same time, by setting the maximum search depth, the search is performed within a reasonable solution space, avoiding the waste of computing resources.

[0073] Optimizing different objectives requires different emphases. Therefore, designing different large neighborhood operators is crucial for optimizing the MOVRPTW problem. In the objective-driven local search operation, the following three neighborhood operation operators are mainly used: : Randomly select a path i in the corresponding archived solution using the roulette wheel selection strategy; select a customer node from path i , excluding the customer node , and then select another customer node ; Reverse the order of the customers between customer node and customer node . : Randomly select two paths in the corresponding archived solution using the roulette wheel selection strategy; randomly remove p customer nodes from these two paths. If the number of customer nodes in these two paths is k, then 1 < p < k; Insert the removed p customer nodes into the best position of the solution in the archive . : Randomly select two paths in the corresponding archived solution, find the adjacent customer nodes in these two paths, and check whether these two paths can be merged. At the same time, adjust the order of the customer nodes to optimize the paths.

[0074] 9. Test the experimental results To test the effectiveness of the proposed algorithm, use the real instance library of the vehicle routing problem with time windows for testing and experiments.

[0075] The instances in the instance library involve three factors: 3 different numbers of customer nodes, 3 different vehicle capacities, and 5 types of time windows. Different problem instances are created by using different combinations of the above three factors , that is: , where and respectively represent the maximum demand of customer nodes and the total demand of all customer nodes, represents the vehicle capacity. The specific values of these three factors are as follows: Number of customer nodes: 50, 150, 250 Capacity of the vehicle : 60, 20, 5 Type of time window: 1, 2, 3, 4, 5 Time window type 1 indicates a time window ranging from 0 minutes to 480 minutes from the start of the workday; type 2 divides the daily workday into three time windows: [0, 160], [160, 320], and [320, 480]; type 3 divides the daily workday into three time windows: [0, 130], [175, 305], and [350, 480]; type 4 divides the daily workday into three time windows: [0, 100], [190, 290], and [380, 480]; and type 5 randomly selects one of the time windows from types 1 to 4 for each customer. Using these combinations, a total of 45 different problem instances were generated. In each problem instance, the demand for each customer point was set to 10, 20, or 30, with a probability of 1 / 3; the service time for each customer point was set to 10, 20, or 30, with a probability of 1 / 3; and the maximum allowable delay for each customer point was set to 30 minutes.

[0076] To test the performance of the proposed algorithm, the Multi-Directional Local Search (MDLS) algorithm was used as a comparison algorithm with the proposed method, and a uniform runtime was set as the algorithm's termination criterion. Nonparametric statistical tests were performed on the experimental results obtained by independently running each instance 30 times. The test results showed that the proposed method performed 33 / 4 / 8 (excellent / average / poor) compared to MDLS in terms of Hypervolume, outperforming MDLS 33 times, being on par 4 times, and slightly lagging behind MDLS 8 times. The results for the Inverted Generational Distance (IGD) metric were 32 / 8 / 5 (excellent / average / poor), outperforming MDLS 32 times, being on par 8 times, and slightly lagging behind MDLS 5 times.

[0077] In this embodiment, the Multi-Directional Local Search (MDLS) algorithm is a heuristic search algorithm designed to solve optimization problems. It generally combines the idea of local search and explores multiple directions or neighborhoods during the search process to increase the possibility of finding a global optimal solution.

[0078] In this embodiment, the Hypervolume metric is an important indicator used to measure the performance of an optimization algorithm in solving multi-objective optimization problems. It refers to the volume occupied by multiple non-dominated solutions (i.e., solutions that are not dominated by other solutions) in a multi-dimensional space. A non-dominated solution is one for which no other solution outperforms it on all objectives in a multi-objective optimization problem. The Hypervolume metric is typically calculated by enclosing multiple non-dominated solutions with a hyperplane and then calculating the volume between the hyperplane and a reference point. The choice of the reference point is typically problem-specific and should generally be located at the optimal solution for all objective functions. A larger Hypervolume metric value indicates that the algorithm finds more non-dominated solutions when solving a multi-objective optimization problem, and that these non-dominated solutions perform better on all objective functions. Therefore, it is widely used to compare the performance of different optimization algorithms in multi-objective optimization problems.

[0079] The Inverted Generational Distance (IGD) metric measures the distance between solutions in a solution set and the true frontier. It measures the average distance between the true frontier and the approximate frontier. A smaller value indicates that the solution set found by the algorithm is closer to the optimal solution set, thus reflecting the algorithm's convergence and diversity. The IGD metric is also important in the performance evaluation of multi-objective optimization algorithms because it simultaneously considers the quality and diversity of the solution set.

[0080] In summary, the method of the present invention adopts a multi-task optimization framework and integrates two core technologies in the fields of constraint handling mechanism (CHT) and local search (LS). The technical solution of the present invention is mainly reflected in the following three key aspects: First, a multi-task mechanism is introduced. By retaining uncontracted solutions during the local search process, dynamic auxiliary tasks are constructed for the main task. This creates a multi-task optimization environment with the main task for collaborative optimization. This strategy not only maintains the convergence of the main task but also significantly improves the diversity of solutions.

[0081] Second, a step-by-step constraint relaxation strategy is introduced in the construction of auxiliary tasks. By gradually reducing the constraint relaxation variables during the local search process, a temporary non-contract route can be generated after the customer is inserted, effectively breaking through the limitations of the infeasible area and searching for more discontinuous feasible solution areas.

[0082] Third, a multi-archive mechanism is employed to archive and update both contract and non-contract solutions separately. Changes in the archives are then used to switch between single-task and multi-task optimization and select different task solutions. This comprehensive strategy enables a more efficient search process and a richer set of solutions during the optimization process.

[0083] The present invention can effectively enhance existing local search operations, solve multi-objective vehicle routing problems with time windows, and is portable, while providing a new and efficient solution to the problem.

[0084] Example 2 like Figure 4 As shown, the second embodiment of the present invention further provides a multi-task and multi-objective vehicle path planning device based on auxiliary tasks, comprising: The main task construction unit is used to construct the objective function and constraint conditions of the vehicle path optimization main task F based on the time window; An auxiliary task construction unit is used to dynamically construct the objective function and constraints of a dynamic auxiliary task S based on a step-by-step constraint relaxation strategy; wherein the objective function of the auxiliary task S is consistent with the objective function of the main task F; the dynamic auxiliary task S based on the step-by-step constraint relaxation strategy is to gradually reduce the constraint relaxation variables during the local search process, allowing the insertion of customers to generate a temporary non-contract route, and obtain a non-contract solution, so as to effectively break through the limitations of the infeasible region and search for more discontinuous feasible solution regions; The initial solution generation unit is used to generate the initial solution based on the customer set consisting of several customers and save it to the archive , initialize auxiliary archive ; The task coordination mechanism unit is used to start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; Local search unit, used to search from archive files after the main task F is opened Select a solution from the set to perform a target-driven local search, and update the dominant planning solution that meets the main task constraints, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; Output unit, used to terminate the search and output the archive when it is determined that the current optimization task has reached the stop condition All the solutions in the are the multi-task and multi-objective vehicle path planning solutions; otherwise, the task coordination mechanism is continued to be executed.

[0085] Example 3 The third embodiment of the present invention also provides a multi-task and multi-objective vehicle path planning device based on auxiliary tasks, which includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement the multi-task and multi-objective vehicle path planning method based on auxiliary tasks as described above.

[0086] Example 4 The fourth embodiment of the present invention also provides a computer-readable storage medium, which stores computer-readable instructions. When the computer-readable instructions are executed by the processor of the device where the computer-readable storage medium is located, the multi-task and multi-objective vehicle path planning method based on auxiliary tasks as described above is implemented.

[0087] In the several embodiments provided in the embodiments of the present invention, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device and method embodiments described above are merely illustrative. For example, the flowcharts in the accompanying drawings show the possible architectures, functions, and operations of the devices, methods, and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or part of a code, which contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the boxes can also occur in an order different from that marked in the drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, as well as the combination of boxes in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified functions or actions, or can be implemented using a combination of dedicated hardware and computer instructions.

[0088] In addition, the functional modules in the various embodiments of the present invention may be integrated together to form an independent part, or each module may exist independently, or two or more modules may be integrated to form an independent part.

[0089] If the functions are implemented in the form of software modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, electronic device, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks. It should be noted that, in this document, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or device that includes a series of elements includes not only those elements but also other elements not explicitly listed, or also includes elements inherent to such process, method, article, or device. Without further constraints, an element defined by the phrase "comprises a..." does not preclude the existence of additional identical elements in the process, method, article or apparatus that includes the element.

[0090] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "an", "the" and "the" used in the embodiments of the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise.

[0091] It should be understood that the term "and / or" as used herein is merely a description of the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the associated objects are in an "or" relationship.

[0092] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0093] The "first" and "second" mentioned in the embodiments are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that the specific order or precedence of "first" and "second" can be interchanged where appropriate. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein.

[0094] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A multi-task and multi-objective vehicle path planning method based on auxiliary tasks, characterized in that: include: S1, construct the objective function and constraints of the main task F of vehicle routing optimization based on time window; S2, dynamically constructing the objective function and constraints of a dynamic auxiliary task S based on a step-by-step constraint relaxation strategy; wherein the objective function of the auxiliary task S is consistent with the objective function of the main task F; the dynamic auxiliary task S based on the step-by-step constraint relaxation strategy is: by gradually reducing the constraint relaxation variables during the local search process, allowing for the generation of temporary non-contract routes after the insertion of customers, and obtaining a non-contract solution, thereby effectively breaking through the limitations of the infeasible region and searching for more discontinuous feasible solution regions; S3, based on the obtained customer set consisting of several customers, generates an initial solution and saves it to the archive , initialize auxiliary archive ; S4, start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; S5, after the main task F is opened, from the archive Select a solution for target-driven local search and update the planning solution that meets the main task constraints and is dominant, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; S6, when it is determined that the current optimization task has reached the stop condition, the search is terminated and the output is archived. If all the solutions in the , then they are the multi-task and multi-objective vehicle path planning solutions; otherwise, continue to execute the task coordination mechanism.

2. A multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 1, characterized in that , the objective function includes the number of vehicles used in scheduling , total driving distance , the maximum travel time of the route , the total waiting time of all vehicles And the sum of delay times for all customer points , the formulas are: ； ； ； ； ； Where R represents the path set of the solution; M represents the dimension of R, that is, the total number of solution; Represents the distance of the i-th driving path, and the expression is: ； in, Indicates customer point To customer point The driving distance between represents the customer variable; represents the number of customer points on path i; It represents the travel time of the i-th path, and the expression is: ； in, Indicates that the vehicle is at the customer point to The travel time between Indicates that the vehicle has arrived at the customer point Time The earliest service time earlier than the customer point When , the waiting time generated is expressed as: ； ； in, Indicates leaving the customer point time; Indicates customer point Required service time; It represents the sum of waiting time of all customer points on the i-th path, and the expression is: ； in, Indicates that the vehicle has arrived at the customer point Waiting time generated when It represents the sum of the delay times of all customer points on the i-th path, and its expression is: ； ； in, Indicates customer point the latest service time; Indicates that the vehicle has arrived at the customer point delay time.

3. A multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 2, characterized in that The constraints include demand constraints, travel time constraints, and return time constraints; among them, the constraints of the main task F are: Demand constraints for F , which means that the total passenger demand for each route should not exceed the vehicle capacity, and the expression is: ； The travel time constraint of F , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ； Return time constraint of F , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ； in, Indicates customer point the number of passengers; Indicates vehicle capacity; Indicates customer point Delay time; Indicates the maximum allowed delay time set; Indicates that the vehicle is returning to the parking lot Time of hour; Indicates the set parking lot closing time; The constraints of the auxiliary task S are: Demand constraints for S Demand constraints with F consistent; S's travel time constraint , indicating that the delay time should not exceed the maximum allowed delay time, the expression is: ； Return time constraint of S , indicating that the vehicle should return to the parking lot before the closing time, the expression is: ； in, Represents the constraint slack variable, used to reinsert a customer into a route when the route temporarily violates the constraint and , The definition is as follows: ； in, Indicates the maximum search depth of the target-driven local search; The current search depth.

4. The multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 3 is characterized in that , all paths in the initial solution start from the parking lot and end at the parking lot; S3 is specifically: Randomly select two customers A and B from the customer set, create a path for customer A, build an initial solution, and add the created path to the initial solution; Without violating the constraints of F, insert customer B into the next position of the path created by customer A; If inserting customer B will violate the constraints of F, then the insertion operation will not be performed. The other paths in the initial solution will be traversed to iteratively check whether the customer can be inserted without violating the constraints of F. If no insertion position that meets the constraints is found after traversing all the paths in the initial solution, then customer B will create a new path. The initial solution is added until all customers in the customer set are inserted into the path of the initial solution, completing the construction of the initial solution.

5. The multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 3 is characterized in that ,The task coordination mechanism is specifically as follows: From the archive Choose a solution ,exclude , from the remaining archive Choose two solutions from , ; Get the archive at the same time Boundary solution in ; Wherein, the boundary solution is located in the extreme area of the solution space, that is, the solution where the objective function value reaches the minimum or maximum; Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; Calculation solution reconciliation The sum of the Euclidean distances between each target value in is recorded as ; Calculate boundary solutions reconciliation The sum of the Euclidean distances between each target value in is recorded as ; like When the current archive The solution aggregation is relatively concentrated and falls into the local optimum, so it is necessary to enhance the archiving If the solution of the current archive is evenly distributed, the auxiliary task S is started; otherwise, the auxiliary task S does not need to be started, and the computing resources are concentrated on the search of the main task to further converge the archive. .

6. The multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 5 is characterized in that ,The single task optimization is specifically as follows: only run the main task F, optimize the objective function of the main task F while satisfying the constraints of the main task F, perform local search with the goal driven, obtain a new solution, and update it to the archive. ; The multi-task optimization is as follows: optimize the main task F and the auxiliary task S at the same time; the optimization process of the main task F is the same as the single-task optimization; when optimizing the auxiliary task S, optimize the objective function of the auxiliary task S while satisfying the constraints of the auxiliary task S, perform local search driven by the goal, and gradually relax the constraints of the auxiliary task S according to the constraint relaxation variables, explore a wider solution space, obtain a new solution, and add it to the set in; general The solution that satisfies the constraints of F is updated to the archive Otherwise, it is a non-contract solution and updated to the archive .

7. The multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 1 is characterized in that When optimizing the main task F and the auxiliary task S, each of them actively initiates knowledge transfer with the other task, and indirectly transfers knowledge through archiving; among them, the knowledge transfer initiated by the main task F is specifically: When the main task F is searched and optimized, a new solution with better convergence is obtained and saved to the archive middle; At this time, the new solution is selected for local search in the auxiliary task S; The auxiliary task S destroys and reconstructs the new solution, breaks through the obstacles around the original solution, and searches for a solution in the new feasible area; The main task F completes the knowledge transfer to the auxiliary task S; The knowledge transfer initiated by the auxiliary task S is specifically: The auxiliary task S obtains the solution of the new feasible area during the search process and updates it to the archive middle; The solution of this new feasible region is selected during the search of the main task F; The main task F selects the solution of the new feasible region for search, thereby obtaining more feasible and high-quality solutions in the feasible region; The auxiliary tasks complete the knowledge transfer to the main task.

8. A multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to any one of claims 1 to 7, characterized in that ,When updating the archive, the archive update strategy is executed, specifically: Suppose the solution to be updated to the archive is ; Solve the solution Update to archive If the current archive If it is empty, Save to Archive ; Otherwise, traverse the archive Delete all solutions in The dominant solution is if Than Archive If any of the solutions is worse, it will not be added; if Than Archive If any of the solutions is better, Add to Archive In, end the update; Solve the solution Update to archive If the current archive If it is empty, Add to Archive ; Traverse archive Delete all solutions in Dominant and constraint violation less severe than Solution of the solution; if Than Archive If any of the solutions is worse, it will not be added; if Than Archive Any one of the solutions is better and The constraint violation degree of Add to Archive , end the update.

9. The multi-task and multi-objective vehicle path planning method based on auxiliary tasks according to claim 3 is characterized in that ,When performing goal-driven local search operations, different ,strategies are applied according to the current goal to be optimized, ,specifically: When the optimization goal is the number of vehicles used for scheduling When: Select the path with the least number of vehicles in the corresponding archived solution, that is, the minimum vehicle path, and add the customers of the minimum vehicle path to the best positions of the remaining paths in turn. Then evaluate whether the solution meets the existing constraints and is better than the solution before the search. If it meets the constraints, the optimization goal is Success; otherwise, the optimization fails and the solution is restored; When the optimization goal is Other goals to When: Randomly select a path from the corresponding archived solution, use the large neighborhood operator to destroy and reconstruct the path, and evaluate whether it meets the constraints and is better than the solution before the search. If it meets the constraints, the optimization is successful; otherwise, the optimization fails and the solution is restored; In goal-driven local search, according to the search depth , find a solution x that is better than the previous target and determine whether the maximum search depth has been reached; if not, continue searching on the optimized target with solution x; otherwise, return the solution at the maximum search depth; Among them, the large neighborhood operator includes 、 and Three ways, specifically: :Use the roulette wheel selection strategy to randomly select a path i in the corresponding archive solution; select a customer point from path i , exclude customer points , then select a customer point ; To the customer point Reverse the order of customers between :Use the roulette wheel selection strategy to randomly select two paths in the corresponding archive plan; randomly remove p customers from these two paths. If the number of customers in these two paths is k, then 1 < p < k; insert the removed p customers into the archive in sequence The best position of the middle solution; : Randomly select two paths in the corresponding archive plan, find adjacent customers in the two paths, and check whether the two paths can be merged. At the same time, adjust the order of customers to optimize the path.

10. A multi-task and multi-objective vehicle path planning device based on auxiliary tasks, characterized in that: include: The main task construction unit is used to construct the objective function and constraint conditions of the vehicle path optimization main task F based on the time window; An auxiliary task construction unit is used to dynamically construct the objective function and constraints of a dynamic auxiliary task S based on a step-by-step constraint relaxation strategy; wherein the objective function of the auxiliary task S is consistent with the objective function of the main task F; the dynamic auxiliary task S based on the step-by-step constraint relaxation strategy is to gradually reduce the constraint relaxation variables during the local search process, allowing the insertion of customers to generate a temporary non-contract route, and obtain a non-contract solution, so as to effectively break through the limitations of the infeasible region and search for more discontinuous feasible solution regions; The initial solution generation unit is used to generate the initial solution based on the customer set consisting of several customers and save it to the archive , initialize auxiliary archive ; The task coordination mechanism unit is used to start the main task F, execute the task coordination mechanism, and dynamically start the auxiliary task S; wherein, the dynamic start is: when the archive When the diversity of the solutions is insufficient, the auxiliary task S is enabled and multi-task optimization is performed; otherwise, the auxiliary task S is not enabled and single-task optimization is performed; Local search unit, used to search from archive files after the main task F is opened Select a solution from the set to perform a target-driven local search, and update the dominant planning solution that meets the main task constraints, i.e., the contract solution, to the archive. ; When auxiliary task S is turned on, if auxiliary archive If empty, then from the archive Select a solution from the archive for target-driven local search, otherwise Select a solution from the list to perform a target-driven local search and update the contract solution to the archive. , update the non-contract solution to the archive ; Output unit, used to terminate the search and output the archive when it is determined that the current optimization task has reached the stop condition All the solutions in the are the multi-task and multi-objective vehicle path planning solutions; otherwise, the task coordination mechanism is continued to be executed.

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