Self-adaptive hybrid neighborhood search method for solving vehicle path problem of unmanned aerial vehicle

Abstract

The invention relates to a self-adaptive hybrid neighborhood search method for solving a vehicle path problem of an unmanned aerial vehicle, and the method comprises the following steps: generating an initial solution only containing a vehicle path through an initial solution generation program, recording the initial solution as a best solution, and calculating an initial temperature; exploring a potential better solution space by using guide type destruction recombination operation, and generating a new solution; using a double-layer mixed neighborhood search algorithm to optimize the solution, and updating the solution; a new annealing temperature is calculated, whether a new solution is accepted or not is considered according to an acceptance criterion, the best solution is updated, and the weights of a damage operator method and a repair operator method are updated; the step (2) to the step (4) are repeated until a set stop condition is met, and an optimal solution of the problem is obtained; according to the method, three efficient modules including efficient unmanned aerial vehicle path construction operation, guide type damage recombination operation and double-layer mixed neighborhood search are integrated, an acceptance mechanism of a simulated annealing solution is introduced, and the method has the advantages of being high in solution quality, high in robustness, wide in application range and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle-UAV collaborative path optimization, and in particular to an adaptive hybrid neighborhood search method for solving UAV vehicle path problems. Background Art

[0002] The Vehicle Routing Problem with Drones (VRPD) is a variant of the Capacitated Vehicle Routing Problem (CVRP). Building on CVRP, VRPD equips each vehicle in the fleet with a drone, allowing the vehicle and drone to move together or independently. The drone can detach from the vehicle at a warehouse or any customer location and complete a single delivery. Meanwhile, the vehicle continues to travel independently, serving other customers. In all cases, the drone must reunite with the same vehicle at the customer's location or warehouse. VRPD effectively simulates a variety of real-world applications, such as last-mile delivery, urban-rural distribution, surveillance, internal logistics, 3D geological and environmental mapping and data collection, and Wi-Fi connectivity.

[0003] The difficulty of the routing problem for collaborative vehicles and drones lies in task synchronization, that is, the spatial movement synchronization and temporal operation synchronization of vehicles and drones, and the problem requires making additional decisions to determine which customer subsets are served by which type of vehicle or drone.

[0004] Therefore, the present invention proposes an adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem to solve the above problems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem, which can achieve high robustness and high quality solution to the vehicle-UAV collaborative routing problem VRPD.

[0006] To solve the above technical problems, the technical solution of the present invention is: an adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem, the innovation of which is that it includes the following steps: Step (1): Generate an initial solution containing only the vehicle path through the initial solution generation program , recorded as the best solution, and calculate the initial temperature; Step (2): Use guided destruction and recombination operations to explore the potential better solution space and generate new solutions. ; Step (3), using a two-layer hybrid neighborhood search algorithm to optimize the solution and update the solution; Step (4), calculate the new annealing temperature, consider whether to accept the new solution according to the acceptance criteria, update the best solution, and update the weights of the destruction operator and repair operator methods; Step (5): Repeat steps (2) to (4) until the set stopping condition is reached and the optimal solution to the problem is obtained.

[0007] Furthermore, the specific steps of the initial solution generation procedure described in step (1) include: Step (1.1): First, generate an empty path and insert the customer closest to the warehouse node among the currently unvisited customers into the empty path; Step (1.2), taking into account the vehicle capacity limit, select the unvisited customer closest to the last selected customer and insert it at the end of the currently visited customer sequence. Once the vehicle capacity reaches the upper limit, a new empty path is opened. This operation process is repeated until all customers are successfully visited, thus completing the entire vehicle route planning; Step (1.3), if there are customers that have not been visited and cannot be visited by any vehicle, optimize the loading rate of the path by exchanging customers of different vehicle paths, and repeat the exchange operation until all customers are successfully visited and the initial solution is obtained. .

[0008] Furthermore, the guided destructive reconstruction operation in step (2) specifically includes the following steps: Step (2.1): Use the roulette wheel strategy to select the destruction operator and the repair operator. According to the weights of the respective methods of the destruction operator and the repair operator, the methods of the destruction operator and the repair operator are determined in a probabilistic manner. Step (2.2), calculate the expected maximum number of customers to be removed, and generate a random integer within the expected maximum number of customers to be removed, representing the number of customers actually removed in the current iteration; Step (2.3): Use the destruction operator method determined in step (2.1) to remove customers. If the number of drone customers in the path where a customer is located does not meet the constraint after the customer is removed, cancel the removal operation to ensure the feasibility of the drone path. Step (2.4), first assign the customer to the corresponding vehicle path or drone path In the sequence, the efficient UAV path construction operation EDPC is then called to regenerate the UAV flight subpath ; Step (2.5) uses the repair operator determined in step (2.1) to adopt the optimal improved insertion strategy with the smallest distance increase on the new path, inserting the customers one by one back to the appropriate position, ensuring that the inserted path satisfies both the vehicle capacity constraint Q and the number constraint between drone customers and vehicle customers. If a feasible insertion position cannot be found in the current partial solution, the customer will be temporarily retained until the subsequent insertion attempt, or a new path will be opened to provide services for it, thereby ensuring that every customer can be served and a new solution is obtained. .

[0009] Furthermore, the methods of destroying operators described in step (2.1) include random destruction operators, cluster destruction operators and worst destruction operators.

[0010] Furthermore, the methods of repairing operators described in step (2.1) include a random repair operator, a maximum demand repair operator, a recent repair operator, and a minimum remaining capacity repair operator.

[0011] Furthermore, the specific steps of the efficient UAV path construction operation EDPC described in step (2.4) include: Step (2.4.1), in the legal solution of VRPD, the vehicle path sequence The number of nodes and drone paths The number of nodes The following quantity constraints exist: ; if ,but ; Step (2.4.2), generate dynamic take-off and landing interval constraints, for the UAV flight subpaths , the range of take-off and landing node selection is controlled by the dynamic interval constraint: ; in, represents the number of paths that a vehicle serves customers, Indicates the number of subpaths of the UAV flight; Lower bound constraint ,make sure Takeoff node At least in After vehicle nodes; Upper bound constraint , for the follow-up UAV flight subpaths are reserved for at least vehicle nodes to ensure that when processing the last UAV flight subpath When, there are still feasible space; Step (2.4.3), the first subpath is optimized independently, i.e. , when processing the first UAV flight subpath When the vehicle node interval Execute the greedy strategy to quickly obtain a feasible solution and select the first drone service customer in the interval The two nearest nodes, through their The relative position in the Subscript combination of , thus obtaining the cost of flying the drone Minimum subpath; in, Indicates that the drone is moving from the vehicle path To the drone path The flight cost, Indicates the drone is moving from the drone path To vehicle path Flight costs; Step (2.4.4), joint optimization of multiple subpaths, by allowing the modification of the previously determined take-off and landing nodes when optimizing the current subpath, to achieve global cost re-optimization, for subsequent subpaths , Introducing the preorder subpath The take-off and landing nodes are jointly optimized. The joint optimization methods include: preceding path constraint, dual constraint optimization and cost minimization.

[0012] Furthermore, the specific steps of the double-layer variable neighborhood search algorithm described in step (3) include: Step (3.1), the new solution generated by step (2) The vehicle paths are optimized within the path using the LKH solver, and the UAV flight sequence is then reconstructed using the Efficient UAV Path Construction Operator (EDPC). Step (3.2): The new solution after optimization in step (3.1) is explored in different neighborhoods in turn, and the corresponding movement operator is used to perturb the vehicle and drone paths. After each movement, EDPC is called to regenerate the drone flight sequence, and the First-Improvement insertion strategy is used to reduce the increase in the distance of the newly generated path. If the new neighborhood solution violates the constraint on the number of drone customers, the move is canceled and other neighborhood operations are tried to obtain a new solution. .

[0013] Furthermore, the movement operator described in step (3.2) includes: Vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle exchange, drone flight exchange, vehicle repositioning, drone repositioning, and hybrid exchange within the same route; Cross-path vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle swap, drone flight swap, vehicle repositioning, drone repositioning, hybrid swap; The service order of vehicles within the same route is reversed and cross-routes are exchanged.

[0014] Furthermore, the specific steps of updating the solution in step (4) include: Step (4.1), calculate the new annealing temperature, and decide whether to accept the new solution obtained in step (3) according to the acceptance criteria ; The annealing temperature update formula is: ; in, is the temperature parameter, is the elapsed time since the algorithm started, It is a pre-set time limit; In order to determine reasonable corresponding initial values ​​for examples of different scales, let From the initial solution The objective function value of At the beginning, it gradually approaches zero in a linear decreasing manner; when When the algorithm terminates immediately, the time The algorithm is accurately measured by CPU time. If the quality of the solution does not improve during multiple iterations, the algorithm will automatically revert to the best solution found so far. When a destruction and repair operation generates a new solution The objective function value of Better than current solutions The objective function value of hour, will be accepted unconditionally; if the new The objective function value of Worse than the current solution The objective function value of ,but Accepted by probability; The formula for the probability of acceptance is: ; Step (4.2), if accepted and Better than the current best solution , then use replace , and update the non-improvement counter. When the non-improvement counter reaches the maximum allowed non-improvement generation, use Reset the current solution; Step (4.3), update the factor based on the weight And the corresponding method scores for different situations in each predefined iteration , update the method weights of the destruction operator and the repair operator, set represents the weight of method i at the jth iteration. After each iteration, the weight update formula is: .

[0015] The advantages of the present invention are: (1) The adaptive large-scale hybrid neighborhood search method of the present invention integrates three efficient modules on the basis of solution initialization: efficient UAV path construction operation, guided destruction and reconstruction operation and double-layer hybrid neighborhood search, and introduces the solution acceptance mechanism of simulated annealing. It has the advantages of high solution quality, strong robustness and wide application range.

[0016] (2) The core idea of ​​the efficient UAV path construction operation in the present invention is to use a two-layer optimization mechanism to adjust the UAV take-off and landing nodes under the premise of fixing the vehicle path, while ensuring the feasibility of the path sequence and the optimality of the cost; the guided destruction and reconstruction operation is to structurally destroy and reconstruct the current solution through a series of destruction and repair operators, exploring the potential space of better solutions, so as to enhance the search ability of the algorithm while maintaining the feasibility of the solution; the two-layer hybrid neighborhood search first optimizes the vehicle path within the path; then reconstructs the UAV flight sequence, and then uses the corresponding movement operator to perturb the vehicle and UAV paths. If the new neighborhood solution is constrained, the movement is canceled and other neighborhood operations are tried, thereby achieving a balance between global and local search and improving the solution quality. Compared with the existing methods, the method of the present invention has a high competitive advantage and effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Figure 1 Schematic diagram of a calculation example of the path problem of vehicle and drone collaboration in the present invention.

[0019] Figure 2 Schematic diagram comparing the solution results of ALHNS1 and ALHNS of the present invention.

[0020] Figure 3 This is a flow chart of the adaptive large-scale hybrid neighborhood search method of the present invention. DETAILED DESCRIPTION

[0021] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0022] Example The vehicle-UAV collaborative routing problem VRPD to be solved in this embodiment is defined as an undirected complete graph On which the vertex set Includes two warehouse nodes and , two warehouse nodes and Represents the starting point and end point, as well as the customer set , is the total number of customers, each customer There is a demand , this demand needs to be delivered by vehicle or drone. Demand Exceeds a preset threshold , then the customer is called a "vehicle-exclusive customer", that is, he cannot be delivered by drone. homogeneous vehicles, each with a capacity of , and is equipped with a drone. The vehicle and its drone can move together or separately. When the vehicle and drone move together, only the vehicle can provide service to customers, while the drone can take off from the vehicle and independently perform delivery tasks at the warehouse or any customer location.

[0023] Meanwhile, the vehicle continues to drive and service other customers. The drone must return to the original vehicle at the same customer or warehouse location. However, it is prohibited for a drone to leave the same customer location and return to the same vehicle. Each drone can only service a maximum of one customer before returning to the vehicle. VRPD Path By a pair Indicates that represents the vehicle path, Represents the corresponding drone path. The vehicle path from the warehouse Start serving customers one by one , and finally returned to the warehouse Each UAV flight subpath Contains three vertices: Indicates the take-off position of the drone. Represents customers of drone services, Indicates the location where the drone returns to the vehicle. For each subpath, there must be two indexes satisfy and and , that is, the vehicle provides services to customers independently between these two locations. In addition, for two adjacent drone flight subpaths and To ensure that the independent service intervals of vehicles and drones do not overlap, there are two indexes satisfy and and .

[0024] A viable VRPD path The following conditions must be met: and All elements in are different, and the sum of the demands of vehicles and drones for the same route does not exceed the vehicle capacity, that is, for all routes ,have Established. For all ,have In VRPD, every edge of an undirected complete graph There is a non-negative path cost for each vehicle. and the non-negative path cost of the UAV Since vehicles need to travel on roads, the path cost of vehicles is Manhattan distance, while drones are not restricted by traditional roads, and the flight speed of drones is different from that of vehicles, so their path cost is Euclidean distance divided by the drone cost coefficient. .path The total path cost It is the sum of the routing costs of all edges traversed by vehicles and drones.

[0025] This embodiment provides an adaptive large hybrid neighborhood search (ALHNS) method for solving the above-mentioned UAV vehicle routing problem, combining Figure 1 An example of VRPD is described along with the representation and evaluation of the solution.

[0026] Given a containing customers and For a VRPD case involving a vehicle equipped with a drone, ALHNS describes its solution in two levels. ALHNS represents a VRPD solution as a There are two sets of path sets, namely the vehicle path set and the drone path set. The vehicle path set is the order of a set of customers visited by vehicles, while the drone path set represents the order of a set of sub-paths visited by drones. Given the hierarchical combination structure of VRPD, a candidate solution is defined as a triple .in, Indicates that all client nodes are assigned groups, each Assigned to For vehicles and drones. Each group It is further divided into two subsets and , represents the vehicle path, Represents the drone path.

[0027] Figure 1 The example contains paths, each path contains a vehicle path and a drone path, with capacity constraints Both are 100. Figure 1 Each circle represents a customer who needs service. There are 19 customers in total. The first number on the left side of the circle represents the customer number, and the number in the brackets represents the demand of the corresponding customer. Among them, the demand of three customers numbered 2, 12, and 15 exceeds the threshold. , can only be served by vehicles. The vehicle paths of each group are expressed as , which represents the sequence of nodes visited by the vehicle in order, including the warehouse node.

[0028] Figure 1 The vehicle path above the warehouse in can be expressed as: . No. The paths of the drones in each group are expressed as , which consists of multiple drone flight subpaths. Each drone flight subpath Represents a node in the vehicle's path from the drone Take off and serve customers , and then returns to another node in the vehicle's path ,in exist Appears in after. Figure 1 The drone’s flight path above the warehouse in Figure 1 includes the following flight subpaths: , , .

[0029] untie The total cost is calculated as the sum of the distance traveled by the vehicle and the distance flown by the drone: ; in, .

[0030] in Represents the vehicle path The edge set of Represents an edge The corresponding Manhattan distance is, Represents the UAV flight subpath calculated using Euclidean distance Flight costs, Indicates that the drone takes off from the node To the service client node The Euclidean distance, Indicates that the drone serves the client node To the return node The Euclidean distance of .

[0031] The adaptive hybrid neighborhood search method of this embodiment is as follows: Figure 3 As shown, the following steps are included: Step (1) Generate an initial solution S containing only vehicle paths through the population initialization procedure, record it as the best solution, and calculate the initial temperature; The specific steps of the population initialization program include: Step (1.1): First, generate an empty path and insert the customer closest to the warehouse node among the currently unvisited customers into the empty path; Step (1.2), taking into account the vehicle capacity limit, select the unvisited customer closest to the last selected customer and insert it at the end of the currently visited customer sequence. Once the vehicle capacity reaches the upper limit, a new empty path is opened. This operation process is repeated until all customers are successfully visited, thus completing the entire vehicle route planning; In step (1.3), if there are customers that have not been visited and cannot be visited by any vehicle, that is, the number of paths has reached m and the remaining capacity of all vehicles is less than the remaining customer demand, the loading rate of the path is optimized by exchanging customers of different vehicle paths. Specifically, two vehicle paths are randomly selected. , Two customers , , swap the positions of two customers, get two new vehicle paths, try to insert the unvisited customers into the new vehicle paths. Repeat the swap operation until all customers are successfully visited and get the initial solution. .

[0032] Step (2), using guided destruction and recombination operations to explore the potential better solution space and generate new solutions; The specific steps of the guided destruction and reconstruction operation include: In step (2.1), a roulette wheel strategy is used to select the destruction and repair operators. The destruction and repair methods are determined probabilistically based on the weights of the destruction and repair methods. Initially, the weights of all methods are set to the same initial value, and then the weights are updated in step (4.3). Among them, the methods of destroying operators include: Random destruction operator: removes customers from the current solution through unbiased selection to increase the diversity of the solution space; Cluster destruction operator: guided by spatial clustering, removes customers around the dynamic cluster center to concentrate on destroying the structure of the local area; Worst destruction operator: Remove customers based on cost savings, and prioritize destroying those that contribute little to the current solution.

[0033] Methods for repairing operators include: Random repair operator: reintegrates customers into the path in an unbiased manner; Maximum demand repair operator: prioritizes customers with high demand to optimize resource allocation; Nearest repair operator: optimizes path coherence using spatial proximity; Minimum Remaining Capacity Repair Operator: Optimizes resource utilization.

[0034] Step (2.2), first according to the total number of customers and damage rate parameters The expected maximum number of removed customers is calculated by multiplying is a pre-set ratio parameter to indicate the expected destruction ratio; then, in the range of the expected maximum number of removed customers Generate a random integer in , represents the number of customers actually removed in the current iteration; In order to avoid the random generated results being too small and resulting in insufficient destructive power, it is specially stipulated that if , then Forced to 1, this ensures that at least one customer is removed per destruction operation.

[0035] Step (2.3): Use the destruction operator method determined in step (2.1) to remove customers. During the removal process, if the number of drone customers in the path where a customer is located does not meet the constraint after the customer is removed, the removal operation is canceled to ensure the feasibility of the drone path. Step (2.4), first assign the customer to the corresponding vehicle path or drone path In the sequence, the Efficient Drone Path Construction (EDPC) operation is then called to regenerate the drone flight subpath ; EDPC targets the scenario of collaborative delivery between vehicles and drones, and achieves global cost optimization by dynamically coordinating the take-off and landing locations of drone flight sub-paths. Its core idea is to use a two-layer optimization mechanism to adjust the drone take-off and landing nodes under the premise of a fixed vehicle path, while ensuring the feasibility of the path timing and the optimal cost. EDPC can be divided into four steps: Step (2.4.1), in the legal solution of VRPD, the vehicle path sequence The number of nodes (including 0 and 0' for departure and return to the warehouse) and the drone path The number of nodes The following quantity constraints exist: ; if ,but ; The above constraints ensure that all moves are feasible without recalculating the entire solution or path, thereby enabling the management of coupled customers in the path.

[0036] Step (2.4.2), generate dynamic take-off and landing interval constraints, for the UAV flight subpaths , the range of take-off and landing node selection is controlled by the dynamic interval constraint: ; in, represents the number of paths that a vehicle serves customers, Indicates the number of drone flight subpaths.

[0037] Lower bound constraint ,make sure Takeoff node At least in After vehicle nodes; for example, when When currently serving customers You must wait until the drone completes the first two services before taking off to avoid mission overlap.

[0038] Upper bound constraint , for the follow-up UAV flight subpaths are reserved for at least vehicle nodes to ensure that when processing the last UAV flight subpath When, there are still feasible space; Step (2.4.3), first subpath independent optimization ( ), when processing the first UAV flight subpath When the vehicle node interval Execute the greedy strategy to quickly obtain a feasible solution. Select the first drone service customer in the interval The two nearest nodes, through their The relative position in the Subscript combination of , thus obtaining the cost of flying the drone The smallest subpath; where Indicates that the drone is moving from the vehicle path To the drone path The flight cost, Indicates the drone is moving from the drone path To vehicle path flight costs.

[0039] Step (2.4.4), joint optimization of multiple subpaths, by allowing the modification of the previously determined take-off and landing nodes when optimizing the current subpath, achieves global cost re-optimization. , Introducing the preorder subpath The take-off and landing nodes are jointly optimized. The joint optimization method is: ① Precursor path constraint: If ,set up ;otherwise, Take the preceding subpath Return node The index in the vehicle path ensures that the return node task is not started earlier than the previous task. ,set up ;otherwise, Take the post-order subpath Takeoff node , forming a chain constraint.

[0040] ②Dual constraint optimization: In the current subpath interval Select ,satisfy ;exist Select ,satisfy ; mandatory , ensuring that the preceding drone returns to the node No later than the current task departure node ; For the current subpath interval and the preceding interval Generate sorting sequences separately: the current interval node is based on the current non-negative path cost Sort ascending by , the nodes in the preceding interval follow the preceding non-negative path cost Sort ascending by ; Using the double pointer method and Synchronous search: Initialize pointer , ,choose [ ]and [ ] corresponding node, if it satisfies Constraint, calculate the joint cost. Otherwise, move or Pointer, select the side that minimizes the cost increment. Repeat until the optimal combination that satisfies the constraints is found.

[0041] ③ Cost minimization: through joint cost Minimize the optimized subpath ;in, Indicates that the drone is moving from the vehicle path To the drone path The flight cost, Indicates the drone is moving from the drone path To vehicle path Flight costs, Indicates that the drone is moving from the vehicle path To the drone path The flight cost, From the drone path To vehicle path flight costs.

[0042] In step (2.5), the repair operator determined in step (2.1) is used to adopt the optimal improved insertion strategy with the smallest distance increase of the new path to insert the customers one by one back to the appropriate position, ensuring that the inserted path satisfies both the vehicle capacity constraint Q and the number constraint between drone customers and vehicle customers. If a feasible insertion position cannot be found in the current partial solution, the customer will be temporarily retained until the subsequent insertion attempt, or a new path will be opened to provide services for it, so as to ensure that every customer can be served, and the operator method is given a corresponding weight according to the performance to obtain a new solution. .

[0043] Step (3), using a two-layer hybrid neighborhood search algorithm to optimize the solution and update the solution; The specific steps of the two-layer hybrid neighborhood search algorithm include: Step (3.1), the new solution generated by step (2) The vehicle path is optimized within the path using the LKH solver, and then the UAV flight sequence is reconstructed using the efficient UAV path construction operator EDPC to ensure the high quality of the UAV path under the given vehicle path conditions; In step (3.2), the new solution after optimization in (3.1) is explored in different neighborhoods (including intra-path and inter-path operations) and the paths of vehicles and drones are perturbed using the corresponding movement operators. Among them, the movement operators include: Vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle exchange, drone flight exchange, vehicle repositioning, drone repositioning, and hybrid exchange within the same route; Cross-path vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle swap, drone flight swap, vehicle repositioning, drone repositioning, hybrid swap; The service order of vehicles within the same route is reversed and cross-routes are exchanged.

[0044] After each move, EDPC is called to regenerate the UAV flight sequence and the First-Improvement insertion strategy is used to reduce the added distance of the newly generated path. If the new neighborhood solution violates the constraint on the number of UAV customers, the move is undone and other neighborhood operations are tried to obtain a new solution. .

[0045] Among them, vehicle-to-drone conversion aims to remove a customer currently served by a vehicle from the vehicle sequence and convert him to be served by a drone; drone-to-vehicle conversion aims to convert a customer currently served by a drone to be served by a vehicle; vehicle exchange aims to select two candidate customers and exchange their positions in the path; drone flight exchange selects two different drone flights and exchanges their positions in the sequence; vehicle repositioning rearranges the positions of customers served by the vehicle in the vehicle sequence; drone repositioning deletes a drone flight from its original position and tries to reinsert it at another position in the drone sequence; hybrid exchange operations involve both drone and vehicle service parts; vehicle service sequence reversal within the same path focuses on optimizing the vehicle service sequence within the same path; cross-path cross-exchange decomposes different paths and then interchanges them to construct a new path.

[0046] Step (4), calculate the new annealing temperature, consider whether to accept the new solution according to the acceptance criteria, update the best solution, and update the weights of the destruction and repair methods; The specific steps of updating the solution include: Step (4.1), calculate the new annealing temperature, and decide whether to accept the new solution obtained in step (3) according to the acceptance criteria ; The annealing temperature update formula is: ; in, is the temperature parameter, is the elapsed time since the algorithm started, It is a pre-set time limit; In order to determine reasonable corresponding initial values ​​for examples of different scales, let From the initial solution The objective function value of At the beginning, it gradually approaches zero in a linear decreasing manner. When the algorithm terminates immediately, the time It is precisely measured by CPU time; if the quality of the solution does not improve during multiple consecutive iterations, the algorithm will automatically revert to the best solution currently found.

[0047] When a destruction and repair operation generates a new solution The objective function value of Better than current solutions hour, will be accepted unconditionally; if the new The objective function value of Worse than the current solution ,but Accepted by probability; The formula for the probability of acceptance is: ; in, For a new interpretation The objective function value of Total cost; For the current solution , that is, the current solution total cost.

[0048] Step (4.2), if accepted and Better than the current best solution , then use replace , and update the non-improvement counter. When the non-improvement counter reaches the maximum allowed non-improvement generation, use Reset the current solution; Step (4.3), update the factor based on the weight And the corresponding method scores for different situations in each predefined iteration , update the method weights of the destruction operator and the repair operator, set represents the weight of method i at the jth iteration. After each iteration, the weight update formula is: .

[0049] Step (5): Repeat steps (2) to (4) until the set stop condition is reached, such as the running time reaches the maximum running time, and the best solution to the problem is obtained.

[0050] This embodiment verifies the effectiveness of EDPC through ablation experiments. The two algorithms are ALHNS and ALHNS1. ALHNS is the adaptive hybrid neighborhood search method mentioned in this embodiment, and ALHNS1 is obtained by ablating EDPC in ALHNS. Figure 2 The horizontal axis is the number of the 20 cases, and the vertical axis is the difference value with the ALHNS result. Figure 2 As can be seen from the figure, ALHNS1 without EDPC performs worse or on par with ALHNS with EDPC in terms of best solution. In terms of average solution, ALHNS1 without EDPC has a higher average solution cost than ALHNS with EDPC across all 20 cases. This demonstrates that the EDPC approach positively impacts the algorithm's ability to discover high-quality optimal solutions. Removing it leads to a decrease in optimal solution quality. EDPC effectively guides the algorithm to converge stably to higher-quality solutions over multiple runs. Therefore, integrating EDPC as a core component into the ALHNS algorithm is necessary and effective for achieving efficient and high-quality VRPD solutions.

[0051] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as above in terms of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can, without departing from the scope of the technical solution of the present invention, make some changes or modifications to equivalent embodiments using the technical contents disclosed above. However, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. An adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem, characterized by: The following steps are involved: Step (1): Generate an initial solution containing only the vehicle path through the initial solution generation program , recorded as the best solution, and calculate the initial temperature; Step (2): Use guided destruction and recombination operations to explore the potential better solution space and generate new solutions. ; Step (3), using a two-layer hybrid neighborhood search algorithm to optimize the solution and update the solution; Step (4), calculate the new annealing temperature, consider whether to accept the new solution according to the acceptance criteria, update the best solution, and update the weights of the destruction operator and repair operator methods; Step (5): Repeat steps (2) to (4) until the set stopping condition is reached and the optimal solution to the problem is obtained.

2. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 1 is characterized by: The specific steps of the initial solution generation procedure described in step (1) include: Step (1.1): First, generate an empty path and insert the customer closest to the warehouse node among the currently unvisited customers into the empty path; Step (1.2), taking into account the vehicle capacity limit, select the unvisited customer closest to the last selected customer and insert it at the end of the currently visited customer sequence. Once the vehicle capacity reaches the upper limit, a new empty path is opened. This operation process is repeated until all customers are successfully visited, thus completing the entire vehicle route planning; Step (1.3), if there are customers that have not been visited and cannot be visited by any vehicle, optimize the loading rate of the path by exchanging customers of different vehicle paths, and repeat the exchange operation until all customers are successfully visited and the initial solution is obtained. .

3. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 1 is characterized by: The specific steps of the guided destructive reconstruction operation described in step (2) include: Step (2.1): Use the roulette wheel strategy to select the destruction operator and the repair operator. According to the weights of the respective methods of the destruction operator and the repair operator, the methods of the destruction operator and the repair operator are determined in a probabilistic manner. Step (2.2), calculate the expected maximum number of customers to be removed, and generate a random integer within the expected maximum number of customers to be removed, representing the number of customers actually removed in the current iteration; Step (2.3): Use the destruction operator method determined in step (2.1) to remove customers. If the number of drone customers in the path where a customer is located does not meet the constraint after the customer is removed, cancel the removal operation to ensure the feasibility of the drone path. Step (2.4), first assign the customer to the corresponding vehicle path or drone path In the sequence, the efficient drone path construction operation EDPC is then called to regenerate the drone flight subpath ; Step (2.5) uses the repair operator determined in step (2.1) to adopt the optimal improved insertion strategy with the smallest distance increase on the new path, inserting the customers one by one back to the appropriate position, ensuring that the inserted path satisfies both the vehicle capacity constraint Q and the number constraint between drone customers and vehicle customers. If a feasible insertion position cannot be found in the current partial solution, the customer will be temporarily retained until the subsequent insertion attempt, or a new path will be opened to provide services for it, thereby ensuring that every customer can be served and a new solution is obtained. .

4. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 3 is characterized by: The methods of destroying operators described in step (2.1) include random destruction operators, cluster destruction operators and worst destruction operators.

5. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 3 is characterized by: The methods of repairing operators described in step (2.1) include a random repair operator, a maximum demand repair operator, a recent repair operator, and a minimum remaining capacity repair operator.

6. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 3, characterized in that: The specific steps of the efficient UAV path construction operation EDPC described in step (2.4) include: Step (2.4.1), in the legal solution of VRPD, the vehicle path sequence The number of nodes and drone paths The number of nodes The following quantity constraints exist: ； if ,but ; Step (2.4.2), generate dynamic take-off and landing interval constraints, for the UAV flight subpaths , the range of take-off and landing node selection is controlled by the dynamic interval constraint: ； in, represents the number of paths that a vehicle serves customers, Indicates the number of UAV flight subpaths; Lower bound constraint ,make sure Takeoff node At least in the After vehicle nodes; Upper bound constraint , for the follow-up UAV flight subpaths are reserved for at least vehicle nodes to ensure that when processing the last UAV flight subpath When, there are still feasible space; Step (2.4.3), the first subpath is optimized independently, i.e. , when processing the first drone flight subpath When the vehicle node interval Execute the greedy strategy to quickly obtain a feasible solution and select the first drone service customer in the interval The two nearest nodes, through their The relative position in the Subscript combination of , thus obtaining the cost of flying the drone Minimum subpath; in, Indicates that the drone is moving from the vehicle path To the drone path The flight cost, Indicates the drone is moving from the drone path To vehicle path Flight costs; Step (2.4.4), joint optimization of multiple subpaths, by allowing the modification of the previously determined take-off and landing nodes when optimizing the current subpath, to achieve global cost re-optimization, for subsequent subpaths , Introducing the preorder subpath The take-off and landing nodes are jointly optimized. The joint optimization methods include: preceding path constraint, dual constraint optimization and cost minimization.

7. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 1, characterized in that: The specific steps of the double-layer variable neighborhood search algorithm described in step (3) include: Step (3.1), the new solution generated by step (2) The vehicle paths are optimized within the path using the LKH solver, and the UAV flight sequence is then reconstructed using the Efficient UAV Path Construction Operator (EDPC). Step (3.2): The new solution after optimization in step (3.1) is explored in different neighborhoods in turn, and the corresponding movement operator is used to perturb the vehicle and drone paths. After each movement, EDPC is called to regenerate the drone flight sequence, and the First-Improvement insertion strategy is used to reduce the increase in the distance of the newly generated path. If the new neighborhood solution violates the constraint on the number of drone customers, the move is canceled and other neighborhood operations are tried to obtain a new solution. .

8. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 7, characterized in that: The movement operators described in step (3.2) include: Vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle exchange, drone flight exchange, vehicle repositioning, drone repositioning, and hybrid exchange within the same route; Cross-path vehicle-to-drone conversion, drone-to-vehicle conversion, vehicle swap, drone flight swap, vehicle repositioning, drone repositioning, hybrid swap; The service order of vehicles within the same route is reversed and cross-routes are exchanged.

9. The adaptive hybrid neighborhood search method for solving the UAV vehicle routing problem according to claim 1, characterized in that: The specific steps of updating the solution described in step (4) include: Step (4.1), calculate the new annealing temperature, and decide whether to accept the new solution obtained in step (3) according to the acceptance criteria ; The annealing temperature update formula is: ; in, is the temperature parameter, is the elapsed time since the algorithm started, It is a pre-set time limit; In order to determine reasonable corresponding initial values ​​for examples of different scales, let From the initial solution The objective function value of At the beginning, it gradually approaches zero in a linear decreasing manner; when When the algorithm terminates immediately, the time The algorithm is accurately measured by CPU time. If the quality of the solution does not improve during multiple iterations, the algorithm will automatically revert to the best solution found so far. When a destruction and repair operation generates a new solution The objective function value of Better than current solutions The objective function value of hour, will be accepted unconditionally; if the new The objective function value of Worse than the current solution The objective function value of ,but Accepted by probability; The formula for the probability of acceptance is: ; Step (4.2), if accepted and Better than the current best solution , then use replace , and update the non-improvement counter. When the non-improvement counter reaches the maximum allowed non-improvement generation, use Reset the current solution; Step (4.3), update the factor based on the weight And the corresponding method scores for different situations in each predefined iteration , update the method weights of the destruction operator and the repair operator, set represents the weight of method i at the jth iteration. After each iteration, the weight update formula is: 。

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