Iterative greedy search method for solving cooperative path problem of unmanned aerial vehicle and vehicle

Abstract

The invention relates to an iterative greedy search method for solving a cooperative path problem of an unmanned aerial vehicle and a vehicle. The iterative greedy search method inherits the idea of an iterative greedy algorithm, integrates a self-adaptive operator selection mechanism, and totally integrates four efficient modules: a guided destruction recombination operation module, a rapid similarity detection module, a double-layer hybrid neighborhood search module and a population updating strategy, and the core idea of the iterative greedy search method is that individuals are iteratively selected from a population of a solution, and the population updating strategy is selected from the population of the solution. Carrying out guide type destruction and recombination operation; through rapid similarity detection, time-consuming evaluation or local search operation performed on a newly generated solution highly similar to an existing solution in a population is effectively avoided; a multi-neighborhood thought is fused, a double-layer hybrid neighborhood search strategy is provided, and the purpose is to systematically explore vehicle paths, unmanned aerial vehicle task allocation and a wide solution space for cooperation of the vehicle paths and the unmanned aerial vehicle task allocation; and finally updating the population based on quality and diversity standards. Compared with the existing method, the method provided by the invention has very high competitive performance and effectiveness.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) and vehicle collaborative path optimization, and in particular to an iterative greedy search method for solving the UAV and vehicle collaborative path problem. Background Art

[0002] The Vehicle Routing Problem with Drones (VRPD) is a variant of the Capacitated Vehicle Routing Problem (CVRP). Building on the CVRP, VRPD equips each vehicle in the fleet with a drone, allowing the vehicle and drone to move together or independently. A drone can also detach from the vehicle at a warehouse or any customer location and complete a single delivery, while the vehicle continues to travel independently to serve other customers. In all cases, the drone must reunite with the same vehicle at the customer's location or warehouse.

[0003] The goal of the VRPD problem is to find an optimal solution S that contains a set of customer partitions and the corresponding Group vehicle-drone paths. Each group of paths ,in For the The path of the vehicle, For the A feasible solution S must minimize the total cost while satisfying all constraints. For a path to be feasible, its start and end points should both be located at the designated warehouse, and the capacity constraints of vehicles and drones must be met on all drone sub-paths.

[0004] Like CVRP, VRPD is also an NP-hard problem. The difficulty lies in task synchronization, that is, the spatial movement synchronization and temporal operation synchronization of vehicles and drones. The problem also requires making additional decisions to determine which customer subsets are served by which type of vehicle or drone. Therefore, VRPD is more complex.

[0005] Therefore, the present invention proposes an iterative greedy search method for solving the cooperative path problem of drones and vehicles to solve the above problems. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an iterative greedy search method for solving the cooperative path problem of UAVs and vehicles, and to achieve a high robustness and high-quality solution to the VRPD problem.

[0007] To solve the above technical problems, the technical solution of the present invention is: an iterative greedy search method for solving the cooperative path problem of drones and vehicles, the innovation of which is that it includes the following steps: Step (1) Build a The initial population of solution individuals , and initialize the solution with the best objective function value in the population as the current global optimal solution ; Step (2), from the current population Randomly select a solution As a parent, Apply guided destruction and reconstruction operation, namely GDR operation, based on the destruction rate and a new solution generated by the operator selection mechanism based on dynamic weights ; Step (3) To maintain population diversity and avoid redundant calculations, a fast similarity test is performed to and populations Every existing solution in Calculating distance If any one , making Less than a preset minimum threshold , then determine Similar to the solution in the current population; Step (4), if it is determined If the solution is similar to the solution in the current population, it will be skipped directly; if it is determined If the two layers are not similar, it is considered to be novel enough, and a two-layer hybrid neighborhood search THNS is performed for local optimization. If it is better than the current global best solution , then update ; Step (5) Through the population update strategy, the optimized and dissimilar new solution Incorporate into the population At the same time, the population size is always maintained according to specific rules. ; Step (6), regardless of whether the new solution is included in the population, at the end of each iteration, the weights of the destruction and repair operators used will be updated according to the effect of this GDR operation; Step (7), repeat steps (2) to (6) until the termination condition is met, and finally return the recorded global optimal solution .

[0008] Furthermore, the initialization process described in step (1) specifically includes the following steps: Step (1.1), all customer points Perform random permutation and initialize an empty vehicle path; Step (1.2), process and assign each customer in the random order , traverse all current vehicle paths , find all the vehicle paths and randomly select a vehicle path , the customer Insert into the vehicle path A feasible position is removed from the queue of customers to be processed ; Step (1.3), repeat step (1.2) until all customers are processed and assigned; Step (1.4), for each current vehicle path generated , independently use the intra-path optimization algorithm to perform intra-path optimization to improve the quality of the initial solution; Step (1.5), repeat the above steps times, generate Different initial solutions constitute the initial population .

[0009] Furthermore, the guided destructive reconstruction operation in step (2) specifically includes the following steps: Step (2.1), use the roulette strategy to select the destruction operator and the repair operator: in the initial stage, the weights of all operators are set to the same initial value, Indicates the The operator at the iteration After each iteration, the weight update formula is: in, is the weight update factor; The scores corresponding to the different results of each predefined operator used, including: ① Score : The new solution updates the global optimal solution; ②Score :The new solution does not update the global optimal solution, but All solutions in are dissimilar and the population is updated successfully ; ③Score :The new solution does not update the global optimal solution, and All solutions in are dissimilar, but the population cannot be updated ; ④ Score :New interpretation and A solution is similar or fails to pass the similarity test, but ultimately fails to update the population; Step (2.2), destroy operation to remove customers: First, according to the total number of customers in the example and damage rate parameters The product of , calculates the expected maximum number of removed customers, that is, the upper limit is ,in is a pre-set damage rate parameter, which is used to indicate the expected damage ratio; in the interval The random integer generated internally is denoted as , represents the number of customers actually removed in the current iteration, if , then Forced to 1, ensuring that at least one customer is removed for each destruction operation; During the removal process, if a customer is removed, the number of drone customers in the path of the removed customer will be If the constraints are not satisfied, the removal operation is canceled; Step (2.3), repair operation: first assign the customers in the customer set removed in the destruction operation to the corresponding vehicle path or drone flight path Dr i In the sequence, the efficient drone path construction operation EDPC is then called to regenerate the drone flight subpath sequence ; For customers assigned to each route, the optimal improved insertion strategy with the smallest distance added to the new route is used to select the best insertion location and ensure that the inserted route meets the vehicle capacity constraint. and the number of drone customers constraint; If a feasible insertion location cannot be found, the customer is temporarily retained until a subsequent insertion attempt, or a new path is created to serve it, thus ensuring that every customer can be served.

[0010] Furthermore, the specific steps of the rapid similarity detection described in step (3) include: Step (3.1), define two paths for quantification and Path similarity in terms of customer composition and service model for: in, Respectively represent the path Customers served by vehicles, 、 They represent the set of customers served by the vehicle in the route, excluding the warehouse; Respectively represent the path Customers served by drones, 、 Respectively represent the path The set of customers served by the drone; Step (3.2) uses the Hungarian algorithm to As the matching weight, by solving two complete solutions and of The maximum weight matching problem between the paths is used to calculate the overall similarity weight ; Step (3.3), two solutions and The distance between Defined as: in is the total number of customers.

[0011] Furthermore, the specific steps of the two-layer hybrid neighborhood search described in step (4) include: Step (4.1), Perform intra-path optimization of vehicle paths using the LKH solver; Step (4.2): Optimize the UAV flight sequence using EDPC for the current vehicle path to ensure the high quality of the UAV path under the given vehicle path conditions. In step (4.3), the new solution after optimization in step (4.2) is explored in different neighborhoods in turn, and the corresponding neighborhood 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.

[0012] Furthermore, the neighborhood movement operator described in step (4.3) includes but is not limited to intra-path movement and inter-path movement.

[0013] Furthermore, the population update strategy described in step (5) specifically includes the following steps: Step (5.1), the new solution Temporarily add to the population to form a Temporary population of solutions ; Step (5.2) is Every solution in Calculating fitness scores ,in The specific calculation process is: Define solution To the population distance For solution The minimum distance to all other solutions in the population, The expression is: In order to balance quality and diversity, and new solutions to be evaluated The scale is Temporary population For each solution Calculate the comprehensive fitness score function , The expression is: in, is a balancing parameter that adjusts the relative importance of quality and diversity; is the normalized objective function value, is the normalized distance from the solution to the population, normalized using the minimum-maximum normalization method in the temporary population Conducted within, 、 The expressions are: in, Indicates the current temporary group Individual solutions in ; , indicating the current temporary population The minimum value of the objective function in ; , indicating the current temporary population The maximum value of the objective function in ; , indicating the current temporary population Minimum value of the middle distance; , indicating the current temporary population Maximum value at mid-range; Fitness score The smaller the In the current temporary population The better the overall performance; Step (5.3), identify The solution with the highest fitness score , the specific expression is: ; Step (5.4), make a replacement decision: If the new solution It's not the worst solution ,Right now , then from Removed, so that Officially enter the population, updated population That is ,if It happens to be The worst solution in the population is discarded. Remain unchanged.

[0014] The advantages of the present invention are: (1) The iterative greedy search method of the present invention inherits the idea of ​​the iterative greedy algorithm and incorporates an adaptive operator selection mechanism. The core idea is to iteratively select individuals from a population of solutions, perform guided destruction and recombination operations on them, and avoid redundant two-layer mixed neighborhood searches for similar solutions through fast similarity detection. Finally, the population is updated based on quality and diversity standards. It has the advantages of high solution quality, strong robustness, and a wide range of applications.

[0015] (2) The iterative greedy search method of the present invention integrates four efficient modules: guided destruction and recombination operation, fast similarity detection, two-layer hybrid neighborhood search and population update strategy. Its core idea is to iteratively select individuals from a population of solutions and perform guided destruction and recombination operation on them; through fast similarity detection, it effectively avoids time-consuming evaluation or local search operations on newly generated solutions that are highly similar to existing solutions in the population; integrating the "multi-neighborhood" idea, a two-layer hybrid neighborhood search strategy is proposed, aiming to systematically explore the vast solution space of vehicle paths, drone task allocation and the collaboration between the two; finally, the population is updated based on quality and diversity criteria. A large number of experimental results show that compared with existing methods, the method of the present invention has highly competitive performance and effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Figure 1 This is a schematic diagram of a calculation example of a path problem for collaboration between a vehicle and a drone according to the present invention.

[0018] Figure 2 This is the repetition probability change curve of the first 10,000 iterations of the fast similarity detection strategy of the present invention.

[0019] Figure 3 This is a comparative diagram comparing the solution results of APIG1 and APIG of the present invention.

[0020] Figure 4 Flowchart of the iterative greedy 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", which means that delivery by drones cannot be made.

[0023] The system in question has homogeneous vehicles, each with a capacity of , and 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 serve customers, while the drone can take off from the vehicle at the warehouse or any customer location and independently perform delivery tasks. Meanwhile, the vehicle continues to move and serve other customers. The drone must return to the original vehicle at the same customer or warehouse location. However, a drone is prohibited from leaving and returning to the same vehicle at the same customer location. Each drone can only serve a maximum of one customer before returning to the vehicle.

[0024] VRPD Path By a pair Indicates that represents the path of the vehicle, Represents the corresponding drone subpath. The vehicle path starts from the warehouse Set out and serve customers in turn , and finally returned to the warehouse Each UAV subpath Contains three vertices: Indicates the take-off position of the drone. Represents customers of drone services, Indicates the position of the drone returning to the vehicle.

[0025] For each subpath, two indices must exist satisfy and and , that is, the vehicle provides services to customers independently between these two locations. In addition, for two adjacent drone sub-paths and To ensure that the independent service intervals of vehicles and drones do not overlap, there are two indexes satisfy and and .

[0026] 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 Established. 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.

[0027] This embodiment provides an iterative greedy search method (APIG) for solving the cooperative routing problem of UAVs and vehicles. Figure 1 An example of VRPD is described along with the representation and evaluation of the solution.

[0028] Given a containing customers and The VRPD example of a vehicle equipped with a drone can be solved by The two sets of paths are represented by the vehicle path set and the drone path set. The vehicle path set is the order of the customers visited by the vehicle, while the drone path set represents the order of the sub-paths visited by the drone. 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. Figure 1 Shows an example of VRPD, which contains paths, each path contains a vehicle path and a drone path, with capacity constraints . 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.

[0029] 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 flight subpaths. Each 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: , , .untie The total cost is calculated as the sum of the distance traveled by the vehicle and the distance flown by the drone: in, in, Represents the vehicle path The edge set of Represents an edge The corresponding Manhattan distance is, Represents the drone 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 .

[0030] The iterative greedy search method of this embodiment is as follows: Figure 4 As shown, the following steps are included: Step (1) Build a The initial population of solution individuals , and initialize the solution with the best objective function value in the population as the current global optimal solution ; Step (1) uses a purely random approach to construct an initial solution containing only vehicle paths, i.e., the CVRP solution corresponding to the VRPD problem. The specific steps of the initialization process include: Step (1.1), all customer points Perform random permutation and initialize an empty vehicle path; Step (1.2), process and assign each customer in the random order , traverse all current vehicle paths , find all the vehicle paths and randomly select a vehicle path , the customer Insert into the vehicle path A feasible position is removed from the queue of customers to be processed ; Step (1.3), repeat step (1.2) until all customers are processed and assigned; Step (1.4), for each current vehicle path generated , independently use the path internal optimization algorithm LKH (Lin-Kernighan-Helsgaun) algorithm for path optimization to improve the quality of the initial solution; Step (1.5), repeat the above steps times, generate Different initial solutions constitute the initial population .

[0031] Step (2), from the current population Randomly select a solution As a parent, Apply guided destruction and reconstruction operation, namely GDR (Guided Destruction-Reconstruction) operation, based on the destruction rate and a new solution generated by the operator selection mechanism based on dynamic weights ; Step (2) Definition and are respectively the set of destruction methods and the set of repair methods. In each iteration, Select a destruction operator from and from Select a repair operator , guiding the current solution to optimize through destruction and repair operations. The specific steps of guided destruction and reconstruction operations include: Step (2.1), use the roulette strategy to select the destruction operator and the repair operator: in the initial stage, the weights of all operators are set to the same initial value, Indicates the The operator at the iteration After each iteration, the weight update formula is: in, is the weight update factor; The scores corresponding to the different results of each predefined operator used, including: ① Score : The new solution updates the global optimal solution; ②Score :The new solution does not update the global optimal solution, but All solutions in are dissimilar and the population is updated successfully ; ③Score :The new solution does not update the global optimal solution, and All solutions in are dissimilar, but the population cannot be updated ; ④ Score :New interpretation and A solution is similar or fails to pass the similarity test, but ultimately fails to update the population; Step (2.2), destroy operation to remove customers: First, according to the total number of customers in the example and damage rate parameters The product of , calculates the expected maximum number of removed customers, that is, the upper limit is ,in is a pre-set damage rate parameter, which is used to indicate the expected damage ratio; in the interval The random integer generated internally is denoted as , represents the number of customers actually removed in the current iteration. In order to avoid the random generated result being too small and causing insufficient damage, it is specially stipulated that if , then Forced to 1, ensuring that at least one customer is removed for each destruction operation; During the removal process, if a customer is removed, the number of drone customers in the path of the removed customer will be If the constraints are not satisfied, the removal operation is canceled; Step (2.3), repair operation: first assign the customers in the customer set removed in the destruction operation to the corresponding vehicle path or drone flight path Dr i In the sequence, the EfficientDrone Path Construction (EDPC) operation is then called to regenerate the sequence of drone flight subpaths. ; For customers assigned to each route, the optimal improved insertion strategy with the smallest distance added to the new route is used to select the best insertion location and ensure that the inserted route meets the vehicle capacity constraint. and the number of drone customers Constraints; if a feasible insertion location cannot be found, temporarily retain the customer until a subsequent insertion attempt, or create a new path to serve it, thus ensuring that every customer can be served.

[0032] 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 (2.3.1), 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.

[0033] Step (2.3.2), 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.

[0034] 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.

[0035] 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 (2.3.3), 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.

[0036] Step (2.3.4), joint optimization of multiple subpaths, allows modification of previously determined take-off and landing nodes when optimizing the current subpath, thus achieving global cost re-optimization. , Introducing the preorder subpath The take-off and landing nodes are jointly optimized, and 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.

[0037] 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.

[0038] 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.

[0039] Step (3) To maintain population diversity and avoid redundant calculations, a fast similarity test (IsSimilar) is performed. and populations Every existing solution in Calculating distance , if there is any , making Less than a preset minimum threshold , then determine Similar to the solution in the current population, in this embodiment, Set to 0; The core goal of the fast similarity check described in step (3) is to avoid performing the computationally expensive THNS on newly generated solutions that are highly similar to existing solutions in the population. The specific steps of the fast similarity check include: Step (3.1), define two paths for quantification and Path similarity in terms of customer composition and service model for: in, Respectively represent the path Customers served by vehicles, Respectively represent the path The set of customers served by the vehicle, excluding warehouses; Respectively represent the path Customers served by drones, Respectively represent the path The set of customers served by the drone; Step (3.2) uses the Hungarian algorithm to As the matching weight, by solving two complete solutions and of The maximum weight matching problem between the paths is used to calculate the overall similarity weight ; Step (3.3), two solutions and The distance between Defined as: in is the total number of customers.

[0040] Step (4), if it is determined If the solution is similar to the solution in the current population, it will be skipped directly; if it is determined If the two-level hybrid neighborhood search (THNS) is performed for local optimization, the optimized If it is better than the current global best solution , then update ; The specific steps of the two-layer hybrid neighborhood search include: Step (4.1), The vehicle path is optimized within the path using the LKH solver; Step (4.2): Optimize the UAV flight sequence using EDPC for the current vehicle path to ensure the high quality of the UAV path under the given vehicle path conditions. In step (4.3), the new solution optimized in step (4.2) is sequentially explored in different neighborhoods (including intra-path and inter-path operations). The corresponding neighborhood movement operators are used to perturb the vehicle and drone paths. After each movement, the EDPC is called to regenerate the drone flight sequence. The first-improvement insertion strategy is used to reduce the incremental distance of the newly generated path. If the new neighborhood solution violates the constraint on the number of drone customers, the move is undone and other neighborhood operations are tried. Among them, neighborhood movement operators include but are not limited to intra-path movement and inter-path movement.

[0041] Step (5) Through the population updating strategy (Population Updating), the optimized and dissimilar new solution Incorporate into the population At the same time, the population size is always maintained according to specific rules. ,Specific rules can be used to eliminate inferior solutions or the oldest solutions; Step (5) aims to simultaneously combine the quality and diversity of the solution population update strategy. The specific steps include: Step (5.1), the new solution Temporarily add to the population to form a Temporary population of solutions ; Step (5.2) is Every solution in Calculating fitness scores ,in The specific calculation process is: Define solution To the population distance For solution The minimum distance to all other solutions in the population, The expression is: In order to balance quality and diversity, and new solutions to be evaluated The scale is Temporary population For each solution Calculate the comprehensive fitness score function , The expression is: in, is a balancing parameter that adjusts the relative importance of quality and diversity; is the normalized objective function value ( The smaller the value, the better). is the normalized distance from the solution to the population ( The larger the value, the better, so reverse normalization is used), normalization uses the minimum-maximum normalization method in the temporary population Conducted within, 、 The expressions are: in, Indicates the current temporary group Individual solutions in ; , indicating the current temporary population The minimum value of the objective function in ; , indicating the current temporary population The maximum value of the objective function in ; , indicating the current temporary population Minimum value of the middle distance; , indicating the current temporary population Maximum value at mid-range; Fitness score The smaller the In the current temporary population The better the overall performance.

[0042] Step (5.3), identify The solution with the highest fitness score (i.e., the worst overall performance) , the specific expression is: ; Step (5.4), make a replacement decision: If the new solution It's not the worst solution ,Right now , then from Removed, so that Officially enter the population, updated population That is .if It happens to be The worst solution in the population is discarded. Remain unchanged.

[0043] Step (6), regardless of whether the new solution is included in the population, at the end of each iteration, the weights of the destruction and repair operators used will be updated according to the effect of this GDR operation; Step (7), repeat steps (2) to (6) until the termination condition is met, that is, the total calculation time reaches the preset upper limit, and finally return the recorded global optimal solution .

[0044] This embodiment combines Figure 2 and Figure 3 This further illustrates the effectiveness of the fast similarity detection strategy and efficient UAV path building operation.

[0045] Figure 2 The operating mechanism of the fast similarity detection strategy and the reason for time saving are explained. Figure 2 The results show how the probability of detecting a "duplicate" (i.e., similar) solution changes with the number of iterations during the first 10,000 iterations of the algorithm on different typical examples. It can be seen that after the initial stage of the algorithm, the probability of duplicates usually stabilizes at a high level (for example, when The repetition probability is about , Time , Time ). Such a high probability of duplication means that the fast similarity detection strategy has plenty of opportunities to identify and skip processing of these similar solutions, thus achieving significant time savings.

[0046] This embodiment verifies the effectiveness of EDPC through ablation experiments. The two algorithms are APIG and APIG1. APIG is the iterative greedy search method of this embodiment, and APIG1 is obtained by ablating EDPC in APIG. Figure 3 The horizontal axis is the number of the case, and the vertical axis is the difference value from the APIG result. Figure 3 The results show that in terms of optimal solution quality, APIG1 without EDPC performs worse or on par with APIG with EDPC. This indicates that the EDPC method has a positive impact on the algorithm's ability to find high-quality optimal solutions, and removing it generally leads to a decrease in optimal solution quality. In terms of average solution quality, APIG1 without EDPC has a higher average solution cost than APIG with EDPC across all 20 cases. This fully demonstrates that the EDPC method can effectively guide the algorithm to stably converge to higher-quality solutions over multiple runs, demonstrating its important contribution to improving the robustness of the algorithm. Therefore, integrating EDPC as a core component into the APIG algorithm is necessary and effective for achieving efficient and high-quality VRPD solutions.

[0047] 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 iterative greedy search method for solving the UAV-vehicle cooperative routing problem, characterized by: The following steps are involved: Step (1) Build a The initial population of solution individuals , and initialize the solution with the best objective function value in the population as the current global optimal solution ; Step (2), from the current population Randomly select a solution As a parent, Apply guided destruction and reconstruction operation, namely GDR operation, based on the destruction rate and a new solution generated by the operator selection mechanism based on dynamic weights ; Step (3) To maintain population diversity and avoid redundant calculations, a fast similarity test is performed to and populations Every existing solution in Calculating distance If any one , making Less than a preset minimum threshold , then determine Similar to the solution in the current population; Step (4), if it is determined If the solution is similar to the solution in the current population, it will be skipped directly; if it is determined If the two layers are not similar, it is considered to be novel enough, and a two-layer hybrid neighborhood search THNS is performed for local optimization. If it is better than the current global best solution , then update ; Step (5) Through the population update strategy, the optimized and dissimilar new solution Incorporate into the population At the same time, the population size is always maintained according to specific rules. ; Step (6), regardless of whether the new solution is included in the population, at the end of each iteration, the weights of the destruction and repair operators used will be updated according to the effect of this GDR operation; Step (7), repeat steps (2) to (6) until the termination condition is met, and finally return the recorded global optimal solution .

2. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 1, characterized in that: The specific steps of the initialization process described in step (1) include: Step (1.1), all customer points Perform random permutation and initialize an empty vehicle path; Step (1.2), process and assign each customer in the random order , traverse all current vehicle paths , find all the vehicle paths and randomly select a vehicle path , the customer Insert into the vehicle path A feasible position is removed from the queue of customers to be processed ; Step (1.3), repeat step (1.2) until all customers are processed and assigned; Step (1.4), for each current vehicle path generated , independently use the intra-path optimization algorithm to perform intra-path optimization to improve the quality of the initial solution; Step (1.5), repeat the above steps times, generate Different initial solutions constitute the initial population .

3. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 1, characterized in that: 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: in the initial stage, the weights of all operators are set to the same initial value. Indicates the The operator at the iteration After each iteration, the weight update formula is: in, is the weight update factor; The scores corresponding to the different results of each predefined operator used, including: ① Score : The new solution updates the global optimal solution; ②Score :The new solution does not update the global optimal solution, but All solutions in are dissimilar and the population is updated successfully ; ③Score :The new solution does not update the global optimal solution, and All solutions in are dissimilar, but the population cannot be updated ; ④ Score :New interpretation and A solution is similar or fails to pass the similarity test, but ultimately fails to update the population; Step (2.2), destroy operation to remove customers: First, according to the total number of customers in the example and damage rate parameters The product of , calculates the expected maximum number of removed customers, that is, the upper limit is ,in is a pre-set damage rate parameter, which is used to indicate the expected damage ratio; in the interval The random integer generated internally is denoted as , represents the number of customers actually removed in the current iteration, if , then Forced to 1, ensuring that at least one customer is removed for each destruction operation; During the removal process, if a customer is removed, the number of drone customers in the path of the removed customer will be If the constraints are not satisfied, the removal operation is canceled; Step (2.3), repair operation: first assign the customers in the customer set removed in the destruction operation to the corresponding vehicle path or drone flight path Dr i In the sequence, the efficient drone path construction operation EDPC is then called to regenerate the drone flight subpath sequence ; For customers assigned to each route, the optimal improved insertion strategy with the smallest distance added to the new route is used to select the best insertion location and ensure that the inserted route meets the vehicle capacity constraint. and the number of drone customers constraint; If a feasible insertion location cannot be found, the customer is temporarily retained until a subsequent insertion attempt, or a new path is created to serve it, thus ensuring that every customer can be served.

4. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 1, characterized in that: The specific steps of the rapid similarity detection described in step (3) include: Step (3.1), define two paths for quantification and Path similarity in terms of customer composition and service model for: in, Respectively represent the path Customers served by vehicles, 、 They represent the set of customers served by the vehicle in the route, excluding the warehouse; Respectively represent the path Customers served by drones, 、 Respectively represent the path The set of customers served by the drone; Step (3.2) uses the Hungarian algorithm to As the matching weight, by solving two complete solutions and of The maximum weight matching problem between the paths is used to calculate the overall similarity weight ; Step (3.3), two solutions and The distance between Defined as: in is the total number of customers.

5. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 1, characterized in that: The specific steps of the double-layer hybrid neighborhood search described in step (4) include: Step (4.1), Perform intra-path optimization of vehicle paths using the LKH solver; Step (4.2): Optimize the UAV flight sequence using EDPC for the current vehicle path to ensure the high quality of the UAV path under the given vehicle path conditions. In step (4.3), the new solution after optimization in step (4.2) is explored in different neighborhoods in turn, and the corresponding neighborhood 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.

6. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 5, characterized in that: The neighborhood movement operators described in step (4.3) include but are not limited to intra-path movement and inter-path movement.

7. The iterative greedy search method for solving the UAV-vehicle cooperative routing problem according to claim 1, characterized in that: The specific steps of the population update strategy described in step (5) include: Step (5.1), the new solution Temporarily add to the population to form a temporary population of solutions ; Step (5.2) is Every solution in Calculating fitness scores ,in The specific calculation process is: Define solution To the population distance For solution The minimum distance to all other solutions in the population, The expression is: In order to balance quality and diversity, and new solutions to be evaluated The scale is Temporary population For each solution Calculate the comprehensive fitness score function , The expression is: in, is a balancing parameter that adjusts the relative importance of quality and diversity; is the normalized objective function value, is the normalized distance from the solution to the population, normalized using the minimum-maximum normalization method in the temporary population Conducted within, 、 The expressions are: in, Indicates the current temporary group Individual solutions in ; , indicating the current temporary population The minimum value of the objective function in ; , indicating the current temporary population The maximum value of the objective function in ; , indicating the current temporary population Minimum value of the middle distance; , indicating the current temporary population Maximum value at mid-range; Fitness score The smaller the solution In the current temporary population The better the overall performance; Step (5.3), identify The solution with the highest fitness score , the specific expression is: ； Step (5.4), make a replacement decision: If the new solution It's not the worst solution ,Right now , then from Removed, so that Officially enter the population, updated population That is ,if It happens to be The worst solution in the population is discarded. Remain unchanged.

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