Method for optimizing distribution path at tail end of high-speed rail through cooperation of unmanned aerial vehicle and vehicle

Abstract

The invention provides a high-speed rail tail end distribution path optimization method based on cooperation of an unmanned aerial vehicle and a vehicle. Relates to the technical field of path planning. The method comprises the following steps: constructing a high-speed rail tail end distribution network; establishing a distribution optimization model by taking minimization of total distribution time and total distribution cost in a high-speed rail tail end distribution network as an optimization target and taking distribution path constraints of vehicles and unmanned aerial vehicles as well as cargo batch distribution time sequence and distribution resource dynamic allocation constraints as constraint conditions; solving the distribution optimization model through an improved adaptive large neighborhood search algorithm to obtain a distribution path scheme; an adaptive large neighborhood search algorithm is improved, and a vehicle distribution path is optimized through path topology reconstruction; the unmanned aerial vehicle distribution path is optimized through unmanned aerial vehicle take-off and landing point reconfiguration, unmanned aerial vehicle distribution task transfer and vehicle and unmanned aerial vehicle distribution service interchange; and cargo batch scheduling optimization is carried out by adjusting the distribution sequence of different cargo batches and the configuration proportion of the vehicle and the unmanned aerial vehicle in each batch of distribution.

Description

Technical Field

[0001] This invention relates to the field of route planning technology, and in particular to a method for optimizing the last-mile delivery route of high-speed rail using a combination of drones and vehicles. Background Technology

[0002] High-speed rail networks, with their advantages of speed, punctuality, and large capacity, are gradually becoming core hubs in regional logistics systems. As key nodes connecting trunk line transportation and last-mile delivery, the efficiency of "last-mile" delivery at high-speed rail stations directly determines the service quality and operating costs of the overall supply chain. Traditional last-mile delivery mainly relies on single-vehicle models, facing challenges such as urban traffic congestion, tight delivery windows, and insufficient coverage of high-value areas. In recent years, drone-vehicle collaborative delivery models have received widespread attention due to their flexibility and efficiency, and are particularly suitable for hub-and-spoke delivery scenarios like high-speed rail stations.

[0003] However, existing research mostly focuses on static delivery networks and fails to fully consider the uneven distribution of vehicle and drone resources over time caused by the dynamic arrival characteristics of high-speed rail with multiple trains. This results in a significant disconnect between theoretical models and actual application scenarios, and the feasibility and optimization efficiency of delivery solutions need to be improved. Summary of the Invention

[0004] Therefore, it is necessary to provide a method for optimizing the last-mile delivery route of high-speed rail using a combination of drones and vehicles, in order to address the aforementioned technical problems.

[0005] The following technical solution is adopted in this specification: This specification provides a method for optimizing the last-mile delivery route on high-speed rail using a combination of drones and vehicles, including: A high-speed rail last-mile delivery network will be constructed, with high-speed rail stations serving as distribution centers and target delivery locations around high-speed rail stations serving as last-mile delivery nodes. With the goal of minimizing the total delivery time and total delivery cost within the high-speed rail last-mile delivery network, and constrained by the delivery route constraints of vehicles and drones, as well as the constraints of the batch delivery timing of goods based on the arrival time series of multiple high-speed rail trains and the dynamic allocation of delivery resources, a delivery optimization model is constructed. The delivery optimization model is solved by improving the adaptive large neighborhood search algorithm to obtain delivery route solutions. Specifically, the improved adaptive large neighborhood search algorithm adds three types of local search strategies to the standard large neighborhood search algorithm framework: Optimize vehicle delivery routes through route topology reconstruction; Optimize drone delivery routes by reconfiguring drone take-off and landing points, transferring drone delivery tasks, and exchanging vehicle and drone delivery services. The scheduling of cargo batches was optimized by adjusting the delivery sequence of different cargo batches and the configuration ratio of vehicles and drones in each batch delivery.

[0006] Furthermore, the improved adaptive large neighborhood search algorithm also includes generating an initial solution through a three-stage hybrid heuristic strategy, which includes: In the first stage, the delivery nodes in the high-speed rail last-mile delivery network are clustered according to their geographical distribution, and an initial service area is divided for each delivery vehicle to construct an initial path framework that includes the spatial distribution of the vehicles. In the second stage, delivery nodes that have not been assigned to the initial path framework are inserted into the feasible vehicle delivery paths in the initial path framework to generate intermediate solutions that contain only vehicle delivery paths. In the third stage, the vehicle delivery path of the intermediate solution is used as the launch node or recovery node of the drone. Drone delivery tasks are assigned to the remaining delivery nodes in the high-speed rail terminal delivery network that cannot be covered by the vehicle delivery path, and a complete initial solution containing the collaborative path of vehicles and drones is generated.

[0007] Furthermore, the construction of the initial path framework including the spatial distribution of vehicles includes: The improved K-means clustering algorithm divides delivery nodes into a preset number of clusters. The improved K-means clustering algorithm introduces a demand weight factor when obtaining the distance between the delivery node and the cluster center. The demand weight factor is positively correlated with the delivery demand of the delivery node and is used to enhance the aggregation tendency of high-demand delivery nodes to the cluster center during the clustering process. After clustering is completed, the nearest neighbor heuristic algorithm is used to construct delivery routes for the set of delivery nodes in each cluster, thereby obtaining an initial path framework that includes the spatial distribution of vehicles.

[0008] Furthermore, the generation of intermediate solutions containing only vehicle delivery routes includes: For the set of delivery nodes not assigned to the initial path framework, sort them in descending order according to the amount of goods to be delivered, and generate a sequence of nodes to be processed; A multi-constraint feasibility test is performed on all candidate insertion positions in the initial path framework to select a set of feasible insertion positions that simultaneously satisfy the preset vehicle load constraints, service time window constraints, and maximum vehicle travel distance constraints. For each location in the set of feasible insertion locations, calculate the comprehensive cost increment, which includes the travel distance increment, time delay increment, and energy consumption increment; sort the locations in the set of feasible insertion locations in ascending order according to the comprehensive cost increment, and insert the delivery node in the node sequence to be processed into the first feasible location in the sorted order; process all delivery nodes in the node sequence to be processed in sequence to obtain an intermediate solution containing the vehicle delivery route.

[0009] Furthermore, if the multi-constraint feasibility check fails to filter out a set of feasible insertion positions, a path reconstruction sub-operation is executed. The path reconstruction sub-operation adjusts the node allocation relationship by swapping the positions of already allocated nodes in the path or creating new delivery sub-paths.

[0010] Furthermore, the path topology reconstruction includes: The 2-opt swap operation is used to disconnect two non-adjacent edges in a single vehicle delivery route and reconnect the disconnected route segments to eliminate intersections in the route. Cross-path node swapping is used to select one delivery node from each of two different vehicle delivery routes and swap their positions to change the distribution sequence of path nodes. The node migration operation is used to remove one or more delivery nodes from one vehicle delivery route and insert them into another vehicle delivery route, thereby reducing the empty driving distance by adjusting the task load between vehicles.

[0011] Furthermore, the improved adaptive large neighborhood search algorithm is executed sequentially in each iteration: The destruction operator performs destruction operations on the current solution. The destruction operation expands the scope of solution space exploration by destroying the path structure of vehicles and drones in the current solution. Repair operators are used to repair the damaged solution. The repair operation reorganizes the path structure and restores the feasibility of the solution by inserting delivery nodes into the current solution after it has been damaged. Three types of local search strategies are used to optimize the current solution after repair, and the current solution is updated based on the optimization results.

[0012] Furthermore, the destruction operator includes: The random removal operator is used to randomly remove a preset proportion of delivery nodes from the current solution to increase search diversity; The worst-case removal operator is used to identify and remove delivery nodes that contribute the least to the optimization objective, thereby improving the quality of the solution; The time window removal operator is used to remove delivery nodes that do not meet the preset time window constraints, thereby improving the time window satisfaction rate. Cluster removal operators are used to remove geographically clustered delivery nodes in order to restructure regional delivery strategies.

[0013] Furthermore, the repair operator includes: The greedy insertion operator is used to calculate the incremental delivery cost of the node to be inserted at each feasible position in the high-speed rail terminal delivery network, and insert the node to be inserted into the feasible position with the minimum incremental delivery cost. The regret insertion operator is used to insert delivery nodes in descending order of regret value, using the cost difference between the optimal insertion position and the k-th best insertion position as the regret value, in order to avoid suboptimal solutions caused by local greedy selection; where the optimal insertion position and the k-th best insertion position are the feasible positions with the minimum incremental delivery cost and the k-th smallest, respectively, and k is a preset positive integer; The learning-guided insertion operator is used to construct a probability distribution model based on the successful insertion frequency of each delivery node in feasible positions during historical iterations. It prioritizes inserting nodes into high-probability preferred positions where the historical success probability is higher than a preset threshold, thereby leveraging prior knowledge to improve global search efficiency.

[0014] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: This invention addresses the core characteristics of dynamic arrival of multiple high-speed trains and the collaborative requirements of "vehicle-drone-cargo batches." Building upon the standard framework, it adds three highly targeted local search strategies: a path topology reconstruction strategy flexibly optimizes vehicle delivery routes to adapt to the end-point distribution of different cargo batches; a drone take-off and landing point reconfiguration, task transfer, and service exchange strategy dynamically adjusts drone capacity to match the spatiotemporal demands of cargo batches; and a strategy for adjusting the delivery order of different cargo batches and optimizing the capacity allocation ratio within batches directly responds to the time-series characteristics of multiple high-speed train arrivals, achieving flexible matching of delivery resources with the arrival rhythm of high-speed trains. Through the synergistic effect of these three strategies, the algorithm can dynamically balance the resource allocation of vehicles and drones in real time during the solution process, breaking the limitations of static delivery networks. Simultaneously, this multi-dimensional collaborative optimization reduces idle waste through dynamic adaptation of capacity resources and further compresses total delivery time and cost through collaborative optimization of path and batch scheduling, significantly improving the feasibility and optimization efficiency of the delivery solution. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0016] Figure 1 This document provides a flowchart illustrating a method for optimizing the last-mile delivery route on high-speed rail using a combination of drones and vehicles. Figure 2 This manual provides a schematic diagram of a traditional high-speed rail express "to the distribution center" model. Figure 3 This specification provides a schematic diagram of a novel high-speed rail express "to the distribution center" model. Figure 4This specification provides a schematic diagram of a method for the collaborative transportation and delivery of different batches of goods using multiple drones and multiple vehicles. Figure 5 This document provides a flowchart illustrating the framework of an adaptive large neighborhood search algorithm. Figure 6 This manual provides a schematic diagram of the departure and return times for each batch of vehicles. Figure 7 This is a schematic diagram of an optimal delivery route provided in this manual; Figure 8a This document provides a schematic diagram of the delivery routes for batches 1 to 3 in an optimal solution for 10 batches of goods. Figure 8b This document provides a schematic diagram of the delivery routes for batches 4 to 5 in an optimal solution for 10 batches of goods. Figure 9 This document provides a schematic diagram of an optimal delivery route with 20 nodes. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0018] The technical solution provided by this invention can be applied to the optimization of high-speed rail last-mile delivery routes using drones and vehicles. With the rapid development of e-commerce and high-speed rail networks, high-speed rail express, as an emerging logistics model, has become an important way to solve medium- and long-distance express delivery problems due to its advantages such as high timeliness and stable capacity. However, in the last-mile delivery stage, traditional ground vehicles still face challenges of low delivery efficiency and high costs due to urban traffic congestion and insufficient road network coverage in remote areas. Taking SF Express as an example, the timeliness fluctuation coefficient of its high-speed rail express orders in the last-mile delivery stage is as high as 0.38, seriously restricting the stability of high-end logistics services. In 2023, my country's express delivery volume exceeded 130 billion pieces, of which time-sensitive pieces accounted for more than 30%, placing higher demands on last-mile delivery efficiency. Although high-speed rail express can reduce trunk line transportation time, the last-mile delivery stage accounts for more than 40% of the total timeliness, becoming a bottleneck restricting service quality. Against this backdrop, drone delivery technology, with its high flexibility and lack of terrain limitations, offers an innovative solution for the "last mile" of last-mile logistics. How to coordinate drones with ground vehicles to build an efficient high-speed rail express last-mile delivery system has become a key issue that urgently needs to be addressed in the field of smart logistics. To overcome the reduced timeliness caused by last-mile delivery, this article innovatively proposes a "decentralized" multi-truck, multi-drone delivery model. This model involves delivery vehicles directly delivering goods arriving by high-speed rail express to urban last-mile logistics stations without transferring them through distribution centers.

[0019] The innovative development of high-speed rail express delivery organization models has become an important pillar of the modern comprehensive transportation system, and its research exhibits a full-chain optimization characteristic from top-level design to implementation. The problem of drone-assisted ground vehicle delivery route optimization has become an important direction in modern logistics research, and its development has shown an evolution from theoretical framework construction to multi-scenario applications. Many scholars have conducted in-depth research on high-speed rail express last-mile cargo organization models, drone-assisted ground vehicle route optimization algorithms, models, and application scenarios; however, research on drone-assisted vehicle delivery at the high-speed rail express last mile is currently lacking.

[0020] Therefore, this invention innovatively combines high-speed rail express delivery with drone-assisted vehicles to address the last-mile delivery problem. Through a "decentralized" organizational model, multiple batches of goods arriving via high-speed rail express are delivered collaboratively by multiple vehicles and drones. Based on the high-speed rail express arrival timetable, and with the goal of minimizing total last-mile delivery time and cost, and constrained by vehicle and drone routes, dynamic cyclical use of vehicles and drones, and delivery time windows, a multi-vehicle, multi-drone, multi-batch goods delivery model is established. This model is then solved using an Adaptive Neighborhood Search (ALNS) algorithm to obtain the optimal delivery solution for high-speed rail express last-mile goods.

[0021] The following is combined Figures 1-9This invention describes a method for optimizing high-speed rail last-mile delivery routes that combines drones and vehicles.

[0022] Figure 1 This is a flowchart illustrating the high-speed rail last-mile delivery route optimization method using drones and vehicles provided by the present invention, as shown below. Figure 1 As shown, the method includes the following: S100, with high-speed rail stations as distribution centers and target distribution locations around high-speed rail stations as end-point distribution nodes, constructs a high-speed rail end-point distribution network.

[0023] S200. With the goal of minimizing the total delivery time and total delivery cost within the high-speed rail terminal delivery network, and with constraints on delivery routes of vehicles and drones, as well as constraints on the batch delivery sequence of goods based on the arrival time series of multiple high-speed rail trains and the dynamic allocation of delivery resources, a delivery optimization model is constructed.

[0024] For example, the delivery optimization model simultaneously considers vehicle routing constraints, drone routing constraints, cargo delivery time window constraints, vehicle capacity constraints, and drone range constraints.

[0025] S300. The delivery optimization model is solved by improving the adaptive large neighborhood search algorithm to obtain the delivery route scheme. Among them, the improved adaptive large neighborhood search algorithm adds three types of local search strategies on the framework of the standard large neighborhood search algorithm: optimizing vehicle delivery routes by reconstructing the path topology; optimizing drone delivery routes by reconfiguring drone take-off and landing points, transferring drone delivery tasks, and exchanging vehicle and drone delivery services; and optimizing cargo batch scheduling by adjusting the delivery order of different cargo batches and the configuration ratio of vehicles and drones in each batch of delivery.

[0026] For example, path topology reconstruction includes: a 2-opt swap operation, used to disconnect two non-adjacent connecting edges in a single vehicle delivery path and reconnect the disconnected path segments to eliminate intersections in the path; a cross-path node swap operation, used to select one delivery node from each of two different vehicle delivery paths and swap their positions to change the distribution sequence of path nodes; and a node migration operation, used to remove one or more delivery nodes from one vehicle delivery path and insert them into another vehicle delivery path to reduce the idle travel distance by adjusting the task load between vehicles.

[0027] For example, the improved adaptive large neighborhood search algorithm also includes generating an initial solution through a three-stage hybrid heuristic strategy. This strategy comprises: First, clustering delivery nodes in the high-speed rail last-mile delivery network based on geographical distribution, assigning an initial service area to each delivery vehicle, and constructing an initial path framework containing the spatial distribution of vehicles. Second, inserting delivery nodes not assigned to the initial path framework into feasible vehicle delivery paths within the initial path framework, generating an intermediate solution containing only vehicle delivery paths. Third, using the vehicle delivery paths from the intermediate solution as drone launch or recovery nodes, assigning drone delivery tasks to the remaining delivery nodes in the high-speed rail last-mile delivery network that are not covered by the vehicle delivery paths, generating a complete initial solution containing collaborative paths between vehicles and drones.

[0028] Specifically, in the first stage, the delivery nodes are divided into a preset number of clusters by improving the K-means clustering algorithm. The improved K-means clustering algorithm introduces a demand weight factor when obtaining the distance between the delivery node and the cluster center. The demand weight factor is positively correlated with the amount of goods delivery demand of the delivery node, which is used to enhance the aggregation tendency of high-demand delivery nodes to the cluster center during the clustering process. After the clustering is completed, the nearest neighbor heuristic algorithm is used to construct the delivery path for the set of delivery nodes in each cluster, and obtain an initial path framework containing the spatial distribution of vehicles.

[0029] Specifically, in the second stage, the set of delivery nodes not assigned to the initial path framework is sorted in descending order according to the demand for goods delivery, generating a sequence of nodes to be processed. A multi-constraint feasibility test is performed on all candidate insertion positions in the initial path framework to select a set of feasible insertion positions that simultaneously satisfy preset vehicle load constraints, service time window constraints, and maximum vehicle travel distance constraints. For each position in the set of feasible insertion positions, a comprehensive cost increment is calculated, including travel distance increment, time delay increment, and energy consumption increment. The positions in the set of feasible insertion positions are then sorted in ascending order according to the comprehensive cost increment, and the delivery node in the sequence of nodes to be processed is inserted into the first feasible position in the sorted list. All delivery nodes in the sequence of nodes to be processed are processed sequentially to obtain an intermediate solution containing the vehicle delivery path. It should be noted that in the second stage, if the multi-constraint feasibility test does not select a set of feasible insertion positions, a path reconstruction sub-operation is executed. This path reconstruction sub-operation adjusts the node allocation relationship by swapping the positions of already assigned nodes in the path or creating new delivery sub-paths.

[0030] Based on the above Figure 1 The illustrated embodiments, by way of example, describe the problems of the present invention: High-speed rail express, as an emerging logistics model, is gradually becoming an important means of transporting high-value-added goods over medium and long distances due to its efficiency and punctuality. However, in the last-mile delivery stage, the traditional transshipment model relying on distribution centers suffers from problems such as low timeliness, high cost, and insufficient flexibility. Furthermore, the traditional logistics delivery model, completed by individual vehicles, is subject to low delivery efficiency and high costs due to terrain and road congestion. Traditional high-speed rail express last-mile delivery is based on a "de-distribution-center" model: pre-arranged freight handlers unload goods arriving in batches at the platform, sorting different goods and unloading them into different designated safe areas; forklifts are used for small parcels and standard containers, while conveyor belts are used for large and heavy goods; after transportation to designated locations, goods are loaded onto trucks, and then directly delivered to the last-mile logistics station. Figure 2 This specification provides a schematic diagram of a traditional high-speed rail express "to the distribution center" model, as shown below. Figure 2 As shown, while existing research has explored route optimization for collaborative delivery using drones and ground vehicles, it has not yet been deeply integrated with the last-mile delivery scenario of high-speed rail express, especially lacking systematic research on dynamic arrival of multiple batches of goods and collaborative cyclical scheduling of multiple transport vehicles. A novel "de-distribution-center" organizational model for high-speed rail express last-mile delivery is proposed to address key issues in this area. Figure 3 This specification provides a schematic diagram of a novel high-speed rail express "to-distribution-center" model, as shown below. Figure 3 As shown. Traditional high-speed rail express delivery relies on individual vehicles for last-mile delivery. Considering the high transportation costs and low efficiency caused by limited delivery capacity, road congestion, and long vehicle travel distances at the high-speed rail last-mile, this method fails to meet customers' timeliness requirements for high-value-added high-speed rail express products. Therefore, this invention constructs a collaborative transportation and delivery method for different batches of goods based on multi-UAV and multi-vehicle coordination. Figure 4 This specification provides a schematic diagram of a method for the collaborative transportation and delivery of different batches of goods using multiple drones and multiple vehicles. The delivery method is as follows: Figure 4 As shown, the delivery method is specifically described as follows:

[0031] (1) Organize multiple batches of goods. High-speed rail express goods arrive in batches according to the timetable. The number of vehicles and drones is limited. In the "de-distribution center" mode, multiple vehicles and multiple drones are directly coordinated to carry out dynamic task allocation and path planning.

[0032] (2) Multi-vehicle collaborative optimization: Simultaneously optimize the path, load allocation and dynamic scheduling of vehicles and drones, and consider their collaborative cyclical use. When a vehicle arrives at a certain node, it launches a drone according to the scheduling instruction to perform a delivery task at another node. At this time, the vehicle does not wait for the drone to be retrieved and goes to the next node to perform the delivery task. After the drone completes the delivery task, it can meet up with the vehicle at any node other than the node where the drone was launched and charge, or return directly to the starting node.

[0033] (3) Multi-objective constraint modeling: Minimize the total time and total cost of last-mile delivery while satisfying constraints such as cargo delivery time window, vehicle capacity, and drone endurance.

[0034] Based on any of the above embodiments, the optimization objective of the delivery optimization model of the present invention is described as follows: To better establish the mathematical model, based on the problem description above, the following assumptions are made: 1) It is assumed that both the vehicle and the drone operate normally during the delivery process. 2) It is assumed that the drone can fly freely in the airspace and possesses basic functions such as navigation, communication, and maintenance. 3) It is assumed that the high-speed rail station does not have storage functions, and the arriving goods can be directly sorted and loaded into freight cars. 4) The coordinates of the high-speed rail station and the customer's location are known, and the maximum load and maximum mileage of the vehicle and drone are fixed.

[0035] To address the "last mile" problem in high-speed rail express delivery and provide an innovative model with practical application, this paper addresses the issue of multi-batch, multi-drone, and multi-vehicle collaborative delivery routes. With minimizing the total delivery cost as the objective function, and considering the time-sensitive requirements of high-speed rail express delivery, a bi-objective programming model is incorporated, minimizing the total delivery time. The objective functions are as follows: (1) (2) in, and These refer to total delivery time and total delivery cost, respectively. For use by vehicles at high-speed rail stations For the collection of batches of goods arriving by high-speed rail express; For vehicles Completed goods batch The moment the delivery mission returned to the high-speed rail station; This represents the maximum number of nodes in the high-speed rail last-mile delivery network. This refers to the collection of all terminal stations in the high-speed rail last-mile delivery network. When the vehicle Cargo batch From node Move to node hour, It is 1 if it is true, otherwise it is 0; For the node Move to node Delivery time; Cost per kilometer of vehicle operation; Drones can be used to assemble at high-speed rail stations; When drones Cargo batch From node Launch and access nodes And at the node During recycling, It is 1 if it is true, otherwise it is 0. ; The cost per use of the drone. Equation (1) represents the time when all vehicles finally return to the high-speed rail station after completing all batches of delivery tasks, i.e., the total time to complete the delivery tasks. , which indicates vehicles Completed goods batch The delivery task returns to the high-speed rail station at the specified time; Equation (2) represents the total delivery cost, including vehicle transportation cost and drone usage cost. Based on Pareto front analysis to solve multi-objective programming problems, the baseline weights are first fixed. Choose a group Values, covering a preference range from "extremely time-intensive" to "extremely cost-intensive," are adjusted... and The algorithm is guided to explore different regions on the Pareto front, so the final objective function is as follows (3):

[0036] (3) in, To optimize the objective; and These are preset time weights and cost weights, respectively.

[0037] Based on any of the above embodiments, the constraints in the delivery optimization model of the present invention are described.

[0038] Before describing the constraints, the model notation is explained. For high-speed rail station nodes ; The maximum number of nodes in the network is ; The set of all nodes in the network. ; The set of nodes that vehicles can reach and leave. ; The set of nodes that can be reached by drones. ; It is the set of all end stations in the network. ; For batches of goods arriving by high-speed rail express ; The number of vehicles available for use at the high-speed rail station is ; The number of drones available for use at high-speed rail stations is ; This refers to the vehicle's maximum speed. This represents the maximum flight distance of the drone. The time consumed in launching the drone; The time spent recovering the drone; This represents the maximum flight range of the drone. For end stations The demand for goods, ; For vehicles At the high-speed rail station Time spent loading goods; For vehicles At the node Time spent unloading cargo; For drones At the node Time spent unloading cargo; End node Earliest start time for logistics and delivery; End node Latest end time for logistics and delivery; For nodes The x-coordinate of the position; node The ordinate of the position; The flight speed of the drone; For vehicles from nodes Drive to the node The distance; The maximum number of drones a vehicle can carry when completing a delivery of a batch of goods; It is a sufficiently large number.

[0039] Explain the decision variables: For vehicles Cargo batch From node Move to node The value is 1 if it is true, and 0 otherwise. For drones Carrying cargo batch At the node Launch, access node and at the node The value is 1 when recycling occurs, otherwise it is 0. For vehicles Cargo batch From node Drive to the node Time; For drones Carrying cargo batch From node Drive to the node Time; For vehicles Cargo batch Reaching the node Time; For drones Carrying cargo batch Reaching the node Time; For goods batch Latest delivery completion time; For nodes The access order is used to eliminate sub-loops; For nodes The value is 1 if the node was visited before it, and 0 otherwise. If the vehicle arrives first while driving Arrived later ,but =1, otherwise 0.

[0040] For example, the drone delivery route constraints are shown in equations (4) to (12): (4) (5) (6) (7) (8) (9) (10) (11) (12) Constraint (4) means that the vehicle departs from the high-speed rail station once for each delivery mission; Constraint (5) means that the vehicle returns to the high-speed rail station once for each delivery mission; Constraint (6) means that the maximum flight distance of the drone cannot exceed its maximum range; Constraint (7) means that the drone's take-off and return points must be on the vehicle's path; Constraint (8) means that the drone launch time is constrained, i.e., the drone can only launch when the vehicle arrives at the launch point. After completing launch preparations, the drone took off and flew to the target point. The time must be included in the launch preparation time and flight time; constraint (9) represents the UAV recovery constraint, that is, the UAV recovers from the target point Fly back to the recovery point Afterwards, the truck must have arrived. Only after the drone has been launched can it be recovered. Constraint (10) indicates the time order in which the drone visits the site; constraint (11) indicates that the drone can only be launched again after it has been launched and is waiting to be recovered; constraint (12) indicates that the drone cannot fly beyond the maximum endurance constraint.

[0041] For example, the vehicle delivery route constraints are shown in equations (13) to (22): (13) (14) (15) (16) (17) (18) (19) (20) (twenty one) (twenty two) Among them, constraint (14) is used to eliminate vehicle path sub-loops; constraint (14) is used to limit The access order; constraint (15) indicates that the vehicle path flow reaches equilibrium; constraint (16) indicates that if the drone starts from... Take off at point, If the vehicle is recycled at a designated point, it must pass through the recycling point. Point and Point; constraint (17)~(18) indicates that if the vehicle is in If the drone is launched from a designated point, the vehicle and the drone will arrive at the same time. Point; constraint (19)~(20) indicates that if the vehicle is in If the drone is launched from a designated point, the vehicle and the drone will arrive at the same time. The constraint (21) means that the time for a vehicle to reach the intermediate point plus the time to reach the next point plus the time for launching or recovering the drone shall not exceed the time for the vehicle to start service at the next point; the constraint (22) means that all vehicles depart from the starting point once.

[0042] For example, the constraints on the timing of goods batch delivery and the dynamic allocation of delivery resources are shown in equations (23) to (31): (twenty three) (twenty four) (25) (26) (27) (28) (29) (30) (31) Constraint (23) indicates that the vehicle is in the batch The task must wait for batch It can only begin after all tasks are completed; constraint (24) represents the maximum number of drones that each vehicle can carry when completing a batch of goods delivery tasks; constraint (25) represents the maximum number of drones that each customer node can carry. In each batch It must be served by at least one truck or one drone. Constraints (26) to (31) represent the decision variable constraints.

[0043] Based on any of the above embodiments, an example is described of solving the delivery optimization model using an improved adaptive large neighborhood search algorithm.

[0044] To address the problem of route optimization for multi-batch delivery of goods using drones and vehicles, a hybrid heuristic algorithm based on adaptive large neighborhood search is proposed. This problem is NP-hard, involving complex constraints such as multiple vehicles, multiple drones, multiple batches, capacity constraints, and time windows. Traditional exact algorithms struggle to solve large-scale instances within a reasonable timeframe. Therefore, this paper designs a metaheuristic algorithm framework integrating multiple heuristic strategies. This hybrid heuristic algorithm based on adaptive large neighborhood search offers faster solution speed and relatively higher accuracy compared to other traditional algorithms.

[0045] Figure 5 This document provides a flowchart illustrating the framework of an adaptive large neighborhood search algorithm. Figure 5 As shown, the Adaptive Large Neighborhood Search (ALNS) algorithm consists of three main stages: the initialization stage, the main loop stage, and the adaptive mechanism stage. The initialization stage includes parameter initialization and initial population generation. Parameter initialization involves setting all key parameters before the algorithm begins, including control variables such as the weight coefficients of the destruction and repair operators, the upper limit of the number of iterations, and the population size. Initial population generation uses heuristic methods or random generation to construct a set of feasible initial solutions that satisfy the constraints, serving as the basis for subsequent optimization.

[0046] The main loop phase forms a closed-loop structure based on the condition that "the number of iterations has reached the upper limit". When the number of iterations has not reached the upper limit, the main loop executes the following steps: 1. Select the current solution: Select a solution to be optimized from the current population as the processing object.

[0047] 2. Adaptive operator selection: The selection probability of damage operators and repair operators is dynamically adjusted based on historical performance data, and the combination of operators with better performance is given priority.

[0048] 3. Destructive Operation: Remove some delivery nodes or path segments from the current solution, break the existing path structure, and increase the diversity of solution space exploration.

[0049] 4. Repair operation: Reinsert the removed nodes into the path to restore the feasibility of the solution and may introduce a new path configuration.

[0050] 5. Local search optimization: Perform neighborhood search on the repaired solution and further optimize the path quality through strategies such as 2-opt swapping and node migration.

[0051] 6. Solution validity verification: Check whether the optimized new solution meets all constraints (such as vehicle capacity, time window, drone flight distance, etc.). If it is invalid, return to the previous step and try again; if it is valid, continue with subsequent processing.

[0052] The adaptive mechanism phase is used to realize the intelligent adjustment function of the algorithm, including updating the Pamela parameters and adjusting the operator weights. Updating the Pamela parameters dynamically adjusts the performance evaluation index of the destruction and repair operators based on the changes in the quality of the current solution; adjusting the operator weights reallocates the selection probability of each operator based on the changes in the Pamela parameters, enabling the algorithm to adaptively balance exploration and exploitation capabilities.

[0053] The optimal solution is output when the number of iterations reaches the preset upper limit.

[0054] Based on the above Figure 5 The illustrated embodiment, for example, describes the generation of initial solutions in adaptive large neighborhood search. The initial solution construction employs a three-stage hybrid heuristic strategy that comprehensively considers geographical clustering, customer demand characteristics, and UAV-assisted vehicle features, aiming to generate high-quality and feasible initial solution schemes.

[0055] (1) Stage 1: Cluster the delivery nodes in the high-speed rail terminal delivery network according to their geographical distribution, divide the initial service area for each delivery vehicle, and construct an initial path framework that includes the spatial distribution of vehicles.

[0056] To address the complex spatiotemporal characteristics of multi-batch cargo delivery, this invention employs a spatial partitioning strategy based on the K-means clustering algorithm to achieve rational allocation of high-speed rail express resources and scientific organization of route planning. The clustering algorithm, through data-driven cluster analysis, divides geographically adjacent customer nodes into the same cluster, thereby allocating a relatively concentrated service area to each truck and minimizing empty mileage and cross-transportation.

[0057] 1) K-means clustering process.

[0058] The K-means clustering algorithm divides each customer demand point into clusters through an iterative optimization process, minimizing the Euclidean distance between nodes within the same cluster and maximizing the distance between different clusters. The objective function is expressed as equation (32): (32) in, Indicates the first Clusters, Cluster The coordinates of the centroid, This represents the coordinate vector of the customer node. This article considers the spatiotemporal dynamics of demand across different batches of goods, therefore requiring separate cluster analysis for each batch, such as for batches... First, a set of required nodes is constructed, and then the planar coordinate vectors of these nodes are extracted as clustering feature inputs. The clustering process adopts an improved K-means++ initialization strategy, which effectively avoids the algorithm getting trapped in local optima by intelligently selecting the initial cluster centers. The specific initialization steps are as follows: First, a data point is randomly selected as the first cluster center, and then subsequent center points are selected according to the probability distribution (33), where Point Shortest distance to the selected center:

[0059] (33) 2) Nearest neighbor algorithm for intra-cluster path planning.

[0060] After clustering and assignment, customer nodes within each cluster need to construct reasonable service paths. This invention employs the nearest neighbor heuristic algorithm to construct paths for the Traveling Salesman Problem, an algorithm widely used in path optimization due to its practicality. The execution process of the nearest neighbor algorithm is as follows: For each cluster... From the warehouse node Begin by initializing the path. Then, among the remaining unvisited nodes, select the node closest to the current node. Add the path, and the formula is as follows (34):

[0061] (34) This formula represents the nearest neighbor selection rule, where, This represents the optimal node to be selected. The parameter represents the minimum value, that is, finding the value that minimizes the expression. Value, Ci represents the first value. The set of nodes in a cluster This represents the currently constructed sequence of path nodes. This represents the set of nodes in the cluster that have not yet been visited. Indicates the relationship between the current node and the node. The Euclidean distance between them. While this greedy strategy cannot guarantee a globally optimal solution, it can generate high-quality feasible solutions in polynomial time, with a computational complexity of O(n log n). ,in This represents the number of nodes within the cluster. In practical applications, it has been observed that the path length generated by the nearest neighbor algorithm is typically within 10-15% of the optimal solution, fully satisfying the quality requirements of the initial solution.

[0062] 3) Innovative improvements in spatial zoning optimization.

[0063] Traditional K-means clustering only considers geometric distance, but in logistics and delivery scenarios, factors such as demand characteristics and service time constraints also need to be considered. Weighted distance metric: Introducing a demand weight factor into the distance calculation makes high-demand nodes more attractive to cluster centers, as shown in equation (35).

[0064] (35) in and To adjust the parameters, and They are nodes and The demand.

[0065] (2) Stage 2: Insert delivery nodes that have not been assigned to the initial path frame into the feasible vehicle delivery paths in the initial path frame to generate intermediate solutions that contain only vehicle delivery paths.

[0066] After completing the initial spatial clustering and allocation, the second phase focuses on handling nodes that were not initially allocated due to various constraints, employing a systematic demand filling strategy to ensure that all customer needs are met. The core idea of ​​this phase is "constraint priority, cost optimization," aiming to minimize transportation costs while strictly satisfying all operational constraints.

[0067] 1) Node priority sorting mechanism: A descending order of demand strategy is adopted, based on the principle of "prioritizing important customers". For the set of unassigned nodes, they are first sorted according to demand. The theoretical basis of this sorting strategy is that high-demand nodes usually have greater sensitivity to insertion costs, and prioritizing them can avoid large path disturbances during subsequent insertions.

[0068] 2) Multi-constraint insertion feasibility test: For each node to be inserted, all possible insertion positions need to be comprehensively evaluated. The test criteria include: capacity constraint test, time window constraint test, and distance constraint test.

[0069] 3) Adaptive insertion strategy: Dynamic weight adjustment: Multi-objective weights are introduced into cost calculation. The weight coefficients are dynamically adjusted according to the quality of the current solution. When no feasible insertion position can be found, the path reconstruction mechanism is activated to consider swapping the positions of the assigned nodes, adjusting the allocation relationship of multiple nodes, and creating new sub-paths if necessary.

[0070] (3) Stage 3: Using the vehicle delivery path of the intermediate solution as the launch node or recovery node of the UAV, assign UAV delivery tasks to the remaining delivery nodes in the high-speed rail terminal delivery network that cannot be covered by the vehicle delivery path, and generate a complete initial solution containing the collaborative path of vehicles and UAVs.

[0071] The third phase specifically addresses the remaining nodes that cannot be served by truck services, achieving full coverage through collaborative delivery between drones and trucks. The core of this phase is "resource collaboration and optimal range," maximizing drone service efficiency within limited drone resource constraints. This involves identifying launch / recovery point pairs along the truck routes, calculating feasible drone missions for the remaining unserved nodes, and selecting the shortest possible allocation.

[0072] 1) Collaborative optimization features: Considering the time synchronization between drone missions and truck routes, spatiotemporal coordination is achieved by adjusting launch times. Resource balancing strategy: Avoiding excessive use of drone resources by certain vehicles; Backup plan mechanism: For special nodes that cannot be allocated in the end, an emergency plan is activated, arranging dedicated drone services to adjust the allocation method of other nodes, and accepting minor constraint violations when necessary.

[0073] Based on the above Figure 5The illustrated embodiment, exemplarily, describes a disruption operator in adaptive large neighborhood search. Disruption operators are used to perform disruption operations on the current solution, expanding the solution space exploration range by disrupting the vehicle and drone path structures within the current solution. The disruption operators include: a random removal operator, used to randomly remove a predetermined proportion of delivery nodes from the current solution to increase search diversity; a worst-case removal operator, used to identify and remove delivery nodes that contribute the least to the optimization objective to improve solution quality; a time window removal operator, used to remove delivery nodes that do not meet a predetermined time window constraint to enhance time window satisfaction; and a cluster removal operator, used to remove geographically clustered delivery nodes to reconstruct the regional delivery strategy.

[0074] Based on the above Figure 5 The illustrated embodiment, exemplarily, describes a repair operator in adaptive large neighborhood search. The repair operator repairs a corrupted solution by inserting delivery nodes into the corrupted current solution, thereby reorganizing the path structure and restoring the feasibility of the solution. The repair operator includes: a greedy insertion operator, used to calculate the incremental delivery cost of the node to be inserted at each feasible location in the high-speed rail terminal delivery network, and insert the node to be inserted into the feasible location with the minimum incremental delivery cost; a regret insertion operator, used as the regret value (the cost difference between the optimal insertion location and the k-th best insertion location), inserting delivery nodes in descending order of regret value to avoid suboptimal solutions caused by local greedy selection; where the optimal insertion location and the k-th best insertion location are the feasible locations with the minimum incremental delivery cost and the k-th smallest, respectively, and k is a preset positive integer; and a learning-guided insertion operator, used to construct a probability distribution model based on the successful insertion frequency of each delivery node at feasible locations during historical iterations, prioritizing the insertion of the node to be inserted into high-probability preferred locations with a historical success probability higher than a preset threshold, thereby utilizing prior knowledge to improve global search efficiency.

[0075] Based on the above Figure 5 The illustrated embodiment, for example, describes three types of local search strategies in adaptive large neighborhood search. These include: optimizing vehicle delivery routes through path topology reconstruction; optimizing drone delivery routes through drone take-off and landing point reconfiguration, drone delivery task transfer, and interchange of vehicle and drone delivery services; and optimizing cargo batch scheduling by adjusting the delivery order of different cargo batches and the configuration ratio of vehicles and drones in each batch.

[0076] For example, in the drone mission optimization phase, three types of operations are used to optimize drone delivery routes: First, launch point optimization, which involves re-searching and matching more suitable combination of launch and recovery points for the drones to shorten the flight path between the mission node and the take-off and landing point; second, mission redistribution, which involves transferring delivery missions originally handled by a truck carrying a drone to other trucks carrying drones, thereby balancing the delivery load of different drones by adjusting the truck carriers corresponding to the missions; and third, mode switching, which involves switching the service mode of some missions between "direct truck delivery" and "drone delivery" according to the actual needs of the mission scenario (such as vehicle traffic restrictions, delivery time requirements, etc.) to adapt to the delivery route planning needs under different scenarios.

[0077] For example, in optimizing cargo batch scheduling, we employ two core strategies to improve overall delivery efficiency and resource utilization. First, we adjust the delivery sequence of different cargo batches through batch swapping to find a better delivery sequence and reduce total delivery time or cost. Second, we implement a resource reallocation strategy, flexibly adjusting the ratio of vehicles to drones among batches based on their specific needs and characteristics. This dynamic adjustment considers not only the carrying capacity and operational characteristics of each mode of transport but also multiple factors such as geographical factors, traffic conditions, and time window constraints, thereby achieving comprehensive optimization of cargo batch scheduling. By combining these two methods, we can effectively reduce logistics costs, improve service quality and customer satisfaction, ensure more rational and efficient resource allocation, and ultimately optimize the entire delivery process.

[0078] Furthermore, the present invention also provides examples to verify the technical solution of the present invention.

[0079] Example Design: Due to the high cost of high-speed rail express transportation, the transported products are high value-added products, and the high-speed rail batches can meet the full load rate requirements. Considering economic factors, Shanghai and Beijing are proposed as pilot cities for high-speed rail express transportation, with Beijing South Railway Station selected as the terminal station for drone-assisted vehicle delivery. To meet customers' timeliness needs and ensure same-day and next-day delivery of high-speed rail express products, it is proposed to pilot high-speed rail express transportation using high-speed trains departing between 6:00 and 7:30. According to the 12306 railway system, the Shanghai-Beijing South high-speed rail timetable is shown in Table 3 below.

[0080] Table 3. Timetable for Shanghai-Beijing South High-Speed ​​Railway This invention proposes to use Beijing South Railway Station as the last-mile delivery center, radiating to 15 customer demand nodes. It will process high-speed rail express goods from different trains arriving at Beijing South Railway Station in batches. The batch demand of all goods at the 15 customer demand nodes is shown in Table 4 below, the customer node information is shown in Table 5 below, and other parameters are shown in Table 6.

[0081] Table 4 Customer Node's Demand for Each Batch of Goods Table 5 Customer Node Information Table 6 Relevant Parameters Centered on Beijing South Railway Station, the project will cover 15 customer nodes. The maximum flight range of the drones is 50km, and the maximum load capacity of the vehicles is 100 pieces. A total of 9 professional cargo drones and 3 vehicles will be available. The express delivery service will be piloted using three high-speed trains departing from Shanghai Station. The three trains will carry 363, 352, and 374 pieces of cargo respectively, with arrival times of 11:36, 11:56, and 12:20, which translates to 0 minutes, 25 minutes, and 48 minutes respectively. Considering the unloading, transfer, and sorting of the cargo, the proposed delivery start times are 20 minutes, 45 minutes, and 68 minutes.

[0082] Design code using Python and run the above case study on the Spyder platform. Based on a hybrid heuristic algorithm of adaptive large neighborhood search, and optimized using the optimal weight method, the study found... =1, When the value is 0.5, the following is the optimal solution set for the Parote solution.

[0083] Parote Solution 1: Minimum total delivery time is 116.62 minutes, minimum delivery cost is 1412.92 yuan. Parote Solution 2: Minimum total delivery time is 110.10 minutes, minimum delivery cost is 1415.33 yuan.

[0084] Comparing the two delivery options above, due to the time-sensitive requirements of high-speed rail express products, the option with the shorter delivery time, namely Parote's solution two, is chosen as the optimal solution. This reduces the delivery time by 6.52 minutes, but the cost only increases by 3.41 yuan. Therefore, the total delivery time is approximately 2 hours. The optimal route is shown in Table 7, and the departure and return timetables and optimal route diagrams for each batch of vehicles are shown below. Figure 6 , Figure 7 As shown, Figure 6 This manual provides a schematic diagram of the departure and return times for each batch of vehicles. Figure 7This is a schematic diagram of an optimal delivery route provided in this manual.

[0085] Table 7 Optimal Solution Analysis of the impact of cargo batches and customer nodes: To further analyze the effectiveness of the model and algorithm, multiple cargo batches were analyzed. Keeping the number of high-speed rail express vehicles, drones, and customer nodes at Beijing South Railway Station constant, delivery plans for three different cargo batches were compared and calculated. For cargo batch 4, the running time was 30.64 seconds, the minimum completion time was 216.85 minutes, and the minimum delivery cost was 1988.68 yuan; for cargo batch 5, the running time was 50.71 seconds, the minimum completion time was 272.24 minutes, and the minimum delivery cost was 2557.55 yuan; for cargo batch 10, the minimum completion time was 390.45 minutes, and the minimum delivery cost was 4809.09 yuan. The delivery path diagram for cargo batch 5 is shown in Figure 8, which is a schematic diagram of the optimal delivery path for 10 cargo batches provided in this specification.

[0086] The experimental results show that the model and algorithm of this invention support the scheduling of large-scale batches of goods. Further calculations, such as increasing the number of vehicles and drones, can solve scenarios with a larger number of customer nodes. The analysis was conducted with 20 and 30 customer nodes. With 20 customer nodes, the running time was 11.37 seconds, the minimum completion time was 161.35 minutes, and the minimum delivery cost was 1994.32 yuan. With 30 customer nodes, the running time was 23.28 seconds, the minimum completion time was 323.65 minutes, and the minimum delivery cost was 3706.88 yuan. The optimal delivery route diagram for a node scale of 20 is as follows. Figure 9 As shown, Figure 9 This document provides a schematic diagram of an optimal delivery route with 20 nodes.

[0087] In summary, this invention innovatively proposes a drone-assisted delivery model for the last-mile delivery of high-speed rail express goods, addressing the issue of last-mile delivery via high-speed rail. It employs a vehicle-led, drone-assisted dynamic mobilization of delivery resources within high-speed rail stations, focusing on optimizing the delivery efficiency and cost control of high-value-added goods. For multiple batches of goods, a dual-objective optimization model for drone-assisted vehicle delivery is established, and a hybrid heuristic algorithm based on adaptive large neighborhood search (ALNS) is designed, using the optimal weight method for optimization. A pilot high-speed rail express delivery test is conducted on the Shanghai-Beijing South G2, G104, and G102 trains, designing a case study of 15 delivery nodes around Beijing South Station. Drone-assisted vehicle delivery of three batches of goods is implemented using Python programming, and the results demonstrate its effectiveness. =1, When the efficiency is 0.5, the optimal solution is obtained. The optimal solution has a minimum total delivery time of 110.10 minutes and a minimum delivery cost of 1415.33 yuan, indicating a total delivery time of approximately 2 hours, which meets the timeliness requirements of high-speed rail express products. Further testing with increased batches and node numbers shows that this model and algorithm remain applicable in multi-batch delivery and large-scale node delivery networks. This invention focuses on the core problems of low efficiency, high cost, and insufficient flexibility of traditional models in high-speed rail express last-mile delivery, conducting multi-dimensional research and forming systematic results. The main conclusions are as follows:

[0088] An innovative delivery model effectively addresses last-mile delivery challenges: Addressing the issues of traditional high-speed rail express delivery relying on individual vehicles, being heavily influenced by terrain and road congestion, and the rigid resource scheduling of the "decentralized delivery center" model, this invention innovatively proposes a drone-assisted vehicle delivery model based on multiple high-speed rail trains and multiple batches of goods. This model, with vehicles as the primary mode and drones as an auxiliary, enables dynamic allocation of delivery resources within high-speed rail stations. It breaks through the traditional model's dependence on a single transport vehicle, significantly improving the timeliness and cost controllability of high-value-added goods delivery, and filling the gap in existing research that has not deeply integrated "vehicle-machine collaboration" with the last-mile scenario of high-speed rail express delivery.

[0089] The optimization model and algorithm are scientific and practical: Based on the dynamic arrival characteristics of multiple batches of goods, a dual-objective optimization model for drone-assisted vehicle delivery is constructed, effectively incorporating key constraints such as cargo time windows, vehicle capacity, and drone endurance, achieving collaborative optimization of "minimizing total delivery time" and "minimizing total delivery cost"; the designed hybrid heuristic algorithm based on adaptive large neighborhood search (ALNS), combined with the optimal weight method, has been validated in cases involving the Shanghai-Beijing South G2, G104, and G102 high-speed trains and 15 delivery nodes around Beijing South, with the weight parameters... When the values ​​are 1 and 0.5 respectively, the optimal solution has a total delivery time of only 110.10 minutes (about 2 hours) and a total cost of 1415.33 yuan, which fully meets the timeliness requirements of high-value-added products of high-speed rail express.

[0090] The model and algorithm exhibit strong scalability and wide applicability: Further testing with increased cargo batches and expanded delivery node numbers demonstrates that the delivery mode, optimization model, and solution algorithm proposed in this invention maintain stable performance in continuous delivery of multiple cargo batches and large-scale node delivery networks, without any "scale bottleneck" problem. This means that the research results are not only applicable to small and medium-sized last-mile delivery scenarios but can also be extended to more complex high-speed rail express networks, providing a universal solution for last-mile delivery of high-speed rail express in different regions and with different cargo volumes.

[0091] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0092] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for optimizing the last-mile delivery route on high-speed rail using a combination of drones and vehicles, characterized in that: include: A high-speed rail last-mile delivery network will be constructed, with high-speed rail stations serving as distribution centers and target delivery locations around high-speed rail stations serving as last-mile delivery nodes. With the goal of minimizing the total delivery time and total delivery cost within the high-speed rail last-mile delivery network, and constrained by the delivery route constraints of vehicles and drones, as well as the constraints of the batch delivery timing of goods based on the arrival time series of multiple high-speed rail trains and the dynamic allocation of delivery resources, a delivery optimization model is constructed. The delivery optimization model is solved by improving the adaptive large neighborhood search algorithm to obtain delivery route solutions. Specifically, the improved adaptive large neighborhood search algorithm adds three types of local search strategies to the standard large neighborhood search algorithm framework: Optimize vehicle delivery routes through route topology reconstruction; Optimize drone delivery routes by reconfiguring drone take-off and landing points, transferring drone delivery tasks, and exchanging vehicle and drone delivery services. The scheduling of cargo batches was optimized by adjusting the delivery sequence of different cargo batches and the configuration ratio of vehicles and drones in each batch delivery.

2. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 1, characterized in that, The improved adaptive large neighborhood search algorithm further includes generating an initial solution through a three-stage hybrid heuristic strategy, which includes: In the first stage, the delivery nodes in the high-speed rail last-mile delivery network are clustered according to their geographical distribution, and an initial service area is divided for each delivery vehicle to construct an initial path framework that includes the spatial distribution of the vehicles. In the second stage, delivery nodes that have not been assigned to the initial path framework are inserted into the feasible vehicle delivery paths in the initial path framework to generate intermediate solutions that contain only vehicle delivery paths. In the third stage, the vehicle delivery path of the intermediate solution is used as the launch node or recovery node of the drone. Drone delivery tasks are assigned to the remaining delivery nodes in the high-speed rail terminal delivery network that cannot be covered by the vehicle delivery path, and a complete initial solution containing the collaborative path of vehicles and drones is generated.

3. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 2, characterized in that, The construction of the initial path framework, which includes the spatial distribution of vehicles, includes: The improved K-means clustering algorithm divides delivery nodes into a preset number of clusters. The improved K-means clustering algorithm introduces a demand weight factor when obtaining the distance between the delivery node and the cluster center. The demand weight factor is positively correlated with the delivery demand of the delivery node and is used to enhance the aggregation tendency of high-demand delivery nodes to the cluster center during the clustering process. After clustering is completed, the nearest neighbor heuristic algorithm is used to construct delivery routes for the set of delivery nodes in each cluster, thereby obtaining an initial path framework that includes the spatial distribution of vehicles.

4. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 2, characterized in that, The generation of intermediate solutions that contain only vehicle delivery routes includes: For the set of delivery nodes not assigned to the initial path framework, sort them in descending order according to the amount of goods to be delivered, and generate a sequence of nodes to be processed; A multi-constraint feasibility test is performed on all candidate insertion positions in the initial path framework to select a set of feasible insertion positions that simultaneously satisfy the preset vehicle load constraints, service time window constraints, and maximum vehicle travel distance constraints. For each location in the set of feasible insertion locations, calculate the comprehensive cost increment, which includes the travel distance increment, time delay increment, and energy consumption increment; sort the locations in the set of feasible insertion locations in ascending order according to the comprehensive cost increment, and insert the delivery node in the node sequence to be processed into the first feasible location in the sorted order; process all delivery nodes in the node sequence to be processed in sequence to obtain an intermediate solution containing the vehicle delivery route.

5. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 4, characterized in that, If the multi-constraint feasibility check fails to find a set of feasible insertion positions, a path reconstruction sub-operation is executed. The path reconstruction sub-operation adjusts the node allocation relationship by swapping the positions of already allocated nodes in the path or creating new delivery sub-paths.

6. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 1, characterized in that, The path topology reconstruction includes: The 2-opt swap operation is used to disconnect two non-adjacent edges in a single vehicle delivery route and reconnect the disconnected route segments to eliminate intersections in the route. Cross-path node swapping is used to select one delivery node from each of two different vehicle delivery routes and swap their positions to change the distribution sequence of path nodes. The node migration operation is used to remove one or more delivery nodes from one vehicle delivery route and insert them into another vehicle delivery route, thereby reducing the empty driving distance by adjusting the task load between vehicles.

7. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 1, characterized in that, The improved adaptive large neighborhood search algorithm is executed sequentially in each iteration: The destruction operator performs destruction operations on the current solution. The destruction operation expands the scope of solution space exploration by destroying the path structure of vehicles and drones in the current solution. Repair operators are used to repair the damaged solution. The repair operation reorganizes the path structure and restores the feasibility of the solution by inserting delivery nodes into the current solution after it has been damaged. Three types of local search strategies are used to optimize the current solution after repair, and the current solution is updated based on the optimization results.

8. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 7, characterized in that, The destruction operator includes: The random removal operator is used to randomly remove a preset proportion of delivery nodes from the current solution to increase search diversity; The worst-case removal operator is used to identify and remove delivery nodes that contribute the least to the optimization objective, thereby improving the quality of the solution; The time window removal operator is used to remove delivery nodes that do not meet the preset time window constraints, thereby improving the time window satisfaction rate. Cluster removal operators are used to remove geographically clustered delivery nodes in order to restructure regional delivery strategies.

9. The method for optimizing high-speed rail last-mile delivery routes using drones and vehicles as described in claim 7, characterized in that, Repair operators include: The greedy insertion operator is used to calculate the incremental delivery cost of the node to be inserted at each feasible position in the high-speed rail terminal delivery network, and insert the node to be inserted into the feasible position with the minimum incremental delivery cost. The regret insertion operator is used to insert delivery nodes in descending order of regret value, using the cost difference between the optimal insertion position and the k-th best insertion position as the regret value, in order to avoid suboptimal solutions caused by local greedy selection; where the optimal insertion position and the k-th best insertion position are the feasible positions with the minimum incremental delivery cost and the k-th smallest, respectively, and k is a preset positive integer; The learning-guided insertion operator is used to construct a probability distribution model based on the successful insertion frequency of each delivery node in feasible positions during historical iterations. It prioritizes inserting nodes into high-probability preferred positions where the historical success probability is higher than a preset threshold, thereby leveraging prior knowledge to improve global search efficiency.

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