A dynamic programming method, device and medium for air-ground cooperative terminal distribution

Abstract

The embodiment of the specification discloses a dynamic programming method, equipment and medium for air-ground collaborative end distribution, relates to the technical field of path planning, and is used for solving the problem of poor planning effect caused by the current inability to quickly respond to sudden road failure. The method comprises the following steps: updating the road network map corresponding to the current distribution area in real time, determining whether to trigger the distribution scheme update of the current distribution area based on the failure unit of the road network map; if yes, constructing an air-ground collaborative end distribution model of the current distribution area based on the information corresponding to the road network map; solving the air-ground collaborative end distribution model based on a two-stage hierarchical initialization strategy and a double-layer hybrid crossover strategy to obtain the initial air-ground collaborative end distribution path of the vehicle and the unmanned aerial vehicle; and iteratively updating the initial air-ground collaborative end distribution path based on the Pareto frontier to obtain the optimal solution as the optimal air-ground collaborative end distribution path of the current distribution area.

Description

Technical Field

[0001] This specification relates to the field of route planning technology, and in particular to a dynamic planning method, equipment and medium for air-ground coordinated last-mile delivery. Background Technology

[0002] Traditional urban last-mile delivery relies on couriers using vehicles to traverse the city's road network. However, this road network is susceptible to unpredictable factors such as natural disasters, traffic accidents, public health emergencies, and mass gatherings, leading to localized congestion, closures, and even regional paralysis. This inevitably causes delays or interruptions in last-mile delivery, resulting in losses for both delivery companies and end-customers. With the increasing frequency of natural disasters and emergencies in recent years, research on emergency logistics has grown, making the facility location-route optimization (LRP) problem a research hotspot.

[0003] Current methods for planning joint delivery routes using vehicles and drones are generally based on fixed road network information, which cannot respond in real time to dynamic changes such as road failures and congestion. This makes it difficult to prioritize avoiding high-risk failed road sections when delivery plans fail in unforeseen circumstances. Furthermore, traditional algorithms, such as standard genetic algorithms, struggle to effectively balance conflicts between multi-dimensional objectives when optimizing vehicle-drone collaborative delivery. This can lead to the path planning structure getting stuck in local optima, and the simplistic initial population generation strategy results in insufficient diversity in the solution space, affecting the algorithm's convergence speed and global optimality. Summary of the Invention

[0004] To address the aforementioned technical problems, this specification provides one or more embodiments of a dynamic planning method, device, and medium for air-ground coordinated last-mile delivery.

[0005] One or more embodiments of this specification employ the following technical solutions:

[0006] This specification provides one or more embodiments of a dynamic programming method for air-ground coordinated last-mile delivery, the method comprising:

[0007] Based on delivery demand information and actual road network information of the current delivery area, the road network map corresponding to the current delivery area is updated in real time. Based on the failure units of the road network map, it is determined whether to trigger the delivery plan update of the current delivery area.

[0008] If so, then based on the information corresponding to the road network map, an air-ground coordinated last-mile delivery model for the current delivery area is constructed; wherein, the air-ground coordinated last-mile delivery model includes optimization objectives and constraints, and the optimization objectives include: demand coverage optimization objective, cost optimization objective, and time optimization objective;

[0009] The air-ground collaborative last-mile delivery model is solved based on a two-stage hierarchical initialization strategy and a two-layer hybrid cross strategy to obtain the initial air-ground collaborative last-mile delivery path of vehicles and drones.

[0010] The initial air-ground collaborative last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-ground collaborative last-mile delivery path for the current delivery area.

[0011] Optionally, in one or more embodiments of this specification, based on delivery demand information and the actual road network information of the current delivery area, the road network map corresponding to the current delivery area is updated in real time. Based on the failure units of the road network map, it is determined whether to trigger an update of the delivery plan for the current delivery area, specifically including:

[0012] Based on the actual road network information and delivery demand information of the current delivery area, the node set of the current delivery area is determined; wherein, the node set includes: road intersections, customer demand points, delivery centers, and drone take-off and landing points;

[0013] The weights of each edge are determined based on the toll cost and toll distance of the road segment corresponding to each node;

[0014] Based on the mapping between the set of nodes and the weights of each edge, a road network map corresponding to the current delivery area is obtained; wherein, the road network map is a grid-type road network topology map;

[0015] The vulnerability of road segments is calculated based on the failure units of the road network map to trigger an update of the delivery plan for the current delivery area.

[0016] Optionally, in one or more embodiments of this specification, road segment vulnerability is calculated based on the failure units of the road network map to trigger an update of the delivery plan for the current delivery area, specifically including:

[0017] Obtain the vulnerability identification model corresponding to the failure unit of the road network map; wherein, the vulnerability identification model includes: node failure vulnerability identification model and edge failure vulnerability identification model;

[0018] A preset initial network efficiency is obtained, and the current network efficiency is determined by sequentially removing the road segments corresponding to each failed unit. The network efficiency change rate is determined based on the preset initial network sales and the current network efficiency.

[0019] Based on the failure units, determine the relative size of the largest connected subgraph after removing the road segments corresponding to each failure unit, and determine the road segment importance of the road segment corresponding to each failure unit based on the weight of each edge;

[0020] The vulnerability of a road segment is obtained by substituting the network efficiency change rate, the relative size of the largest connected subgraph, and the comprehensive metric corresponding to the importance of the road segment into the vulnerability identification model, thereby triggering the update of the delivery plan for the current delivery area.

[0021] Optionally, in one or more embodiments of this specification, based on the information corresponding to the road network map, an air-ground coordinated last-mile delivery model for the current delivery area is constructed, specifically including:

[0022] Based on the information corresponding to the road network map, the optimization objective and constraints of the air-ground coordinated last-mile delivery model for the current delivery area are constructed.

[0023] The demand coverage optimization objective in the optimization objectives is to maximize the coverage of customer demand points around the failed road nodes, and the corresponding demand coverage objective function is:

[0024] Where, λ r Let i represent the vulnerability value of a road segment, r represent the road segment, C = {1, 2, 3, ..., n} be the set of all customer demand points, and L = {1, ..., n-1} be the set of drone paths. If a customer node i∈C is located in road segment r∈R, then otherwise The needs of customer i∈C are served by vehicle k. otherwise The needs of customer i∈C are served by the drone path l∈L otherwise

[0025] The cost optimization objective is to minimize the transportation costs of vehicles and drones, and the corresponding cost objective function is:

[0026] Where, θ k θ represents the unit distance transportation cost for vehicles. u For the unit distance transportation cost of drones, Let be the distance the vehicle travels through arc (i,j)∈E. Let x be the flight distance of the UAV along the path l∈L through the arc (i,j)∈E, where E={(i,j),i,j∈V,i≠j} represents the set of all arcs. ij If the delivery route of vehicle k passes through (i,j)∈E, then x ij =1; y ijl If the drone delivery path l∈L passes through arc (i,j)∈E, then y ijl =1;

[0027] The time optimization objective is to minimize delivery time, and the corresponding time objective function is:

[0028] Among them, v k Let v be the speed of vehicle k. u The speed of the drone is u.

[0029] Optionally, in one or more embodiments of this specification, the constraints include:

[0030] The first constraint expression used to indicate that each customer demand can only be served once by a vehicle or drone;

[0031] A second constraint is used to represent all customer points passed by vehicles, with delivery carried out by vehicles.

[0032] The third constraint used to represent all customer points for drone services will be the path traversed by the drone.

[0033] The fourth constraint expression is used to indicate that the UAV is only allowed to pass through each path arc once.

[0034] The fifth constraint is used to constrain the dynamic coordinated take-off and landing points, requiring that each drone launch and recovery point must be traversed by a vehicle, and that each drone delivery route serves at least one customer point.

[0035] The sixth constraint used to constrain the load is that when the UAV path is completed and leaves any customer point i, the load does not exceed the maximum load.

[0036] The seventh constraint expression used to indicate that the battery power at the launch point of the UAV on any path satisfies the maximum flight time.

[0037] The eighth constraint is used to represent the condition that the battery level meets 10% of the maximum flight time when the drone returns to the rendezvous point via any path.

[0038] The ninth constraint equation, used to represent the time constraints for the vehicle's arrival and departure from node i, is as follows: f is the time when the vehicle arrives at node i∈V1; i k For the moment when the vehicle leaves node i∈V1, M is a sufficiently large positive number; r i k The time when the vehicle leaves node i;

[0039] The tenth constraint equation, used to represent the time constraints for the arrival and departure of the drone from node i, is as follows: The time when the vehicle arrives at node i∈V1 The moment when the drone leaves node i∈V1;

[0040] The eleventh constraint expression is used to indicate that at the drone takeoff point, the vehicle's departure time must be later than the drone's departure time;

[0041] The twelfth constraint is used to indicate that at the drone's landing point, the vehicle meets with it, and the vehicle's arrival time must not be later than the drone's arrival time.

[0042] Optionally, in one or more embodiments of this specification, the air-to-ground cooperative last-mile delivery model is solved based on a two-stage hierarchical initialization strategy and a two-layer hybrid crossover strategy to obtain the initial air-to-ground cooperative last-mile delivery path for vehicles and drones, specifically including:

[0043] In the random initialization layer, the distribution center node and the failed node are determined based on the information of the road network map. Based on the random initialization of the distribution center node and the failed node, the first initial vehicle path and the first initial drone path are generated.

[0044] In the heuristic initialization layer, based on a pre-defined truck routing optimization method, the savings value of each node pair is calculated. The node pairs are then sorted in descending order based on these savings values ​​to merge paths and obtain a second initial vehicle path. The savings value s of each node pair is... ij =d(v0,v i )+d(v0,v j )-d(v i ,v j ); d(·) represents point v i The Euclidean distance between v and v;

[0045] The second initial UAV path is obtained by selecting the task with the greatest marginal benefit based on a greedy algorithm;

[0046] The first initial vehicle path and the second initial vehicle path are combined to obtain the initial vehicle path; the first initial drone path and the second initial drone path are combined to obtain the initial drone path.

[0047] By employing a dual-layer hybrid crossover strategy, the initial vehicle path and the initial drone path are processed to obtain an initial solution for the air-ground collaborative last-mile delivery model, which serves as the initial air-ground collaborative last-mile delivery path.

[0048] Optionally, in one or more embodiments of this specification, the initial vehicle path and the initial drone path are processed using a two-layer hybrid crossover strategy to obtain an initial solution for the air-ground cooperative last-mile delivery model, which serves as the initial air-ground cooperative last-mile delivery path. Specifically, this includes:

[0049] A tournament strategy is adopted to select parent individuals from the population consisting of the initial vehicle path and the initial drone path;

[0050] The initial vehicle path is sequentially crossed to preserve continuous segments of the parent individuals of the initial vehicle path, thus obtaining a new child solution of the initial vehicle path.

[0051] The initial drone path is uniformly intersected to blend the parent individuals of the initial drone path through a mask matrix, and a greedy selection is performed on the conflicting tasks to obtain a new child solution of the initial drone path.

[0052] Based on the new child solutions of the initial vehicle path and the new child solutions of the initial drone path, an initial solution for the air-ground collaborative last-mile delivery model is obtained, which serves as the initial air-ground collaborative last-mile delivery path.

[0053] Optionally, in one or more embodiments of this specification, the initial air-to-ground cooperative last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-to-ground cooperative last-mile delivery path for the current delivery area, specifically including:

[0054] The initial air-ground collaborative last-mile delivery routes are hierarchically divided according to their dominance relationship, and the solution set is divided into multiple frontier levels based on the quicksort method;

[0055] Based on the target directions corresponding to the optimization objective, the maximum value solution in that direction on the current Pareto front is defined as the extreme point;

[0056] Based on the extreme points, the target spaces are normalized to calculate the congestion entropy of each solution on the current Pareto front, and the solutions are sorted according to the congestion entropy to filter out low-entropy solutions and obtain new solutions.

[0057] The new solution is merged with each solution on the current Pareto front, and non-dominated solutions are extracted to form a set of next-generation solutions. The solutions on the Pareto front are iteratively updated to obtain the optimal solution as the optimal air-ground collaborative last-mile delivery route for the current delivery area.

[0058] This specification provides one or more embodiments of a dynamic planning device for air-ground coordinated last-mile delivery, the device comprising:

[0059] At least one processor; and,

[0060] A memory communicatively connected to the at least one processor; wherein,

[0061] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform any of the methods described above.

[0062] This specification provides one or more embodiments of a non-volatile computer storage medium storing computer-executable instructions, the computer-executable instructions being configured to execute any of the methods described above.

[0063] The above-described at least one technical solution adopted in the embodiments of this specification can achieve the following beneficial effects:

[0064] By updating the road network map in real time and assessing road segment vulnerability, and dynamically triggering route adjustments, rapid route updates are ensured when roads fail, addressing the problem that existing static planning cannot cope with sudden road network changes and improving the real-time response capability of collaborative delivery. A two-stage hierarchical initialization and a two-layer hybrid crossover strategy are adopted, combined with a Pareto front niche preservation mechanism, balancing the quality and diversity of solutions. This avoids the local optima problem caused by poor initial population quality or insufficient diversity in traditional algorithms, significantly improving the efficiency of multi-objective optimization and enhancing the reliability of air-ground collaborative last-mile delivery under sudden conditions. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0066] Figure 1 A flowchart illustrating a dynamic planning method for air-ground coordinated last-mile delivery provided in an embodiment of this specification;

[0067] Figure 2 This specification provides a schematic diagram of a delivery scenario in an area with disrupted road conditions, as illustrated in the embodiments of this specification.

[0068] Figure 3 This specification provides a road network map for an application scenario in an embodiment of the present invention.

[0069] Figure 4 A schematic diagram of a road segment vulnerability assessment process provided in the embodiments of this specification;

[0070] Figure 5 This diagram illustrates an iterative update of an initial air-to-ground collaborative last-mile delivery route, as provided in an embodiment of this specification.

[0071] Figure 6 A schematic diagram of the structure of a dynamic planning device for air-ground coordinated last-mile delivery provided in the embodiments of this specification;

[0072] Figure 7 This is a schematic diagram of the structure of a non-volatile storage medium provided in the embodiments of this specification. Detailed Implementation

[0073] This specification provides a dynamic planning method, equipment, and medium for air-ground coordinated last-mile delivery.

[0074] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0075] like Figure 1 As shown in the diagram, this specification provides a flowchart illustrating a dynamic programming method for air-ground coordinated last-mile delivery. Figure 1 As can be seen, in one or more embodiments of this specification, a dynamic planning method for air-ground coordinated last-mile delivery specifically includes the following steps:

[0076] S101: Based on delivery demand information and actual road network information of the current delivery area, update the road network map corresponding to the current delivery area in real time, and determine whether to trigger the delivery plan update of the current delivery area based on the failure unit of the road network map.

[0077] First, the scenario diagram described in this instruction manual is as follows: Figure 2As shown, in this problem, the shared distribution center dispatches multiple delivery vehicles (some of which carry drones) to complete the delivery of parcels to customer demand points within its jurisdiction as much as possible. The customer point set is defined as C = {1, ..., n}, and all customer demand points are distributed along urban roads. Each customer point can be visited at most once by one type of delivery facility (vehicle or drone). In summary, the problem described in this paper can be defined as a graph (V, E), where V = C ∪ {0, n+1} represents the set of all nodes (0 and n+1 represent the same shared distribution center), and E = {(i, j), i, j ∈ V, i ≠ j} represents the set of all arcs. In areas where roads are disrupted within the delivery range, a delivery vehicle carries a drone for collaborative delivery. This vehicle serves customer points along normally passable roads, acts as a mobile base station providing a battery replacement and parcel delivery location for the drone, and also functions as a drone take-off and landing site. To facilitate drone management, the same drone must take off and land at a fixed vehicle, and drones are allowed to take off and land at the shared distribution center. Therefore, the dynamic set of drone take-off and landing points can be defined as S = {0, 1, ..., n, n+1}. During delivery, a single drone launch can serve multiple customer points, and its path set is defined as L = {1, ..., n-1}, representing all possible drone paths. After arriving at a customer point, each drone on its path can automatically unload and quickly fly away. After completing tasks for several customers based on its endurance, it returns to a rendezvous point, rendezvous with a designated vehicle, and lands to complete actions such as battery replacement and package handling. Considering drone endurance and payload, each drone is subject to a flight time limit of length ε and a payload limit of weight Q. Traditional methods of planning joint vehicle and drone delivery routes are generally based on fixed road network information and cannot respond in real time to dynamic changes such as road failures and congestion. This makes it difficult to prioritize avoiding high-risk failed road sections when the delivery plan fails in unexpected situations. Therefore, in the scenario described above, in order to achieve timely route adjustments for failed road sections, this embodiment of the specification will update the road network map corresponding to the current delivery area in real time based on delivery demand information and the actual road network information of the current delivery area, as shown below. Figure 3 As shown, based on the failure units of the road network map, it is determined whether to trigger an update of the delivery plan for the current delivery area.

[0078] In one embodiment of this specification, to accurately reflect key information such as the urban road network topology and traffic flow distribution, and to enhance the accuracy of vulnerability identification, a primitive method is first used to construct a network topology graph. Road segments and intersections in the actual road network are mapped to edges and nodes in the graph, respectively. A grid-like road network topology graph is then established based on the information between nodes. In this road network topology, the delivery network is modeled as an undirected weighted graph. The node set includes road intersections, customer demand points, delivery centers, and possible take-off and landing points. Edges represent road segments connecting intersections, and the weight of each edge represents the toll cost or distance of that road segment. Specifically, in one or more embodiments of this specification, based on delivery demand information and the actual road network information of the current delivery area, the road network graph corresponding to the current delivery area is updated in real time. Based on the failure units of the road network graph, it is determined whether to trigger an update of the delivery plan for the current delivery area. This specifically includes:

[0079] First, based on the actual road network information and delivery demand information of the current delivery area, the node set of the current delivery area is determined. This node set includes: road intersections, customer demand points, delivery centers, and drone take-off and landing points. Then, based on the toll cost and distance corresponding to the road segments associated with each node, the cost of path selection is quantified by determining the weights of each edge. By mapping the node set to the weights of each edge, the road network map corresponding to the current delivery area is obtained. For example, Figure 3 The road network diagram shown is a grid-like road network topology. Based on the road network diagram's failure units, such as congested road sections and temporarily closed roads, road segment vulnerability is calculated to trigger updates to the delivery plan for the current delivery area. Failure units can be either failed nodes or failed edges within the road network diagram. When a network node is marked as failed, all edges connected to that node are simultaneously marked as failed. Since the edges connected to nodes in the network topology may not be unique, node failures have a significant impact on the vulnerability of the road network. When a network edge is marked as failed, passage along that edge is impossible, but the two nodes it connects to are unaffected by the edge. The impact of edge failures on the network cannot be uniformly evaluated; it requires comprehensive consideration of the other nodes and edges in the network. Therefore, it is necessary to assess the impact of edge failures on the overall vulnerability of the network.

[0080] In one embodiment, for ease of calculation, the road network information corresponding to the road network map can be represented by an adjacency matrix:

[0081]

[0082] Furthermore, in one or more embodiments of this specification, road segment vulnerability is calculated based on the failure units of the road network map to trigger an update of the delivery plan for the current delivery area, specifically including:

[0083] Obtain the vulnerability identification model corresponding to the failed units in the road network map. The vulnerability identification model includes: a node failure vulnerability identification model and an edge failure vulnerability identification model; the node failure vulnerability identification model is: V Nj =P Nj ×Z Nj ;

[0084] Among them, V Nj P represents the vulnerability identification value in the case of node j failure. Nj Z represents the probability of node j failing. Nj This is a comprehensive metric for the failure of node j.

[0085] The edge failure vulnerability identification model is: V Lj =P Lj ×Z Lj

[0086] Among them, V Lj P is the vulnerability identification value in the case of edge j failure. Lj Z represents the probability that edge j will fail. Lj This is a comprehensive metric for edge j failure.

[0087] The reference indicators used in the calculation of road segment vulnerability among the above comprehensive measurement values ​​are shown in Table 1 below:

[0088] Table 1. Reference Indicators Used in Road Segment Vulnerability Calculation

[0089]

[0090] In the table, E(G) represents the efficiency of the original network, and E(Gr) represents the efficiency of the network after removing path r; n′ represents the number of nodes in the maximum connected subgraph, and n represents the number of nodes in the original network; σ st σ represents the number of shortest paths between nodes s and t. st (r) represents the number of shortest paths passing through segment r, D st This represents the logistics demand between nodes s and t. The network efficiency change rate and the relative size of the largest connected subgraph are static indicators, while the importance of road segments is a dynamic indicator and needs to be calculated based on the actual road network conditions. That is, for example... Figure 4The algorithm obtains a preset initial network efficiency, sequentially removes the road segments corresponding to each failed unit to determine the current network efficiency, and determines the network efficiency change rate based on the preset initial network sales and the current network efficiency. It determines the relative size of the largest connected subgraph after removing the road segments corresponding to each failed unit, and determines the road segment importance based on the weights of each edge. The algorithm then substitutes the network efficiency change rate, the relative size of the largest connected subgraph, and the road segment importance into a vulnerability identification model to obtain road segment vulnerability, triggering an update to the delivery plan for the current delivery area. The pseudocode is shown in Table 2 below.

[0091] Table 2. Vulnerability Assessment Pseudocode

[0092]

[0093] S102: If so, then based on the information corresponding to the road network map, construct an air-ground coordinated last-mile delivery model for the current delivery area; wherein, the air-ground coordinated last-mile delivery model includes optimization objectives and constraints, and the optimization objectives include: demand coverage optimization objective, cost optimization objective, and time optimization objective.

[0094] If it is determined that the delivery plan for the current delivery area needs to be updated, then an air-ground coordinated last-mile delivery model for the current delivery area needs to be constructed based on the information corresponding to the current road network map, so as to solve and optimize the air-ground coordinated last-mile delivery model. It should be noted that the air-ground coordinated last-mile delivery model includes optimization objectives and constraints. The optimization objectives include: demand coverage optimization objective, cost optimization objective, and time optimization objective.

[0095] In one embodiment of this specification, to improve the feasibility of model construction and simplify the problem, the following assumptions are made:

[0096] (1) All customer demand information is known, including location and delivery demand;

[0097] (2) The drone models are the same;

[0098] (3) The drones and vehicles fly and travel at a uniform speed;

[0099] (4) Ensure sufficient energy (fuel) for both drones and vehicles during transport;

[0100] (5) The vehicle has sufficient space and load capacity and there is no overloading problem;

[0101] (6) The time for drone take-off, landing, charging and battery swapping, and loading and unloading is included in the vehicle's service time and is not calculated separately;

[0102] (7) When the drone is parked at an intermediate customer, it will autonomously complete the unloading and take off immediately, without considering any impact on the intermediate customer.

[0103] Service hours at the customer's location;

[0104] (8) The capacity of a single drone is greater than the total demand of all customers on its delivery route.

[0105] In the embodiments described in this specification, seven 0-1 decision variables and five continuous variables are designed. Among them, the 0-1 variable x is defined as follows: ij If the delivery route of delivery vehicle k passes through (i,j)∈E, then x ij =1, otherwise x ij =0; Define a 0-1 variable y ijl If the drone delivery path l∈L passes through arc (i,j)∈E, then y ijl =1, otherwise y ijl =0; Define a 0-1 variable If customer i∈C's demand is served by vehicle k otherwise Define 0-1 variables If customer i∈C's demand is served by drone path l∈L otherwise Define 0-1 variables If node i is the launch point of the UAV path l∈L, then otherwise Define 0-1 variables If node i is the collection point for the drone path l∈L, then otherwise Define 0-1 variables If customer i∈C is located on road segment r∈R, then otherwise Define continuous variables Represents the time when the vehicle arrives at node i; define continuous variables. The time when the drone arrives at node i is represented by its path; a continuous variable r is defined. i k , representing the time when the vehicle leaves node i; define continuous variables. Represents the time when the drone leaves node i; define a continuous variable. This indicates the time the vehicle waits for the drone at meeting point i.

[0106] Specifically, in one or more embodiments of this specification, an air-ground coordinated last-mile delivery model for the current delivery area is constructed based on information corresponding to the road network map, including:

[0107] Based on the information corresponding to the road network map, we construct the optimization objective and constraints of the air-ground collaborative last-mile delivery model for the current delivery area.

[0108] The model aims to find a reasonable vehicle-drone air-to-ground collaborative delivery scheme to address the vulnerability of road networks caused by disturbances, which makes it difficult to meet delivery service demands at some nodes. It also aims to minimize system delivery costs and collaborative waiting times, establishing three optimization objectives. First, because the greater the vulnerability of the road network, the higher the probability of disruption and failure, and the greater the delivery failure rate at customer points along the route, the purpose of setting up drone-vehicle collaborative delivery is to maximize coverage of customer demand points around failed road nodes, thereby achieving maximum regional delivery demand coverage. Therefore, the demand coverage optimization objective is to maximize coverage of customer demand points around failed road nodes, and the corresponding demand coverage objective function is:

[0109] Where, λ r Let i represent the vulnerability value of a road segment, r represent the road segment, C = {1, 2, 3, ..., n} be the set of all customer demand points, and L = {1, ..., n-1} be the set of drone paths. If a customer node i∈C is located in road segment r∈R, then otherwise The needs of customer i∈C are served by vehicle k. otherwise The needs of customer i∈C are served by the drone path l∈L otherwise

[0110] In the above formula, λ r To determine the vulnerability value of a road segment, this paper combines complex network theory with relevant findings, and selects a road segment importance value I based on the supply and demand characteristics of logistics distribution studied in this paper. r The vulnerability of a road segment is assessed by combining the impact of the segment's failure on the road network under emergency conditions.

[0111] λ r =I r ·ΔE(r), road segment importance I r The weighted edge betweenness number Br, representing the logistics and distribution demand along the road segment, is used for calculation. The impact of road segment failure on the overall network is measured by comparing the rate of change in network efficiency ΔE(r) before and after the road network disturbance. According to complex network theory, the edge betweenness number is the ratio of the number of shortest paths passing through this edge to the total number of shortest paths in the network.

[0112] Where: Br is the segment betweenness number, N i′,j′N represents the number of shortest paths connecting node i′ and node j′ in the road network. i′,j′ (r) represents the number of shortest paths connecting node i′ and node j′ that pass through road segment r. The logistics delivery demand of the road segment is the sum of the delivery demands of each customer demand point along the route.

[0113] Network efficiency E(G) is the average of the reciprocals of the shortest distances between all pairs of nodes in the road network:

[0114]

[0115] Where: N is the total number of nodes in the network, d i′j′ Let be the shortest distance between node i′ and node j′, E(GR) be the network efficiency after deleting road segment r, and ΔE(r) be the rate of change of network efficiency after deleting road segment r. Furthermore, as described in step S101, the calculation of road network demand coverage depends on road network vulnerability, and its calculation formula is as follows:

[0116] Among them, C covered For the customer set covered by the solution, C all For all customers, V r (i) represents the vulnerability value of the road segment where customer i is located.

[0117] The cost optimization objective is to minimize the transportation costs of vehicles and drones, and the corresponding cost objective function is: Where, θ k θ represents the unit distance transportation cost for vehicles. u For the unit distance transportation cost of drones, Let be the distance the vehicle travels through arc (i,j)∈E. Let x be the flight distance of the UAV along the path l∈L through the arc (i,j)∈E, where E={(i,j),i,j∈V,i≠j} represents the set of all arcs. ij If the delivery route of vehicle k passes through (i,j)∈E, then x ij =1; y ijl If the drone delivery path l∈L passes through arc (i,j)∈E, then y ijl =1;

[0118] While emergency supplies delivery must prioritize timeliness during sudden events such as natural disasters, the current situation of residential parcel delivery, which primarily consists of daily necessities, highlights the crucial role of timely delivery in alleviating the difficulties caused by road closures. To improve the overall delivery efficiency of the network, considering vehicle and drone delivery times, as well as potential waiting times for vehicles at customer points and meeting points, the objective function for time optimization is:

[0119] Among them, v k Let v be the speed of vehicle k. u The speed of the drone is u.

[0120] The constraints include a first constraint formula indicating that each customer demand point can only be served once by a vehicle or drone:

[0121] The second constraint, representing all customer points visited by vehicles, is as follows:

[0122] The third constraint used to represent all customer points for drone services is the path traversed by the drone:

[0123] The fourth constraint expression used to indicate that the drone is only allowed to traverse each path arc once:

[0124] The fifth constraint used to constrain dynamic coordinated take-off and landing points is that each drone launch and recovery point must be traversed by a vehicle, and each drone delivery route must serve at least one customer point: j∈{C:j≠i},h∈{C:h≠i≠j}, i∈{C:i≠j},h∈{C:h≠j≠i};

[0125] The sixth constraint used to constrain the load is that when the UAV completes its path and leaves any customer point i, the load does not exceed the maximum load: l∈L;

[0126] The seventh constraint equation used to indicate that the battery level at the launch point along any path of the UAV satisfies the maximum flight time:

[0127] The eighth constraint equation, used to represent the condition that the battery level meets 10% of the maximum flight time when the drone returns to the rendezvous point along any path:

[0128] The ninth constraint equation, used to represent the time constraints for the vehicle's arrival and departure from node i, is as follows: f is the time when the vehicle arrives at node i∈V1; i k For the moment when the vehicle leaves node i∈V1, M is a sufficiently large positive number; r i k The time when the vehicle leaves node i;

[0129] The tenth constraint equation, used to represent the time constraints for the arrival and departure of the drone from node i, is as follows: The time when the vehicle arrives at node i∈V1 The moment when the drone leaves node i∈V1;

[0130] The eleventh constraint, used to indicate that at the drone's takeoff point, the vehicle's departure time must be later than the drone's departure time, is:

[0131] The twelfth constraint, used to indicate that at the drone's landing point, the vehicle must meet it, and the vehicle's arrival time must not be later than the drone's arrival time, is as follows:

[0132] In the above constraint formula, Let node i be the launch point of the UAV path l∈L, then Let node i be the collection point for the drone along path l∈L, then The drone's remaining flight time when it serves the drone's path and leaves customer point i; The payload of the drone when it serves the drone's path and leaves customer point i; The time when the vehicle arrives at node i∈V1; The time when the vehicle arrives at node i∈V1; f i k The moment when the vehicle leaves node i∈V1; Let M be the moment when the drone leaves node i∈V1; M is a sufficiently large positive number.

[0133] S103: Solve the air-ground collaborative last-mile delivery model based on the two-stage hierarchical initialization strategy and the two-layer hybrid cross strategy to obtain the initial air-ground collaborative last-mile delivery path of vehicles and drones.

[0134] To address the problem that traditional random initialization can easily lead to infeasible solutions or low-quality initial populations, this embodiment of the specification uses a two-stage hierarchical initialization strategy to initialize the solution of the air-ground collaborative last-mile delivery model. To achieve collaborative processing of vehicle paths and UAV paths, this embodiment of the specification employs a two-layer hybrid crossover strategy to solve the air-ground collaborative last-mile delivery model, obtaining the initial air-ground collaborative last-mile delivery paths for vehicles and UAVs, thereby avoiding invalid crossover operations at the vehicle path layer and the UAV path layer.

[0135] Specifically, in one or more embodiments of this specification, the air-to-ground cooperative last-mile delivery model is solved based on a two-stage hierarchical initialization strategy and a two-stage hybrid cross strategy to obtain the initial air-to-ground cooperative last-mile delivery path for vehicles and drones. This process includes the following steps:

[0136] In the random initialization layer, delivery center nodes and failed nodes are determined based on road network graph information. Based on these nodes, initial vehicle routes and initial drone routes are generated. Specifically, from all nodes in the road network graph G, delivery centers are selected by comprehensively considering demand density and delivery volume, prioritizing nodes closer to dense demand areas to reduce delivery distance and time. Simultaneously, failed nodes and road segments are randomly simulated, and the information of delivery centers and failed nodes is saved to the graph's structure information G. The operating parameters of the optimization algorithm are defined, such as population size and number of iterations, as well as key parameters of the road network information, such as truck and drone load and speed. Finally, delivery routes for trucks and drones are generated. The solution to the air-ground collaborative delivery problem is encoded as a sequence containing vehicle routes and drone task assignments. Each solution consists of two parts, each stored as a vector. In the random initialization layer, the number of trucks T is randomly assigned to each delivery center. d ~U[1,T max The initial vehicle path R is generated using a random walk strategy. t ={v0,v rand1 ,…,v randk ,v0}, where v0 is the distribution center, v randi Let k be a path node, and k be the path length. The UAV path can be viewed as the assignment of tasks along the route. The task target is selected as its nearest failed node. Where d(·) represents point v i The Euclidean distance between V and v, V failed This is the set of failed nodes.

[0137] The heuristic initialization layer requires calculating the savings value of each node pair based on a pre-defined truck routing optimization method. The node pairs are then sorted in descending order based on their node values, and paths are merged until the capacity constraint is met to obtain the second initial vehicle path. The savings value s of each node pair is... ij =d(v0,v i )+d(v0,v j )-d(v i ,v j ); d(·) represents point v i The Euclidean distance between v and v.

[0138] In the heuristic initialization layer, the pre-assignment of drone paths requires selecting the task with the greatest marginal benefit based on a greedy algorithm. Prioritize coverage of high-demand, nearby failed nodes to obtain a second initial drone path.

[0139] By summing the first initial vehicle path and the second initial vehicle path, we obtain the initial vehicle path. Similarly, by summing the first initial drone path and the second initial drone path, we obtain the initial drone path. Then, as follows... Figure 5 The diagram shows that a two-layer hybrid crossover strategy is used to process the initial vehicle path and the initial drone path to obtain the initial solution of the air-ground collaborative last-mile delivery model, which serves as the initial air-ground collaborative last-mile delivery path.

[0140] Furthermore, in one or more embodiments of this specification, in order to achieve air-to-ground cooperative delivery, given the heterogeneous characteristics of truck routes and drone missions, a two-layer hybrid crossover strategy is needed to process the initial vehicle routes and initial drone routes to obtain an initial solution for the air-to-ground cooperative last-mile delivery model, which serves as the initial air-to-ground cooperative last-mile delivery route. Specifically, the process includes the following steps:

[0141] First, a tournament strategy is adopted to select parent individuals from the population formed by the initial vehicle paths and the initial drone paths; the selection probability is calculated using the following formula:

[0142] Where β is the selection pressure coefficient, rank(x) i ) represents the non-dominated ranking of the i-th individual in the tournament subset S.

[0143] The initial vehicle path is sequentially crossed to preserve continuous segments of the parent individuals of the initial vehicle path, thus obtaining a new child solution of the initial vehicle path. That is, the starting point and ending point a, b are randomly selected in the parent paths P1 and P2, and the nodes in the interval [a, b] of P1 and the nodes outside the interval [a, b] of P2 are combined to form a new child solution.

[0144] The initial drone paths are uniformly intersected to blend the parent instances of the initial drone paths using a mask matrix. A greedy selection process is then used to choose conflicting tasks, resulting in new child solutions for the initial drone paths. This involves binary encoding the drone task vectors, denoted as parent tasks U1 and U2, and then applying the mask matrix M. ij ~B(0.5) performs bit operations, and the formula for calculating the new solution of the UAV offspring is: Where B(·) is the Bernoulli equation, and finally, a greedy selection is performed on overlapping tasks to eliminate conflicts, prioritizing the retention of low-energy solutions. Then, based on the new child solutions of the initial vehicle path and the new child solutions of the initial UAV path, the initial solution of the air-ground cooperative last-mile delivery model is obtained, which serves as the initial air-ground cooperative last-mile delivery path.

[0145] S104: The initial air-ground collaborative last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-ground collaborative last-mile delivery path for the current delivery area.

[0146] The Pareto front is a core concept in multi-objective optimization, serving to provide a set of optimal trade-off solutions for multiple conflicting objectives. In multi-objective problems, due to the mutual constraints between objectives, a single globally optimal solution often does not exist. The Pareto front, by defining all non-dominated solutions, provides decision-makers with a diverse choice space. Therefore, in the embodiments of this specification, to obtain the optimal solution while avoiding the problem of getting trapped in local optima using traditional methods, the initial air-to-ground coordinated last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-to-ground coordinated last-mile delivery path for the current delivery area. Specifically, in one or more embodiments of this specification, iteratively updating the initial air-to-ground coordinated last-mile delivery path based on the Pareto front to obtain the optimal solution as the optimal air-to-ground coordinated last-mile delivery path for the current delivery area includes the following steps:

[0147] First, the initial air-to-ground coordinated last-mile delivery routes are hierarchically divided according to dominance relationships. A quicksort algorithm is used to divide the solution set into multiple frontier levels, achieving non-dominated sorting. Then, based on the target directions corresponding to the optimization objective, the maximum solution in that direction on the current Pareto front is defined as the extremum point. That is, to address the issue of target spatial scale variations, an extremum point tracking method is used to define the maximum solution on each target defense line as... The periodic extreme points are updated during the evolutionary process to reflect the frontier expansion. Where, σ i (t) represents the standard deviation of the current Pareto target i in the direction of t iterations, and δ is the relaxation coefficient. The target space is normalized based on the obtained extreme points to calculate the congestion entropy of each solution on the current Pareto front. Solutions are then sorted according to congestion entropy, and low-entropy solutions are filtered to obtain new solutions. In other words, a congestion entropy strategy is used to update the niche of the Pareto front to ensure population diversity for any solution x. i Its crowding entropy is defined as in After calculating the crowding entropy of all solutions, they are sorted from high to low. Low-entropy solutions at the bottom of the list are excluded with a certain probability.

[0148] After each generation of evolution, the new solutions obtained after elimination are merged with the existing solutions on the current Pareto front (i.e., the old solutions), and non-dominated solutions are extracted to form the set of solutions for the next generation. If the size of the solution exceeds the limit, Pareto pruning is performed, retaining high-entropy solutions according to the crowding entropy sorting method and randomly pruning low-entropy solutions, but retaining at least one extreme solution in each direction. Then, the solutions on the Pareto front are iteratively updated to obtain the optimal solution as the optimal air-ground coordinated last-mile delivery path for the current delivery area.

[0149] like Figure 6 As shown in the diagram, this specification provides a structural schematic of a dynamic planning device for air-ground coordinated last-mile delivery. Figure 6 As can be seen from one or more embodiments of this specification, a dynamic planning device for air-ground coordinated last-mile delivery includes:

[0150] At least one processor; and,

[0151] A memory communicatively connected to the at least one processor; wherein,

[0152] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform any of the methods described above.

[0153] like Figure 7 As shown in the diagram, this specification provides a schematic diagram of a non-volatile storage structure. Figure 7 As can be seen, in one or more embodiments of this specification, a non-volatile storage medium stores computer-executable instructions, characterized in that the computer-executable instructions are capable of executing any of the methods described above.

[0154] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of apparatus, devices, and non-volatile computer storage media are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0155] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0156] The above description is merely one or more embodiments of this specification and is not intended to limit this specification. Various modifications and variations can be made to the one or more embodiments of this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of one or more embodiments of this specification should be included within the scope of the claims of this specification.

Claims

1. A dynamic programming method for air-ground coordinated last-mile delivery, characterized in that, The method includes: Based on delivery demand information and actual road network information of the current delivery area, the road network map corresponding to the current delivery area is updated in real time. Based on the failure units of the road network map, it is determined whether to trigger the delivery plan update of the current delivery area. If so, then based on the information corresponding to the road network map, an air-ground coordinated last-mile delivery model for the current delivery area is constructed; wherein, the air-ground coordinated last-mile delivery model includes optimization objectives and constraints, and the optimization objectives include: demand coverage optimization objective, cost optimization objective, and time optimization objective; The air-ground collaborative last-mile delivery model is solved based on a two-stage hierarchical initialization strategy and a two-layer hybrid cross strategy to obtain the initial air-ground collaborative last-mile delivery path of vehicles and drones. The initial air-ground collaborative last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-ground collaborative last-mile delivery path for the current delivery area. The air-to-ground cooperative last-mile delivery model is solved based on a two-stage hierarchical initialization strategy and a two-stage hybrid crossover strategy to obtain the initial air-to-ground cooperative last-mile delivery path for vehicles and drones, specifically including: In the random initialization layer, the distribution center node and the failed node are determined based on the information of the road network map. Based on the random initialization of the distribution center node and the failed node, the first initial vehicle path and the first initial drone path are generated. In the heuristic initialization layer, based on a pre-defined truck routing optimization method, the savings value of each node pair is calculated. The node pairs are then sorted in descending order based on their node values ​​to merge paths and obtain a second initial vehicle path. The savings value of each node pair... ; For point and Euclidean distance between them; The second initial UAV path is obtained by selecting the task with the greatest marginal benefit based on a greedy algorithm; The first initial vehicle path and the second initial vehicle path are combined to obtain the initial vehicle path; the first initial drone path and the second initial drone path are combined to obtain the initial drone path. By employing a dual-layer hybrid crossover strategy, the initial vehicle path and the initial drone path are processed to obtain an initial solution for the air-ground collaborative last-mile delivery model, which serves as the initial air-ground collaborative last-mile delivery path. A two-layer hybrid crossover strategy is used to process the initial vehicle path and the initial drone path to obtain an initial solution for the air-ground cooperative last-mile delivery model, which serves as the initial air-ground cooperative last-mile delivery path. Specifically, this includes: A tournament strategy is adopted to select parent individuals from the population consisting of the initial vehicle path and the initial drone path; The initial vehicle path is sequentially crossed to preserve continuous segments of the parent individuals of the initial vehicle path, thus obtaining a new child solution of the initial vehicle path. The initial drone path is uniformly intersected to blend the parent individuals of the initial drone path through a mask matrix, and a greedy selection is performed on the conflicting tasks to obtain a new child solution of the initial drone path. Based on the new child solutions of the initial vehicle path and the new child solutions of the initial drone path, an initial solution for the air-ground collaborative last-mile delivery model is obtained, which serves as the initial air-ground collaborative last-mile delivery path.

2. The dynamic planning method for air-ground coordinated last-mile delivery according to claim 1, characterized in that, Based on delivery demand information and the actual road network information of the current delivery area, the road network map corresponding to the current delivery area is updated in real time. Based on the failure units of the road network map, it is determined whether to trigger an update of the delivery plan for the current delivery area, specifically including: Based on the actual road network information and delivery demand information of the current delivery area, the node set of the current delivery area is determined; wherein, the node set includes: road intersections, customer demand points, delivery centers, and drone take-off and landing points; The weights of each edge are determined based on the toll cost and toll distance of the road segment corresponding to each node; Based on the mapping between the set of nodes and the weights of each edge, a road network map corresponding to the current delivery area is obtained; wherein, the road network map is a grid-type road network topology map; The vulnerability of road segments is calculated based on the failure units of the road network map to trigger an update of the delivery plan for the current delivery area.

3. The dynamic planning method for air-ground coordinated last-mile delivery according to claim 2, characterized in that, Based on the failure units of the road network map, the vulnerability of road segments is calculated to trigger an update of the delivery plan for the current delivery area, specifically including: Obtain the vulnerability identification model corresponding to the failure unit of the road network map; wherein, the vulnerability identification model includes: node failure vulnerability identification model and edge failure vulnerability identification model; A preset initial network efficiency is obtained, and the current network efficiency is determined by sequentially removing the road segments corresponding to each failed unit. The network efficiency change rate is determined based on the preset initial network sales and the current network efficiency. Based on the failure units, determine the relative size of the largest connected subgraph after removing the road segments corresponding to each failure unit, and determine the road segment importance of the road segment corresponding to each failure unit based on the weight of each edge; The vulnerability of a road segment is obtained by substituting the network efficiency change rate, the relative size of the largest connected subgraph, and the comprehensive metric corresponding to the importance of the road segment into the vulnerability identification model, thereby triggering the update of the delivery plan for the current delivery area.

4. The dynamic planning method for air-ground coordinated last-mile delivery according to claim 1, characterized in that, Based on the information corresponding to the road network map, an air-ground coordinated last-mile delivery model for the current delivery area is constructed, specifically including: Based on the information corresponding to the road network map, the optimization objective and constraints of the air-ground coordinated last-mile delivery model for the current delivery area are constructed. The demand coverage optimization objective in the optimization objectives is to maximize the coverage of customer demand points around the failed road nodes, and the corresponding demand coverage objective function is: ;in, Let i represent the vulnerability value of a road segment, r represent the road segment, and C = {1, 2, 3, ..., n} be the set of all customer demand points. For the set of drone paths, Represents client node Located on the road section ,but ;otherwise , For customers The demand is provided by vehicle k service ;otherwise , For customers The demand is driven by drone paths Serve ;otherwise ; The cost optimization objective is to minimize the transportation costs of vehicles and drones, and the corresponding cost objective function is: ;in, The unit distance transportation cost for vehicles. For the unit distance transportation cost of drones, For vehicles to pass through the arc driving distance, For the path of the drone Through arc Flight distance, Represents the set of all arcs. For the delivery route of vehicle k ,but ; Drone delivery routes Through arc ,but ; The time optimization objective is to minimize delivery time, and the corresponding time objective function is: ;in, Let k be the speed of the vehicle. The speed of the drone u; For 0-1 variables, if node i is a drone path The recycling points, ,otherwise ; The time when the vehicle arrives at node i∈V1; The time when the vehicle arrives at node i∈V1; Let be the average service time of the vehicle at node i.

5. The dynamic planning method for air-ground coordinated last-mile delivery according to claim 4, characterized in that, The constraints include: The first constraint expression used to indicate that each customer demand can only be served once by a vehicle or drone; A second constraint is used to represent all customer points passed by vehicles, with delivery carried out by vehicles. The third constraint used to represent all customer points for drone services will be the path traversed by the drone. The fourth constraint expression is used to indicate that the UAV is only allowed to pass through each path arc once. The fifth constraint is used to constrain the dynamic coordinated take-off and landing points, requiring that each drone launch and recovery point must be traversed by a vehicle, and that each drone delivery route serves at least one customer point. The sixth constraint used to constrain the load is that when the UAV path is completed and leaves any customer point i, the load does not exceed the maximum load. The seventh constraint expression used to indicate that the battery power at the launch point of the UAV on any path satisfies the maximum flight time. The eighth constraint is used to represent the condition that the battery level meets 10% of the maximum flight time when the drone returns to the rendezvous point via any path. The ninth constraint equation, used to represent the time constraints for the vehicle's arrival and departure from node i, is as follows: , ; The time when the vehicle arrives at node i∈V1; M is a sufficiently large positive number, representing the moment when the vehicle leaves node i∈V1. The time when the vehicle leaves node i; The tenth constraint equation, used to represent the time constraints for the arrival and departure of the drone from node i, is as follows: , ; The time when the vehicle arrives at node i∈V1 The moment when the drone leaves node i∈V1; The eleventh constraint expression is used to indicate that at the drone takeoff point, the vehicle's departure time must be later than the drone's departure time; The twelfth constraint is used to indicate that at the drone's landing point, the vehicle meets with it, and the vehicle's arrival time must not be later than the drone's arrival time.

6. The dynamic planning method for air-ground coordinated last-mile delivery according to claim 1, characterized in that, The initial air-to-ground collaborative last-mile delivery path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-to-ground collaborative last-mile delivery path for the current delivery area, specifically including: The initial air-ground collaborative last-mile delivery routes are hierarchically divided according to their dominance relationship, and the solution set is divided into multiple frontier levels based on the quicksort method; Based on the target directions corresponding to the optimization objective, the maximum value solution in that direction on the current Pareto front is defined as the extreme point; Based on the extreme points, the target spaces are normalized to calculate the crowding entropy of each solution on the current Pareto front, and the solutions are sorted according to the crowding entropy to filter out low-entropy solutions and obtain new solutions. The new solution is merged with each solution on the current Pareto front, and non-dominated solutions are extracted to form a set of next-generation solutions. The solutions on the Pareto front are iteratively updated to obtain the optimal solution as the optimal air-ground collaborative last-mile delivery route for the current delivery area.

7. A dynamic planning device for air-ground coordinated last-mile delivery, characterized in that, The device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method described in any one of claims 1-6.

8. A non-volatile storage medium storing computer-executable instructions, characterized in that, The computer-executable instructions are capable of performing the method described in any one of claims 1-6.

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