Dynamic planning method and device for air-ground cooperative end distribution, and medium

Abstract

The embodiment of the invention discloses a dynamic planning method and device for air-ground cooperative tail end distribution and a medium, relates to the technical field of path planning, and is used for solving the problem that the planning effect is poor due to the fact that a sudden road failure problem cannot be quickly responded at present. The method comprises the steps of updating a road network diagram corresponding to a current distribution area in real time, and determining whether to trigger distribution scheme updating of the current distribution area based on a failure unit of the road network diagram; if yes, based on information corresponding to the road network diagram, constructing an air-ground cooperative tail end distribution model of the current distribution area; based on a double-stage hierarchical initialization strategy and a double-layer hybrid intersection strategy, solving the air-ground cooperative tail end distribution model to obtain an initial air-ground cooperative tail end distribution path of the vehicle and the unmanned aerial vehicle; and carrying out iterative updating on the initial air-ground cooperative tail end distribution path based on a Pareto front, and obtaining an optimal solution as an optimal air-ground cooperative tail end distribution path of the current distribution area.

Description

Technical Field

[0001] This specification relates to the field of path planning technology, and in particular to a dynamic planning method, device, and medium for air-ground collaborative terminal delivery. Background Art

[0002] Traditional urban delivery is carried out by couriers using vehicles across the city's road network. However, this road network is susceptible to uncertainties such as natural disasters, traffic accidents, public health incidents, and mass events, leading to localized congestion, closures, and even regional paralysis. This inevitably causes delays or interruptions in 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 steadily increased, and the facility location and routing problem (LRP) has become a research hotspot.

[0003] Current methods for planning joint delivery routes for vehicles and drones are generally based on fixed road network information, which is unable to respond in real time to dynamic changes such as road failures and congestion. This makes it difficult to prioritize high-risk sections of failed roads when delivery plans fail under unexpected circumstances. Furthermore, traditional algorithms, such as standard genetic algorithms, struggle to effectively balance conflicts among multi-dimensional objectives when optimizing collaborative delivery between vehicles and drones, causing the path planning structure to become trapped in a local optimal solution. Furthermore, the single initial population generation strategy results in insufficient diversity in the solution space, impacting the algorithm's convergence speed and global optimality. Summary of the Invention

[0004] In order to solve the above technical problems, one or more embodiments of this specification provide a dynamic planning method, device and medium for air-ground collaborative terminal delivery.

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

[0006] One or more embodiments of this specification provide a dynamic planning method for air-ground coordinated terminal delivery, the method comprising:

[0007] Based on the 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, and based on the invalid units of the road network map, whether to trigger the delivery plan update of the current delivery area;

[0008] If so, then construct an air-ground collaborative terminal delivery model for the current delivery area based on the information corresponding to the road network diagram; wherein the air-ground collaborative terminal 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 terminal 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 terminal delivery path of the vehicle and the UAV.

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

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

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

[0013] Determine the weight of each edge based on the travel cost and travel distance corresponding to the road section corresponding to each node;

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

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

[0016] Optionally, in one or more embodiments of the present specification, calculating the vulnerability of a road section based on the failure unit of the road network graph to trigger the update of the delivery plan for the current delivery area specifically includes:

[0017] Obtaining a vulnerability identification model corresponding to a failure unit of the road network graph; wherein the vulnerability identification model includes: a node failure vulnerability identification model and an edge failure vulnerability identification model;

[0018] Obtaining a preset initial network efficiency, determining a current network efficiency by sequentially removing road sections corresponding to each failed unit, and determining a network efficiency change rate based on the preset initial network sales volume and the current network efficiency;

[0019] Determining the relative size of the maximum connected subgraph after removing the road sections corresponding to the failed units based on the failed units, and determining the section importance of the road sections corresponding to the failed units based on the weights of the edges;

[0020] Substituting the comprehensive measurement value index corresponding to the network efficiency change rate, the relative size of the largest connected subgraph and the importance of the road section into the vulnerability identification model to obtain the road section vulnerability, so as to trigger the update of the distribution plan of the current distribution area.

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

[0022] Based on the information corresponding to the road network diagram, construct the optimization objectives and constraints of the air-ground collaborative terminal delivery model for the current delivery area;

[0023] Among them, the demand coverage optimization objective in the optimization objective is to cover the customer demand points around the failed road node to the greatest extent, and the corresponding demand coverage objective function is:

[0024] Among them, λ r is the vulnerability value of the road section, i represents the node, r represents the road section, C = {1, 2, 3, ... n} is the set of all customer demand points, L = {1, ..., n-1} is the set of drone paths, If customer node i∈C is located on road segment r∈R, then otherwise The demand of customer i∈C is served by vehicle k otherwise The demand of customer i∈C is served by the drone path l∈L otherwise

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

[0026] Among them, θ k is the vehicle transportation cost per unit distance, θ u is the UAV transportation cost per unit distance, is the distance traveled by the vehicle through arc (i, j)∈E, is the flight distance of the drone’s path l∈L through the arc (i, j)∈E, E={(i, j),i,j∈V,i≠j} represents the set of all arcs, x ij The delivery path of vehicle k passes through (i, j)∈E, then x ij =1;y ijl For the drone delivery path l∈L passing through arc (i,j)∈E, then y ijl =1;

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

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

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

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

[0031] It is used to represent the customer points that all vehicles pass through, and the second constraint condition for delivery by vehicles;

[0032] The third constraint condition is used to express that all customer points served by the drone will be passed by the drone path;

[0033] The fourth constraint condition is used to indicate that the drone is only allowed to pass through each path arc once;

[0034] The fifth constraint, used to constrain dynamic coordinated takeoff and landing points, requires that each drone launch and recovery point must be passed by a vehicle, and each drone delivery path must serve at least one customer point;

[0035] The sixth constraint condition for constraining the load constraint is that when the drone path is completed and leaves any customer point i, the load does not exceed the maximum load;

[0036] The seventh constraint condition is used to express that the power of the launch point of any path of the UAV meets the maximum endurance time;

[0037] The eighth constraint condition is used to express that when the UAV returns to the meeting point along any path, the battery level must meet 10% of the maximum flight time;

[0038] The ninth constraint condition is used to express the time constraints of the vehicle arriving at and leaving node i: is the time when the vehicle arrives at node i∈V1; f i k is the moment when the vehicle leaves the node i∈V1, M is a sufficiently large positive number; r i k is the time when the vehicle leaves node i;

[0039] The tenth constraint condition is used to express the time constraints of the drone arriving at and leaving node i: The moment the vehicle arrives at node i∈V1, is the moment when the UAV path leaves the node i∈V1;

[0040] The eleventh constraint condition is used to express that at the take-off point of the drone, the vehicle’s departure time must be later than the drone’s departure time;

[0041] The twelfth constraint condition is used to express that the vehicle must meet the drone at the landing point 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, solving the air-ground coordinated terminal delivery model based on a two-stage hierarchical initialization strategy and a two-layer hybrid cross strategy to obtain an initial air-ground coordinated terminal delivery path for the vehicle and the drone specifically includes:

[0043] In a random initialization layer, a distribution center node and a failure node are determined based on information of the road network graph, and a first initial vehicle path and a first initial drone path are generated based on random initialization of the distribution center node and the failure node;

[0044] In the heuristic initialization layer, based on the preset truck path optimization method, the savings value of each node pair is calculated, and the node pairs are sorted in descending order based on the node value to merge the paths to obtain the second initial vehicle path; wherein, the savings value s of each node pair is ij =d(v0,v i )+d(v0,v j )-d(v i ,v j ); d(·) is point v i The Euclidean distance from v;

[0045] Based on the greedy algorithm, the task with the largest marginal benefit is selected to obtain the second initial UAV path;

[0046] Summarizing the first initial vehicle path and the second initial vehicle path to obtain an initial vehicle path, and summarizing the first initial UAV path and the second initial UAV path to obtain an initial UAV path;

[0047] The initial vehicle path and the initial UAV path are processed through a double-layer hybrid cross strategy to obtain an initial solution to the air-ground collaborative terminal delivery model as the initial air-ground collaborative terminal delivery path.

[0048] Optionally, in one or more embodiments of this specification, the initial vehicle path and the initial UAV path are processed using a double-layer hybrid cross strategy to obtain an initial solution to the air-ground collaborative terminal delivery model as the initial air-ground collaborative terminal delivery path, specifically including:

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

[0050] Performing sequential crossover on the initial vehicle path to retain continuous segments of parent individuals of the initial vehicle path, and obtaining a new child solution of the initial vehicle path;

[0051] Performing uniform crossover on the initial UAV path to mix the parent individuals of the initial UAV path through a mask matrix and performing greedy selection on conflicting tasks to obtain a new child solution of the initial UAV path;

[0052] Based on the new sub-solutions of the initial vehicle path and the new sub-solutions of the initial UAV path, an initial solution of the air-ground collaborative terminal delivery model is obtained as the initial air-ground collaborative terminal delivery path.

[0053] Optionally, in one or more embodiments of this specification, iteratively updating the initial air-ground coordinated terminal delivery path based on the Pareto front to obtain an optimal solution as the optimal air-ground coordinated terminal delivery path for the current delivery area specifically includes:

[0054] The initial air-ground collaborative terminal delivery path is layered according to the dominance relationship, so as to divide the solution set into multiple frontier levels based on the quick sorting method;

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

[0056] Normalizing each target space based on the extreme point to calculate the congestion entropy of each solution on the current Pareto front, sorting them according to the congestion entropy, and filtering low entropy solutions to 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 terminal delivery path for the current delivery area.

[0058] One or more embodiments of this specification provide a dynamic planning device for air-ground coordinated terminal 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, and the instructions are executed by the at least one processor to enable the at least one processor to: perform any of the above methods.

[0062] One or more embodiments of this specification provide a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to execute any of the above-described methods.

[0063] At least one of the above technical solutions 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, dynamically triggering route adjustments ensures rapid route updates in the event of road failures. This addresses the inability of existing static planning to cope with sudden road network changes and improves the real-time responsiveness of collaborative delivery. A two-stage hierarchical initialization and two-layer hybrid crossover strategy, combined with a Pareto frontier niche preservation mechanism, balances solution quality and diversity, avoiding the local optimality issues often encountered in traditional algorithms due to poor initial population quality or insufficient diversity. This significantly improves the efficiency of multi-objective optimization and enhances the reliability of air-ground collaborative terminal delivery under sudden conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are only some of the embodiments described in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without inventive work. In the drawings:

[0066] Figure 1 A schematic diagram of a method flow chart of a dynamic planning method for air-ground coordinated terminal delivery provided in an embodiment of this specification;

[0067] Figure 2 A schematic diagram of a delivery scenario in a road-disturbed area provided in an embodiment of this specification;

[0068] Figure 3 A road network diagram for an application scenario provided in an embodiment of this specification;

[0069] Figure 4 A schematic diagram of a road section vulnerability assessment process provided in an embodiment of this specification;

[0070] Figure 5 A schematic diagram of iteratively updating an initial air-ground collaborative terminal delivery path provided in an embodiment of this specification;

[0071] Figure 6 A schematic diagram of the structure of a dynamic planning device for air-ground collaborative terminal delivery provided in an embodiment of this specification;

[0072] Figure 7A schematic diagram of the structure of a non-volatile storage medium provided in an embodiment of this specification. DETAILED DESCRIPTION

[0073] The embodiments of this specification provide a dynamic planning method, device, and medium for air-ground collaborative terminal delivery.

[0074] To help those skilled in the art better understand the technical solutions in this specification, the following will provide a clear and complete description of the technical solutions in the embodiments of this specification, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of this specification, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this specification without creative work should fall within the scope of protection of this specification.

[0075] like Figure 1 As shown, the embodiment of this specification provides a flow chart of a dynamic planning method for air-ground coordinated terminal delivery. Figure 1 It can be seen that in one or more embodiments of this specification, a dynamic planning method for air-ground coordinated terminal delivery specifically includes the following steps:

[0076] S101: Based on the 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, and based on the failure unit of the road network map, it is determined whether to trigger the delivery plan update of the current delivery area.

[0077] First, the description scene diagram of this manual is as follows Figure 2As shown in Figure 1, in this problem, a shared distribution center dispatches multiple delivery vehicles (some of which carry drones) to complete express delivery to customer demand points within its jurisdiction as much as possible. The customer point set C = {1, …, n} is defined, and all customer demand points are assumed to be distributed along urban roads. Each customer point can only be visited once by a type of delivery facility (vehicle or drone). In summary, the problem described in this article 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 with disrupted roads within the delivery range, a delivery vehicle carries a drone for collaborative delivery. The vehicle not only serves customer points along normally accessible roads, but also acts as a mobile base station, providing a place for drones to replace batteries and deliver packages, and also serves as a drone landing and take-off area. To facilitate drone management, the same drone is required to take off and land on a fixed vehicle, and drones are allowed to take off and land at shared distribution centers. Therefore, the set of dynamic drone takeoff and landing points can be defined as S = {0, 1, ..., n, n+1}. During delivery, a drone can serve multiple customer locations in a single launch. The set of paths is defined as L = {1, ..., n-1}, representing all possible drone paths. Upon arriving at a customer location, a drone in each path can automatically unload its cargo and quickly depart. After completing several customer deliveries based on its flight capacity, it returns to a rendezvous point, rendezvouses with a designated vehicle, and lands to complete tasks such as battery replacement and delivery. Considering drone endurance and payload, each drone is set with a flight time limit of ε and a payload limit of Q. Traditional methods for planning joint delivery routes for vehicles and drones 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 high-risk road sections in the event of unexpected failures. Therefore, in the above-described scenario, in order to achieve timely route adjustment for the invalid road section, the embodiment of this specification will update the road network map corresponding to the current delivery area in real time based on the delivery demand information and the actual road network information of the current delivery area. Figure 3 As shown, based on the failure unit of the road network graph, it is determined whether to trigger the distribution plan update of the current distribution area.

[0078] In one embodiment of this specification, in order to truly reflect key information such as the topological structure of the urban road network and traffic flow distribution, and to enhance the accuracy of vulnerability identification, the original method is first used to construct a network topology map, and the road sections and intersections in the actual road network are mapped to edges and nodes in the map respectively, and a grid-type road network topology map is established based on the information between the nodes. In this road network topology structure, the distribution network is modeled as an undirected weighted graph, and the node set includes road intersections, as well as customer demand points, distribution centers, and possible take-off and landing points; the edges represent road sections connecting intersections, and the weight of each edge represents the travel cost or distance of the section. Specifically, in one or more embodiments of this specification, based on the distribution demand information and the actual road network information of the current distribution area, the road network map corresponding to the current distribution area is updated in real time, and based on the failure units of the road network map, it is determined whether to trigger the distribution plan update for the current distribution area, specifically including:

[0079] First, based on the actual road network information and distribution demand information of the current distribution area, the node set of the current distribution area is determined; the node set includes: road intersections, customer demand points, distribution centers, and drone take-off and landing points. Then, based on the travel cost and travel distance corresponding to the road section corresponding to each node, the weight of each edge is determined to quantify the cost of path selection. By mapping the node set and the weight of each edge, the road network diagram corresponding to the current distribution area is obtained. Among them, if Figure 3 The road network diagram shown is a grid-type road network topology diagram. Based on the failure units of the road network diagram, such as congested sections and temporarily closed roads, the vulnerability of the road sections is calculated to trigger the update of the distribution plan for the current distribution area. Among them, the failure unit can be a failed node or a failed edge in the road network diagram. When a network node is marked as failed, all edges connected to the failed node are also marked as failed. Since the edges connected to the nodes in the network topology may not be unique, the failure of the node has a greater impact on the vulnerability of the road network. When a network edge is marked as failed, the edge cannot be passed, and the two nodes connected to it are not affected by the edge. The impact of edge failure on the network cannot be evaluated uniformly. It is necessary to comprehensively consider the remaining nodes and edges in the network. Therefore, it is necessary to evaluate the impact of edge failure on the overall vulnerability of the network.

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

[0081]

[0082] Furthermore, in one or more embodiments of this specification, calculating the vulnerability of a road segment based on the failure unit of the road network graph to trigger the update of the delivery plan for the current delivery area specifically includes:

[0083] Obtain the vulnerability identification model corresponding to the failure unit of the road network graph. Among them, the vulnerability identification model includes: node failure vulnerability identification model and edge failure vulnerability identification model; the node failure vulnerability identification model is: V Nj =P Nj ×Z Nj ;

[0084] Among them, V Nj is the vulnerability identification value when node j fails, P Nj is the probability of node j failing, Z Nj is the comprehensive measurement value indicator of node j failure.

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

[0086] Among them, V Lj is the vulnerability identification value when edge j fails, P Lj is the probability of edge j failing, Z Lj is the comprehensive measurement value indicator of edge j failure.

[0087] The reference indicators used in calculating the vulnerability of road sections in the above comprehensive measurement value indicators are shown in Table 1 below:

[0088] Table 1. Reference indicators used in calculating road vulnerability

[0089]

[0090] In the table, E(G) represents the efficiency of the original network, E(Gr) represents the efficiency of the network after removing the road segment r; n′ represents the number of nodes in the largest connected subgraph, n represents the number of nodes in the original network; σ st represents the number of shortest paths between nodes s and t, σ st (r) represents the number of shortest paths passing through segment r, D st 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 the road section is a dynamic indicator that needs to be calculated based on the actual situation of the road network. Figure 4As shown, the preset initial network efficiency is obtained, and the current network efficiency is determined by removing the road segments corresponding to each failed unit in sequence. The network efficiency change rate is determined based on the preset initial network sales and the current network efficiency. The relative size of the maximum connected subgraph after removing the road segments corresponding to each failed unit is determined based on the failed units, and the road segment importance of the road segment corresponding to the failed unit is determined based on the weight of each edge. The comprehensive measurement value indicators corresponding to the network efficiency change rate, the relative size of the maximum connected subgraph, and the road segment importance are substituted into the vulnerability identification model to obtain the road segment vulnerability, which triggers the update of the distribution plan for the current distribution area. The pseudo code is shown in Table 2 below:

[0091] Table 2. Vulnerability assessment pseudo code

[0092]

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

[0094] If it's determined that the delivery plan for the current delivery area needs to be updated, then an air-ground collaborative terminal delivery model for the current delivery area must be constructed based on the information corresponding to the current road network map. This allows for optimization of the air-ground collaborative terminal delivery model. It's important to note that the air-ground collaborative terminal delivery model includes optimization objectives and constraints. The optimization objectives include: demand coverage optimization, cost optimization, and time optimization.

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

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

[0097] (2) The drone model is the same;

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

[0099] (4) UAVs and vehicles maintain sufficient energy (fuel) during transportation;

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

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

[0102] (7) When the drone stops at an intermediate customer, it will take off immediately after completing unloading, without considering the intermediate customer.

[0103] Service time at the customer point;

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

[0105] In the embodiment of this specification, 7 0-1 decision variables and 5 continuous variables are designed. ij , if the delivery path of delivery vehicle k passes through (i,j)∈E, then x ij =1, otherwise x ij =0; define 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 0-1 variable If the demand of customer i∈C is served by vehicle k otherwise Defining 0-1 variables If the demand of customer i∈C is served by drone path l∈L otherwise Defining 0-1 variables If node i is the launch point of a UAV path l∈L, then otherwise Defining 0-1 variables If node i is the recycling point of the drone path l∈L, then otherwise Defining 0-1 variables If customer i∈C is located on road segment r∈R, then otherwise Defining continuous variables Indicates the time when the vehicle arrives at node i; define continuous variables Indicates the moment when the drone path reaches node i; define continuous variables Indicates the time when the vehicle leaves node i; define continuous variables Indicates the moment when the drone path leaves node i; define continuous variables represents the time the vehicle waits for the UAV at the rendezvous point i.

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

[0107] Based on the information corresponding to the road network map, the optimization objectives and constraints of the air-ground collaborative terminal delivery model in the current delivery area are constructed.

[0108] Among them, the goal of solving the model is to find a reasonable vehicle-drone air-ground collaborative distribution solution to solve the problem of difficulty in satisfying distribution services at some nodes due to the vulnerability of the road network being disturbed, and to minimize the system distribution cost and collaborative waiting time. A total of three optimization goals are set. First, since the greater the vulnerability of the road network, the greater the possibility of failure due to disturbance, and the greater the distribution failure rate of customer points along the line, the purpose of setting up drone-coordinated vehicle distribution is to maximize the coverage of customer demand points around failed road nodes, thereby achieving the maximum coverage rate of regional distribution demand. Therefore, the demand coverage optimization goal in the optimization objective is to maximize the coverage of customer demand points around failed road nodes, and the corresponding demand coverage objective function is:

[0109] Among them, λ r is the vulnerability value of the road section, i represents the node, r represents the road section, C = {1, 2, 3, ... n} is the set of all customer demand points, L = {1, ..., n-1} is the set of drone paths, If customer node i∈C is located on road segment r∈R, then otherwise The demand of customer i∈C is served by vehicle k otherwise The demand of customer i∈C is served by the drone path l∈L otherwise

[0110] In the above formula, λ r is the vulnerability value of the road section. This paper combines the complex network theory and draws on relevant results. Combined with the supply and demand characteristics of logistics distribution in this paper, the importance of the road section I is selected. r The vulnerability of a road section is evaluated by the impact of the failure of the road section on the road network under sudden conditions:

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

[0112] Among them: Br is the betweenness of the road section, N i′,j′ represents the number of shortest paths connecting node i′ and node j′ in the road network, N i′,j′(r) represents the number of shortest paths connecting node i′ and node j′ and passing through road section r. The logistics distribution demand of the road section is the sum of the distribution demands of all customer demand points along the route.

[0113] The 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′ is the shortest distance between node i′ and node j′, E(GR) is the network efficiency after deleting road segment r, and ΔE(r) is the rate of change of network efficiency after deleting road segment r. In addition, combined with the description of step S101, it can be seen that the calculation of the demand coverage of the road network depends on the vulnerability of the road network, and its calculation formula is as follows:

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

[0117] The cost optimization goal is to minimize the transportation cost of vehicles and drones. The corresponding cost objective function is: Among them, θ k is the vehicle transportation cost per unit distance, θ u is the UAV transportation cost per unit distance, is the distance traveled by the vehicle through arc (i, j)∈E, is the flight distance of the drone’s path l∈L through the arc (i, j)∈E, E={(i, j),i,j∈V,i≠j} represents the set of all arcs, x ij The delivery path of vehicle k passes through (i, j)∈E, then x ij =1;y ijl For the drone delivery path l∈L passing through arc (i,j)∈E, then y ijl =1;

[0118] However, due to emergencies such as natural disasters, the delivery of emergency supplies must prioritize timeliness. Although it is aimed at daily supply delivery in emergency situations, since most of the current residents' express deliveries are daily necessities, timely delivery plays an important role in alleviating the difficulties caused by road failures. To improve the overall delivery timeliness of the network, considering the delivery time of vehicles and drones, as well as the possible waiting time of vehicles at customer points and meeting points, the time objective function corresponding to the time optimization goal is:

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

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

[0121] It is used to represent the customer points that all vehicles pass through, with the second constraint condition for delivery by vehicles:

[0122] The third constraint condition used to express that all customer points served by the drone will be passed by the drone path:

[0123] The fourth constraint condition is used to express that the drone is only allowed to pass through each path arc once:

[0124] The fifth constraint, used to constrain dynamic coordinated take-off and landing points, requires that each drone launch and recovery point must be passed by a vehicle, and each drone delivery path must serve at least one customer point:

[0125] The sixth constraint condition for constraining the load constraint is that when the drone path is completed and leaves any customer point i, the load does not exceed the maximum load:

[0126] The seventh constraint condition for the maximum flight time is expressed as follows:

[0127] The eighth constraint condition is used to express that when the UAV returns to the meeting point along any path, the battery level must meet 10% of the maximum flight time:

[0128] The ninth constraint condition is used to express the time constraints of the vehicle arriving at and leaving node i: is the time when the vehicle arrives at node i∈V1; f i k is the moment when the vehicle leaves the node i∈V1, M is a sufficiently large positive number; r i k is the time when the vehicle leaves node i;

[0129] The tenth constraint condition is used to express the time constraints of the drone arriving at and leaving node i: The moment the vehicle arrives at node i∈V1, is the moment when the UAV path leaves the node i∈V1;

[0130] The eleventh constraint condition is used to express that at the take-off point of the drone, the vehicle’s departure time must be later than the drone’s departure time:

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

[0132] In the above constraints, If node i is the launch point of the UAV path l∈L, then If node i is the recycling point of the drone path l∈L, then The flight time of the drone when it serves the drone path and leaves customer point i; The payload of the drone when it serves the drone path and leaves customer point i; is the time when the vehicle arrives at node i∈V1; The moment when the vehicle arrives at node i∈V1; f i k is the moment when the vehicle leaves the node i∈V1; is the moment when the UAV path leaves the node i∈V1; M is a sufficiently large positive number.

[0133] S103: Solving the air-ground collaborative terminal delivery model based on a two-stage hierarchical initialization strategy and a two-layer hybrid cross strategy to obtain an initial air-ground collaborative terminal delivery path for the vehicle and the UAV.

[0134] In order to solve the problem that traditional random initialization easily leads to infeasible solutions or low-quality initial populations, the embodiment of this specification initializes the solution of the air-ground collaborative terminal delivery model based on a two-stage hierarchical initialization strategy. In order to achieve the coordinated processing of vehicle paths and drone paths, the embodiment of this specification adopts a two-layer hybrid cross strategy to solve the air-ground collaborative terminal delivery model to obtain the initial air-ground collaborative terminal delivery paths of vehicles and drones, thereby avoiding invalid cross operations between the vehicle path layer and the drone path layer.

[0135] Specifically, in one or more embodiments of this specification, the air-ground collaborative terminal 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 terminal delivery path of the vehicle and the drone, specifically including the following steps:

[0136] In the random initialization layer, the distribution center nodes and failure nodes are determined based on the information of the road network graph. Based on the random initialization of the distribution center nodes and failure nodes, the first initial vehicle path and the first initial drone path are generated. That is, first, from all the nodes of the road network graph G, the distribution center is selected by comprehensively considering the density of demand points and the distribution volume, and the nodes close to the dense demand point areas are given priority to reduce the distribution distance and time; at the same time, the failure nodes and road sections are randomly simulated, and the information of the distribution center and failure nodes is saved to the organizational information G of the graph; the operating parameters of the optimization algorithm are defined, such as the population size, the number of optimization iterations, etc., as well as the key parameters of the road network information, such as the load and speed of trucks and drones; finally, the delivery paths of trucks and drones are generated. The solution to the air-ground collaborative distribution problem is encoded as a sequence containing vehicle paths and drone task assignments. Each solution consists of the following two parts, each of which is saved in the form of a vector. The number of trucks T is randomly assigned to each distribution center in the random initialization layer. d ~U[1,T max ], using random walk strategy to generate the initial vehicle path R t ={v0,v rand1 ,…,v randk ,v0}, where v0 is the distribution center, v randi is a path node, and the path length is k. The UAV path can be regarded as the assignment of tasks along the way. The task target is selected as its nearest failure node. Where d(·) is the point v i The Euclidean distance between V and failed The set of failed nodes.

[0137] In the heuristic initialization layer, the saving value of each node pair needs to be calculated based on the preset truck path optimization method, and the node pairs are sorted in descending order based on the node value, so as to merge the paths until the capacity constraint is met to obtain the second initial vehicle path; wherein, the saving value s of each node pair is ij =d(v0,v i )+d(v0,v j )-d(v i ,v j ); d(·) is point v i The Euclidean distance from v.

[0138] In the heuristic initialization layer, for the pre-allocation of drone paths, it is necessary to select the task with the largest marginal benefit based on the greedy algorithm. Prioritize covering high-demand and close-to-failure nodes to obtain the second initial UAV path.

[0139] The first initial vehicle path and the second initial vehicle path are combined to obtain the initial vehicle path, and the first initial drone path and the second initial drone path are combined to obtain the initial drone path. Figure 5 As shown, the initial vehicle path and the initial UAV path are processed through a double-layer hybrid cross strategy to obtain the initial solution of the air-ground collaborative terminal delivery model as the initial air-ground collaborative terminal delivery path.

[0140] Furthermore, in one or more embodiments of this specification, in order to achieve air-ground collaborative delivery based on the heterogeneous characteristics of truck routes and drone missions, a two-layer hybrid crossover strategy is required to process the initial vehicle routes and the initial drone routes to obtain an initial solution to the air-ground collaborative terminal delivery model, which serves as the initial air-ground collaborative terminal delivery route. This specifically includes the following process:

[0141] First, a tournament strategy is used to select parent individuals from the population consisting of the initial vehicle paths and the initial drone paths. The formula for calculating the selection probability is:

[0142] Among them, 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 retain the continuous segments of the parent individuals of the initial vehicle path, and the new child solution of the initial vehicle path is obtained, that is, in the parent path P i Randomly select the starting point and end point a, b in P1 and P2, and combine the nodes in the interval [a, b] in P1 with the nodes outside the interval [a, b] in P2 to form a new solution for the offspring.

[0144] The initial UAV path is uniformly crossed to mix the parent individuals of the initial UAV path through the mask matrix, and the conflicting tasks are greedily selected to obtain the new child solution of the initial UAV path. The UAV task vector is binary-encoded, and the parent tasks are recorded as U1 and U2. According to the mask matrix M ij ~B(0.5) performs bitwise operations, and the calculation formula for the new solution of the drone generation is: Where B(·) is the Bernoulli equation. Finally, a greedy selection is performed on overlapping tasks to eliminate conflicts, prioritizing the low-energy solution. Then, based on the offspring solutions of the initial vehicle path and the initial drone path, an initial solution to the air-ground collaborative terminal delivery model is obtained, which serves as the initial air-ground collaborative terminal delivery path.

[0145] S104: Iteratively update the initial air-ground collaborative terminal delivery path based on the Pareto front to obtain an optimal solution as the optimal air-ground collaborative terminal delivery path for the current delivery area.

[0146] The Pareto front is a core concept in the field of multi-objective optimization, and its role is to provide a set of optimal trade-off solutions for multiple conflicting objectives. In multi-objective problems, due to the mutual constraints between the objectives, a single global optimal solution often does not exist, and the Pareto front provides decision makers with a diverse range of choices by defining all non-dominated solutions. Therefore, in the embodiments of this specification, in order to obtain the optimal solution while avoiding the problem of traditional methods falling into local optimal solutions, the initial air-ground collaborative terminal distribution path will be iteratively updated according to the Pareto front to obtain the optimal solution as the optimal air-ground collaborative terminal distribution path for the current distribution area. Specifically, in one or more embodiments of this specification, the initial air-ground collaborative terminal distribution path is iteratively updated based on the Pareto front to obtain the optimal solution as the optimal air-ground collaborative terminal distribution path for the current distribution area, which specifically includes the following steps:

[0147] First, the initial air-ground collaborative terminal delivery path is layered according to the dominance relationship, and the solution set is divided into multiple frontier levels based on the quick sorting method to achieve non-dominated sorting. Then, based on the target directions corresponding to the optimization objectives, the maximum value solution in that direction on the current Pareto front is defined as the extreme point. In order to solve the change in the target space scale, the extreme point tracking method is used to define the maximum value solution on each target defense line as Update periodic extreme points during evolution to reflect frontier expansion Among them, σ i (t) is the standard deviation of the Pareto current target i direction under t iterations, and δ is the relaxation coefficient. The target space is normalized according to the obtained extreme points to calculate the congestion entropy of each solution on the current Pareto frontier, and sorted according to the congestion entropy, filtering the low entropy solutions to obtain new solutions. In other words, the congestion entropy strategy is used to update the ecological niche of the Pareto frontier to ensure that the diversity of the population is sufficient for any solution x. i , whose crowding entropy is defined as in After calculating the crowding entropy of all solutions, they are sorted from high to low, and the low-entropy solutions at the end are excluded with a certain probability.

[0148] After each generation of evolution, the new solutions obtained after elimination are merged with the solutions on the current Pareto front (i.e., the old solutions), and non-dominated solutions are extracted to form the next generation of solutions. If the solution size exceeds the limit, Pareto pruning is performed. High-entropy solutions are retained according to the congestion entropy ranking method, while low-entropy solutions are randomly pruned, but at least one extreme solution is retained in each direction. The solutions on the Pareto front are then iteratively updated to obtain the optimal solution, which serves as the optimal air-ground coordinated terminal delivery route for the current delivery area.

[0149] like Figure 6 As shown, the embodiment of this specification provides a structural diagram of a dynamic planning device for air-ground collaborative terminal delivery. Figure 6 It can be seen that in one or more embodiments of this specification, a dynamic planning device for air-ground coordinated terminal 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, and the instructions are executed by the at least one processor to enable the at least one processor to: perform any of the above methods.

[0153] like Figure 7 As shown in FIG, the embodiment of this specification provides a structural diagram of non-volatile storage. Figure 7 It can be seen that in one or more embodiments of this specification, a non-volatile storage medium stores computer-executable instructions, characterized in that the computer-executable instructions can: execute any of the methods described above.

[0154] The various embodiments in this specification are described in a progressive manner. Similar portions between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from the other embodiments. In particular, the device, apparatus, and non-volatile computer storage medium embodiments are generally similar to the method embodiments, so their descriptions are relatively simplified. For relevant details, refer to the descriptions of the method embodiments.

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

[0156] The foregoing description is merely one or more embodiments of this specification and is not intended to limit this specification. It will be apparent to those skilled in the art that various modifications and variations may be made to one or more embodiments of this specification. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of one or more embodiments of this specification are intended to be within the scope of the claims of this specification.

Claims

1. A dynamic planning method for air-ground coordinated terminal delivery, characterized in that: The method comprises: Based on the 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, and based on the invalid units of the road network map, whether to trigger the delivery plan update of the current delivery area; If so, then construct an air-ground collaborative terminal delivery model for the current delivery area based on the information corresponding to the road network diagram; wherein the air-ground collaborative terminal 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 terminal 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 terminal delivery path of the vehicle and the UAV. The initial air-ground collaborative terminal delivery path is iteratively updated based on the Pareto front to obtain an optimal solution as the optimal air-ground collaborative terminal delivery path for the current delivery area.

2. The dynamic planning method for air-ground coordinated terminal delivery according to claim 1 is characterized in that: Based on the 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 invalid units of the road network map, it is determined whether to trigger the delivery plan update of the current delivery area. Specifically, it includes: Determine a node set in the current delivery area based on the actual road network information and delivery demand information of the current delivery area; wherein the node set includes: road intersections, customer demand points, delivery centers, and drone take-off and landing points; Determine the weight of each edge based on the travel cost and travel distance corresponding to the road section corresponding to each node; Based on the mapping between the node set and the weight of each edge, a road network graph corresponding to the current delivery area is obtained; wherein the road network graph is a grid-type road network topology graph; The vulnerability of the road section is calculated based on the failure units of the road network graph to trigger the update of the delivery plan for the current delivery area.

3. The dynamic planning method for air-ground coordinated terminal delivery according to claim 2 is characterized in that: Calculating the vulnerability of road sections based on the failure units of the road network graph to trigger the update of the delivery plan for the current delivery area, specifically including: Obtaining a vulnerability identification model corresponding to a failure unit of the road network graph; wherein the vulnerability identification model includes: a node failure vulnerability identification model and an edge failure vulnerability identification model; Obtaining a preset initial network efficiency, determining a current network efficiency by sequentially removing road sections corresponding to each failed unit, and determining a network efficiency change rate based on the preset initial network sales volume and the current network efficiency; Determining the relative size of the maximum connected subgraph after removing the road sections corresponding to the failed units based on the failed units, and determining the section importance of the road sections corresponding to the failed units based on the weights of the edges; Substituting the comprehensive measurement value index corresponding to the network efficiency change rate, the relative size of the largest connected subgraph and the importance of the road section into the vulnerability identification model to obtain the road section vulnerability, so as to trigger the update of the distribution plan of the current distribution area.

4. The dynamic planning method for air-ground coordinated terminal delivery according to claim 1 is characterized in that: Based on the information corresponding to the road network map, an air-ground collaborative terminal delivery model for the current delivery area is constructed, specifically including: Based on the information corresponding to the road network diagram, construct the optimization objectives and constraints of the air-ground collaborative terminal delivery model for the current delivery area; Among them, the demand coverage optimization objective in the optimization objective is to cover the customer demand points around the failed road node to the greatest extent, and the corresponding demand coverage objective function is: Among them, λ r is the vulnerability value of the road section, i represents the node, r represents the road section, C = {1, 2, 3, ... n} is the set of all customer demand points, L = {1, ..., n-1} is the set of drone paths, If customer node i∈C is located on road segment r∈R, then otherwise The demand of customer i∈C is served by vehicle k otherwise The demand of customer i∈C is served by the drone path l∈L otherwise The cost optimization goal is to minimize the transportation cost of vehicles and drones. The corresponding cost objective function is: Among them, θ k is the vehicle transportation cost per unit distance, θ u is the UAV transportation cost per unit distance, is the distance traveled by the vehicle through arc (i, j)∈E, is the flight distance of the drone’s path l∈L through the arc (i, j)∈E, E={(i, j),i,j∈V,i≠j} represents the set of all arcs, x ij The delivery path of vehicle k passes through (i, j)∈E, then x ij =1;y ijl For the drone delivery path l∈L passing through arc (i,j)∈E, then y ijl =1; The time optimization goal is to minimize the delivery time, and the corresponding time objective function is: Among them, v k is the speed of vehicle k, v u is the speed of the drone u.

5. The dynamic planning method for air-ground coordinated terminal delivery according to claim 4 is characterized in that: The constraints include: The first constraint condition used to express that each customer demand point can only be served once by a vehicle or drone; It is used to represent the customer points that all vehicles pass through, and the second constraint condition for delivery by vehicles; The third constraint condition is used to express that all customer points served by the drone will be passed by the drone path; The fourth constraint condition is used to indicate that the drone is only allowed to pass through each path arc once; The fifth constraint, used to constrain dynamic coordinated takeoff and landing points, requires that each drone launch and recovery point must be passed by a vehicle, and each drone delivery path must serve at least one customer point; The sixth constraint condition for constraining the load constraint is that when the drone path is completed and leaves any customer point i, the load does not exceed the maximum load; The seventh constraint condition is used to express that the power of the launch point of any path of the UAV meets the maximum endurance time; The eighth constraint condition is used to express that when the UAV returns to the meeting point along any path, the battery level must meet 10% of the maximum flight time; The ninth constraint condition is used to express the time constraints of the vehicle arriving at and leaving node i: is the time when the vehicle arrives at node i∈V1; f i k is the moment when the vehicle leaves the node i∈V1, M is a sufficiently large positive number; r i k is the time when the vehicle leaves node i; The tenth constraint condition is used to express the time constraints of the drone arriving at and leaving node i: The moment the vehicle arrives at node i∈V1, is the moment when the UAV path leaves the node i∈V1; The eleventh constraint condition is used to express that at the take-off point of the drone, the vehicle’s departure time must be later than the drone’s departure time; The twelfth constraint condition is used to express that the vehicle must meet the drone at the landing point 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 terminal delivery according to claim 1 is characterized in that: The air-ground collaborative terminal 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 terminal delivery paths for vehicles and drones. Specifically, the following steps are performed: In a random initialization layer, a distribution center node and a failure node are determined based on information of the road network graph, and a first initial vehicle path and a first initial drone path are generated based on random initialization of the distribution center node and the failure node; In the heuristic initialization layer, based on the preset truck path optimization method, the savings value of each node pair is calculated, and the node pairs are sorted in descending order based on the node value to merge the paths to obtain the second initial vehicle path; wherein, the savings value s of each node pair is ij =d(v0,v i )+d(v0,v j )-d(v i ,v j ); d(·) is point v i The Euclidean distance from v; Based on the greedy algorithm, the task with the largest marginal benefit is selected to obtain the second initial UAV path; Summarizing the first initial vehicle path and the second initial vehicle path to obtain an initial vehicle path, and summarizing the first initial UAV path and the second initial UAV path to obtain an initial UAV path; The initial vehicle path and the initial UAV path are processed through a double-layer hybrid cross strategy to obtain an initial solution to the air-ground collaborative terminal delivery model as the initial air-ground collaborative terminal delivery path.

7. The dynamic planning method for air-ground coordinated terminal delivery according to claim 1 is characterized in that: The initial vehicle path and the initial UAV path are processed by a double-layer hybrid cross strategy to obtain an initial solution to the air-ground collaborative terminal delivery model as the initial air-ground collaborative terminal delivery path, specifically including: A tournament strategy is adopted to select parent individuals from the population consisting of the initial vehicle paths and the initial UAV paths; Performing sequential crossover on the initial vehicle path to retain continuous segments of parent individuals of the initial vehicle path, and obtaining a new child solution of the initial vehicle path; Performing uniform crossover on the initial UAV path to mix the parent individuals of the initial UAV path through a mask matrix and performing greedy selection on conflicting tasks to obtain a new child solution of the initial UAV path; Based on the new sub-solutions of the initial vehicle path and the new sub-solutions of the initial UAV path, an initial solution of the air-ground collaborative terminal delivery model is obtained as the initial air-ground collaborative terminal delivery path.

8. The dynamic planning method for air-ground coordinated terminal delivery according to claim 1 is characterized in that: The initial air-ground collaborative terminal delivery path is iteratively updated based on the Pareto front to obtain an optimal solution as the optimal air-ground collaborative terminal delivery path for the current delivery area, specifically including: The initial air-ground collaborative terminal delivery path is layered according to the dominance relationship, so as to divide the solution set into multiple frontier levels based on the quick sorting method; Based on each target direction corresponding to the optimization objective, define the maximum value solution in the direction on the current Pareto front as the extreme point; Normalizing each target space based on the extreme point to calculate the congestion entropy of each solution on the current Pareto front, sorting them according to the congestion entropy, and filtering low entropy solutions to 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 terminal delivery path for the current delivery area.

9. A dynamic planning device for air-ground coordinated terminal delivery, characterized in that: The device comprises: 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, and the instructions are executed by the at least one processor to enable the at least one processor to: execute the method according to any one of claims 1 to 8.

10. A non-volatile storage medium storing computer-executable instructions, characterized in that: The computer executable instructions can execute the method according to any one of claims 1 to 8.

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