Vehicle-unmanned aerial vehicle combined distribution method based on mobile parking and self-pickup

Abstract

The invention relates to the technical field of unmanned delivery, in particular to a vehicle-unmanned aerial vehicle combined delivery method based on mobile parking and self-pickup. The method comprises the following steps: constructing a distribution mathematical planning model based on distribution combination of a mobile parking self-pick-up vehicle and an unmanned aerial vehicle, and carrying out optimization based on joint decisions such as parking point opening, customer distribution, truck parking time and path planning of the truck and the unmanned aerial vehicle according to the difference of individual customers; and designing an initial solution based on a greedy construction heuristic method, and representing the solution to obtain a vehicle-unmanned aerial vehicle path. According to the vehicle-unmanned aerial vehicle combined distribution method based on mobile parking and self-picking, a novel vehicle-unmanned aerial vehicle combined scene is provided, and the unmanned aerial vehicle is allowed to execute multiple travels on the basis of considering a home-to-delivery customer time window so as to improve the vehicle-unmanned aerial vehicle combined distribution efficiency; for vehicle moving, parking and self-pickup, a customer self-pickup behavior is associated with the vehicle parking duration, so that the customer self-pickup behavior is more suitable for a distribution scene of the last kilometer.

Description

Technical Field

[0001] The present invention relates to the field of unmanned delivery technology, and in particular to a vehicle-drone joint delivery method based on mobile docking and self-pickup. Background Art

[0002] In recent years, intensified competition in the logistics industry and rising labor costs have prompted logistics companies to continuously seek new technologies and models to gain a competitive advantage. Unmanned delivery technology, with its ability to provide more efficient delivery services, is revolutionizing last-mile delivery.

[0003] Currently, more and more companies are using drones for package delivery, including JD.com, UPS, SF Express, Amazon, and Google. Compared with traditional truck delivery, drones have many advantages, such as faster delivery speeds, lower pollutant emissions, no restrictions on road congestion, and no expensive labor costs. However, the performance of drone delivery systems has some inherent limitations, such as small carrying capacity and short flight time. Truck-drone combined delivery systems that integrate the advantages of trucks and drones are becoming increasingly popular in logistics and delivery. Figure 1 .

[0004] Since there are demands for both home delivery and self-pickup services in last-mile delivery, delivery vehicles allow customers to pick up their goods from designated vehicle stops during the delivery process. This allows delivery vehicles to provide both home delivery and self-pickup services, improving the flexibility and efficiency of last-mile delivery. This model is defined as vehicle mobile parking for customer self-pickup (VMPSP). In actual delivery, couriers will stop at customer gathering areas and wait for customers to pick up their goods. In this delivery model, delivery vehicles are dispatched to designated stops and stay there for one hour so that customers with self-pickup needs can conveniently pick up their goods.

[0005] To this end, a vehicle-UAV joint delivery method based on mobile docking and self-pickup is designed, which combines the truck-UAV delivery system with the vehicle mobile docking and self-pickup (VMPSP) mode, and proposes a vehicle-UAV joint delivery mode based on vehicle mobile docking and self-pickup, providing another technical solution to the above technical problems. Summary of the Invention

[0006] Based on this, it is necessary to provide a vehicle-UAV joint delivery method based on mobile docking and self-pickup to address the above technical problems, so as to solve the technical problems raised in the above background technology.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] The vehicle-drone joint delivery method based on mobile docking and self-pickup has the following steps:

[0009] Build a delivery mathematical programming model based on the combination of mobile docked pickup vehicles and drone delivery. This model optimizes joint decision-making based on dock opening, customer allocation, truck dwell time, and truck and drone routing, taking into account individual customer differences.

[0010] Design an initial solution based on a greedy construction heuristic method and obtain the vehicle-UAV path through the solution representation;

[0011] Design a two-stage local search to optimize customer assignment and vehicle dwell time scheduling.

[0012] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, a delivery mathematical programming model is constructed, and the steps are as follows:

[0013] Customer needs are divided into three categories: drone or vehicle service, drone and vehicle joint service, and pickup at the stop, and a delivery model with the goal of minimizing total cost is established.

[0014] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, the objective function expression is as follows:

[0015]

[0016] in, For trucks in arc Unit operating costs on For trucks in arc 1 when the upward movement occurs, otherwise 0; For trucks in arc Unit operating costs on For drones in arc 1 when the uptrend occurs, otherwise 0; u ij The self-pickup cost assigned to stop j by self-pickup customer i; g ij For customers By stop 1 when providing service, otherwise 0; N CP Collection for self-pickup customers; sd j For trucks at nodes Length of stop.

[0017] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, the solution representation is constructed by the path component R of the vehicle and drone and the natural number array component X, and the steps are as follows:

[0018] By R u and R l Two arrays form R, R u Whether the nodes in R are visited by vehicles or drones; l It reflects whether the node is served by a vehicle alone, a drone alone, a vehicle and drone cooperative service, or a drone performing the trip service. If R l If the i-th digit (i>1) of is 0, it means that the vehicle and the drone return to the distribution center;

[0019] X includes stops represented by {1, 2, .., d} and CP customers represented by {n+r+d+1, ..., n+r+d+m}. If the i-th stop in X is a stop and the next stop is the j-th stop in X, then the CP customer from the i+1-th stop in X to the j-1-th stop in X will be provided with self-pickup service.

[0020] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, the initial solution is constructed by greedy construction heuristics, and the steps are as follows:

[0021] For each CP customer i∈N CP Assign to the nearest stop p∈N P , and the set of stops assigned to customers is called the open stop set N P ';

[0022] Construct a vehicle-only route that serves all HD customers and open stops.

[0023] Improve the TSPTW path through the 2-opt method;

[0024] Assign some customers as drone nodes and some as vehicle nodes, and use the greedy partitioning heuristic method to construct the TSPTW path as a TSPTW-D path;

[0025] Sort the open stops from large to small according to the number of CP customers served, gradually increase the stop time of each stop to its upper limit in sequence, and ensure that the entire route does not violate the time window constraint.

[0026] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, a two-stage local search is designed to optimize customer allocation and vehicle dwell time arrangement, and the steps are as follows:

[0027] 1) Applying the variable neighborhood descent algorithm, four specific neighborhood moves are used to further optimize the paths of vehicles and drones;

[0028] 2). Introduce the assignment and scheduling problem as a new mixed integer programming model to optimize customer assignment and vehicle dwell time arrangement according to the path established in step 1).

[0029] As a preferred embodiment of the vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention, the allocation and scheduling problem model is constructed in the following steps:

[0030] Assumptions is the solution of VND, It is represented as a collection of open stops;

[0031] The allocation and scheduling problem model is only used to find the optimal solution of solution S {g ij ,sd i}, whose objective function aims to minimize the compensation cost and penalty cost.

[0032] It can be seen without a doubt that the above-mentioned technical solution of this application can definitely solve the technical problem to be solved by this application.

[0033] At the same time, through the above technical solutions, the present invention has at least the following beneficial effects:

[0034] 1. The vehicle-drone joint delivery method based on mobile docking and self-pickup provided by the present invention combines vehicle-drone joint delivery with vehicle mobile docking and self-pickup, providing an innovative delivery model for last-mile urban delivery. It also proposes a novel vehicle-drone joint scenario, allowing drones to perform multiple trips based on the home delivery time window to improve the efficiency of vehicle-drone joint delivery. For vehicle mobile docking and self-pickup, the customer's self-pickup behavior is associated with the vehicle's docking time, which is more suitable for last-mile delivery scenarios.

[0035] 2. This paper establishes TSPD-VMPCP as a mixed integer linear program and develops a meta-heuristic algorithm based on adaptive large neighborhood search. At the same time, a two-stage local search based on variable neighborhood descent and mathematical heuristic methods is proposed, which allows UAVs to perform loop delivery operations, that is, UAVs can take off and land from the same location.

[0036] 3. The present invention develops a new mixed integer programming (MIP) model to support Gurobi solution of small-scale examples, and designs a hybrid ALNS solution that integrates VND and mathematical heuristics.

[0037] 4. The ALNS algorithm designed in this invention has good solution quality and efficiency. The proposed mathematical heuristic algorithm component helps to improve the algorithm's solution efficiency.

[0038] 5. Compared with truck-drone delivery and truck-only delivery, the TSPD-VMPSP of the present invention effectively reduces operating costs and has important value in providing mobile docking and self-pickup services in the truck-drone combined delivery system.

[0039] 6. The flexible vehicle stop time of the present invention can reduce operating costs more than fixed time, and flexible stop time scheduling has better economic efficiency in the actual scheduling process.

[0040] 7. The present invention supports multi-trip delivery by drones, enhances the flexibility of drone routes, and helps reduce operating costs. Operating costs can be reduced by appropriately increasing the battery capacity of the drone and increasing the flight distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0042] Figure 1 This is a schematic diagram of the existing distribution operations;

[0043] Figure 2 Schematic diagram of the TSPD-VMPSP collaborative delivery path of the present invention;

[0044] Figure 3 This is a schematic diagram of the probability distribution of customer pickup probability of the present invention;

[0045] Figure 4 It is a schematic diagram representing the solution of the present invention;

[0046] Figure 5 Schematic diagram of four neighborhood structures of the present invention;

[0047] Figure 6 Schematic diagram comparing different delivery scenarios of the present invention;

[0048] Figure 7 A schematic diagram showing a cost comparison of the distribution model of the present invention;

[0049] Figure 8 This is a schematic diagram of the sensitivity analysis of the docking time of the present invention;

[0050] Figure 9 This is a schematic diagram of the UAV travel sensitivity analysis of the present invention;

[0051] Figure 10 This is a schematic diagram of the time window width sensitivity analysis of the present invention;

[0052] Figure 11 This is a schematic diagram of a sensitive analysis of the maximum flight distance of the UAV of the present invention;

[0053] Figure 12 This is a schematic diagram of the unit penalty cost sensitivity analysis of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0056] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features and technical solutions therein may be combined with each other.

[0057] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0058] Example 1

[0059] Reference Figure 2-Figure 5 ,Vehicle-UAV joint delivery method based on mobile docking and self-pickup.

[0060] 1. Problem description

[0061] The TSPD-VMPSP (Traveling Salesman Problem with Drone based on Vehicle Mobile Parking for Customer Self-pickup, TSPD-VMPCP) is a problem in which a truck and its accompanying drone simultaneously provide service to all customers, where customers are divided into those requiring home delivery within a specified time window and those who choose self-pickup service. Drone operations have two significant characteristics. First, drone launch and recovery operations can be performed at both docking points and the HD customer's location. Second, drones are allowed to perform multi-trip operations, in which drones are launched and recovered from the same location, adding new decision-making to drone delivery. Due to limited payload capacity, drones can only visit one customer per trip.

[0062] Furthermore, truck operations have a unique characteristic: trucks arrive at stops and wait at these locations for customers to pick up their parcels. The time it takes for customers to successfully pick up their parcels at a stop varies from customer to customer and exhibits certain statistical distribution characteristics, which we refer to as customer pickup behavior. The expected number of successful CP customers, or coverage, is influenced by the truck's dwell time. In this context, decision makers need to determine the location of open stops, the allocation of CP customers, the duration of truck dwell times, and the routing of trucks and drones.

[0063] The goal of TSPD-VMPSP is to minimize the total operating cost, which includes the truck routing cost, the drone routing cost, the compensation paid to the CP service, and the expected self-pickup failure penalty cost.

[0064] 1.1 Problem Definition

[0065] TSPD-VMPSP can be defined as a graph V, A, where V is a set of nodes and A is a set of arcs. V = {0,0'}∪N, where 0 and 0' represent the same warehouse location at the beginning and end of the trip, respectively, and N = N P ∪N HD ∪N CP , where N P Represents the set of stops, N HD represents the HD customer set, N CP Denotes the CP customer set. Next, we also use N0={0}∪N P ∪N HD To represent the set of nodes from which the drone can take off. In addition, N0′={0}∪N P ∪N HD ∪{0′} represents the set of nodes that the vehicle / drone can directly access. Formally, the arc set A is defined as A=A D ∪A S , where the path arc set AD Defined as {(i,j)|i,j∈N'0}, CP arc set A S Defined as {(i,j)|i∈N P ,j∈N HD}.

[0066] The vehicle carries a drone, and both the vehicle and the drone can perform door-to-door delivery services. Each arc (i, j)∈A has an associated non-negative distance d ij For each arc (i,j)∈A D , the vehicle travel time and cost are respectively expressed as and Similarly, the drone is on arc (i, j)∈A D The travel time and cost on and Assume that the travel time of vehicles and drones satisfies the triangle inequality. Each HD customer There is a time window (e i ,l i ), within this time window, door-to-door delivery service needs to be completed by vehicles or drones, and each customer only needs to be served once. Specifically, HD customers who can accept delivery by vehicle or drone, This refers to HD customers that can only be served by vehicles. This is because there are customers whose demand exceeds the drone's carrying capacity, and customers in areas where drones are prohibited from flying due to complex urban environments.

[0067] The present invention ignores the customer service time. The drone can take off and land from the vehicle at the docking point, HD customer location, and distribution center. Due to the limited capacity of the drone, a single delivery only serves one customer and then returns to the vehicle immediately. The vehicle can launch the drone at the same node and wait for it to return, which is called a trip. Each CP customer i∈N CP Assigned to a stop j∈N P , the cost is u ij After the vehicle arrives at the stop, CP customers will retrieve their packages on their own. ij Indicates the compensation received by customers for self-collection. The calculation formula is as follows:

[0068] u ij =v1·d ij +v2,(i,j)∈A S (1)

[0069] Among them, v1 represents the compensation per kilometer, d ij represents the walking distance from customer i to stop j, and v2 represents the basic compensation.

[0070] The vehicle's stop time at the stop is t j ,j∈N P During this period, CP customers should come to pick up their packages. However, the probability of a CP customer successfully picking up the package depends on the vehicle's residence time and the customer's pickup behavior. CP customers who fail to complete the pickup will incur a penalty cost. To simplify the problem, the vehicle's residence time at the stop is discretized into intervals, denoted as T R =1,2,...,ξ. Assume that the maximum stay time of a vehicle at each stop is T and each interval is τ = T / ξ. Therefore, the stop point j∈N is determined in advance. P The number of intervals sd j , where sd j ∈T R , and t j =sd j ·τ.

[0071] TSPD-VMPSP involves multiple coupled decision-making problems: docking point location selection, pickup customer assignment, docking duration scheduling, vehicle routing, and drone routing. The goal is to minimize the total delivery cost, including vehicle and drone driving costs, CP service compensation, and penalty costs for failed pickups.

[0072] Figure 2 A schematic diagram of a TSPD-VMPSP collaborative delivery route involving 20 customers is shown. HD customers 5, 6, and 12 are delivered by vehicle, while HD customers 7-11 and 13 are served by drone. CP customers 14-20 pick up their items at stops 1, 2, and 3.

[0073] 1.3 Customer Self-Pickup Behavior Model

[0074] Based on the influencing factors of customer self-pickup behavior in the vehicle mobile docking self-pickup mode, a self-pickup behavior model for this scenario is constructed.

[0075] When the truck arrives at the designated stop, the customer who chooses the CP service at that location will receive a notification, prompting them to pick up the package at the same time. In actual applications, customers may pick up the package with a known probability during the truck's stop, which is the customer pickup behavior. Specifically, customer i∈N CP Arrive at the stop point p∈N P Time t ip Due to uncertain response (preparation) time and determined walking time To estimate the uncertain response time, the truncated normal distribution is applied, i.e. This distribution can describe many natural and social phenomena according to the central limit theorem, which is calculated as follows:

[0076]

[0077] Formula (2) represents the time required for a self-service customer to reach the stop. Formula (3) represents the probability density function of the self-service customer response time. Formula (4) provides the formula for the normalization coefficient to ensure that the density function integrates to 1. Here, u i and σ i Represent the mean and standard deviation of the truncated normal distribution respectively; a and b are the upper and lower limits of the truncated density function; Φ is the standard 0-1 normal distribution. Figure 3 shown.

[0078] In addition, the probability density function associated with the truncated normal distribution is used to simulate the customer's pickup behavior. If the truck stays at stop j for a time sd j Exceeds the time t required for customer i to reach the stop ip , the customer is considered to have completed the self-delivery; otherwise, failure to complete the delivery will be subject to a unit penalty k. This penalty not only indicates the urgency but also reflects the priority of the package in the system. Therefore, in a multi-shift setting, the operator may increase the penalty k for undelivered packages after each shift. Therefore, at the stop point j∈N P The expected number of self-collection customers (coverage) can be calculated based on the discretized stay time sd j Sure:

[0079]

[0080] 2. TSPD-VMPSP mathematical model

[0081] In this embodiment, the symbols of the related sets, parameters and variables involved are shown in Table 1.

[0082] Table 1: Symbols used to describe and identify mathematical models

[0083]

[0084]

[0085] 2.1 Model establishment

[0086] Let Binary variable, if the vehicle crosses arc (i, j)∈A (regardless of whether the drone is on the vehicle or in the air), then Similarly, let is a binary variable. If the UAV crosses the arc (i, j)∈A (regardless of whether it is on the car or in the air), then make is a binary variable, if customer i∈N HDOnly served by vehicles (drones), then In addition, is a binary variable, if customer i∈N HD By the joint service of vehicles and drones, Let f i ∈{0,1} is a binary variable. If the stop point i∈N is selected P , then f i =1; let g ij ∈{0,1} is a binary variable. If customer i∈N CP Go to stop j∈N P Pick up the package, then g ij = 1. Let be a binary variable, if the drone performs the trip i→j→i in its rth trip to serve the customer When the vehicle is waiting at node i∈N0,i≠j, then (r∈R, R represents the maximum number of trips per node). Let at i is a continuous variable with a lower limit of 0, indicating the time when the vehicle or drone (or both) arrives at the node i∈N'0; let wt i is a continuous variable with a lower limit of 0, representing the waiting time of the vehicle or drone (or both) at the node i∈N'0. Finally, let sd j ∈T R is an integer variable, indicating the vehicle is at the stop point j∈N P The discrete stop duration.

[0087] The objective function formula (6) aims to minimize the total delivery cost, including the driving costs of trucks and drones, self-pickup compensation, and the penalty for expected self-pickup failure. The expression is as follows:

[0088]

[0089] Constraint formula (7) ensures that each CP customer is served (covered) by one stop, and is expressed as follows:

[0090]

[0091] Constraint formula (8) indicates that if a CP customer is assigned to a stop, the stop must be opened. The expression is as follows:

[0092]

[0093] Constraint formula (9) is the truck flow conservation constraint, which is expressed as follows:

[0094]

[0095] The constraint formula (10) sets the variable and and The variables are associated, and the expression is as follows:

[0096]

[0097] Constraint formula (11) ensures that the truck leaves and returns to the warehouse exactly once, and is expressed as follows:

[0098]

[0099] Constraint formulas (12)-(14) correspond to the UAV constraint formulas (9)-(11) as follows:

[0100]

[0101] Constraint formulas (15)-(16) specify the open stops and The expression for a set of customers to be served by a truck at least once is as follows:

[0102]

[0103] Constraint formula (17) stipulates The customers of the set can be visited by trucks alone, drones alone (via loops), or trucks and drones jointly as follows:

[0104]

[0105] Constraint formula (18) allows the drone to execute the loop i→j→i only when the truck and drone jointly serve customer i. The expression is as follows:

[0106]

[0107] Constraint formula (19) ensures that the drone is transferred from i to j only when the truck has visited at least one of customers i and j, thus ensuring that the drone serves at most one customer per trip. The expression is as follows:

[0108]

[0109] Constraint formulas (20)-(21) are used as sub-path elimination constraints, and the arrival time of trucks / drones at each node is set as follows:

[0110]

[0111] Constraint formulas (22)-(23) ensure that the time window expression is not violated as follows:

[0112]

[0113] Constraint formula (24) states that if the drone executes the loop, the truck must wait for the drone to complete its loop operation. The expression is as follows:

[0114]

[0115] The constraint (Formula 25) guarantees that the truck must wait at an open stop for the dwell time expressed as follows:

[0116]

[0117] Constraint formula (26) ensures that the UAV executes the loop expression at most once in the rth trip as follows:

[0118]

[0119] Constraint formula (27) indicates that the UAV performs multiple loop operations in a specific order; the loop operation expression for the UAV is as follows:

[0120]

[0121] Constraint formula (28) sets the lower limit of the earliest arrival time of the UAV as follows:

[0122]

[0123] Constraint formulas (29)-(35) determine the range expression of the decision variables as follows:

[0124]

[0125] 3. Solution algorithm design

[0126] The ALNS metaheuristic method has proven its effectiveness in solving many drone delivery problems. Based on the effectiveness of this algorithm in solving similar problems, this paper designs a hybrid ALNS metaheuristic method for solving TSPD-VMPSP.

[0127] This includes proposing a new solution encoding, decomposing TSPD-VMPSP into multiple subproblems, and introducing problem-specific destruction and repair operators. Furthermore, a two-phase local search (2P-LS) method, including variable neighborhood descent (VND) and mathematical heuristics, is proposed to enhance the algorithm's local optimization performance.

[0128] The ALNS algorithm accepts multiple destruction and repair operations as input. It starts with an initial solution and improves the current solution by randomly selecting a set of destruction and repair methods based on past performance.

[0129] The pseudo code of the designed ALNS framework is detailed in Algorithm 1. First, a greedy construction heuristic method is used to generate an initial solution (line 2). Then, the optimal solution S is iteratively improved by exploring the neighborhood of solution S in a loop. best , until the number of iterations that allow the optimal solution to continue without improvement is reached (lines 7-25). At each iteration, a subproblem is first selected and a destruction-repair operation is selected through a new selection mechanism. Then, a new solution S' is obtained by executing the selected destruction-repair operation (lines 8-11). With a certain probability P 2P-LS Use 2P-LS including variable neighborhood search and mathematical heuristics to improve the solution S' (lines 12-14). When S' is better than the global optimal solution S best S will be updated only when best (Lines 15-19). The new solution is accepted according to the simulated annealing algorithm (Lines 20-25). Finally, the algorithm updates the weights associated with the subproblems and the destroy-repair operations, as well as the temperature parameter (Lines 23-24).

[0130]

[0131] 3.1 Solution Characterization

[0132] The solution representation consists of two components R and X. R represents the path of the vehicle and the drone, and is a tuple consisting of two arrays: R u and R l . R u R is a list of natural numbers that represents the service order of the nodes. It includes 0 for the distribution center, {1,2,..,d} for the stop, {d+1,...,d+r} for the HD customers that are only served by vehicles, and {d+r+1,...,d+r+n} for the HD customers that can be served by vehicles or drones. l With R u have the same length, indicating R u Whether the nodes in R are visited by vehicles or drones. l It consists of integers, i.e., {0,1,2}. Given a non-negative integer value i∈{1,...,d+r+n}, R l This works as follows:

[0133] (i) If R l The value of the ith digit of is 0, then R u The node represented by the i-th number in will be served by the cooperation of vehicles and drones.

[0134] (ii) If R l The value of the ith digit of is 1, when R u When the (i-1)th digit (previous digit) in is 0, then R u The node represented by the i-th number in will be served by the drone alone.

[0135] (iii) If R l The value of the ith digit of is 1, when R u When the (i-1)th digit in is 1, then R u The node represented by the i-th number in will be served by the vehicle alone.

[0136] (iv) If R l The value of the ith digit of is 2, then R u The node represented by the ith number in the table will be updated by executing R from the previous node. l The first number in the itinerary is 0 and is served by drones alone.

[0137] In this way, R l It reflects whether the node is served by a vehicle alone, a drone alone, a vehicle and a drone in cooperation, or a drone performing the trip service. Obviously, if R l If the i-th digit (i>1) of is 0, it means that the vehicle and drone return to the distribution center.

[0138] X is an array of natural numbers, consisting of stops represented by {1, 2, ..., d} and CP customers represented by {n+r+d+1, ..., n+r+d+m}. In X, if the i-th stop in X is a stop and the next stop is the j-th stop in X, then the CP customer from the i+1-th stop in X to the j-1-th stop in X will be provided with a pickup service.

[0139] Figure 2 The solution to the vehicle-UAV path is coded as Figure 4 As shown. Since the stops can be selectively visited by vehicles, R u and R l The length is not fixed.

[0140] 3.2 Constructing the initial solution

[0141] The ALNS algorithm begins an iterative search from an initial solution. Preliminary experimental observations indicate that using a predefined initialization algorithm is superior to the commonly used random approach. This paper proposes a greedy construction heuristic method to generate an initial solution, which includes the following five steps:

[0142] Step 1: Clustering. Each CP customer i∈N CP Assign to the nearest stop p∈N P , and the set of stops assigned to customers is called the open stop set N P ′.

[0143] Step 2: Construct a vehicle-only route. Construct a vehicle-only route that serves all HD customers and open stops. This is a traveling salesman problem with a time window. Because the time window is a hard constraint, HD customers are sorted in increasing order of their time window end times. Open stops without time windows are inserted between customers with time window end times and before returning to the distribution center.

[0144] Step 3: 2-opt path optimization. The TSPTW path will be improved using the classic 2-opt method. This method systematically rearranges the order of adjacent nodes along the path to minimize the total travel distance while considering the time window constraint.

[0145] Step 4: Construct vehicle-drone paths. By assigning some customers as drone nodes and some as vehicle nodes, the TSPTW paths are constructed as TSPTW-D paths using a greedy partitioning heuristic.

[0146] Step 5: Maximum Stop Duration Scheduling. First, sort the available stops from largest to smallest based on the number of CP customers served. Then, gradually increase the stop duration of each stop to its upper limit, ensuring that the entire route does not violate the time window constraint.

[0147] 3.3 Subproblems and Destroy-Repair Operations

[0148] TSPD-VMPSP consists of three sub-problems: location selection, scheduling, and path planning. In each iteration of ALNS, it is crucial to select one of the sub-problems. After the sub-problems are determined, a destruction operation is randomly selected to remove β nodes from the solution, where β∈[0,Δ / 2]. For the location selection, scheduling, and path planning sub-problems, Δ is defined as |N CP |,|N P ′| and |N HD |. Then, a repair operation is randomly selected to repair the corrupted solution into a new solution, as follows:

[0149] (1) Site selection sub-problem

[0150] In the location subproblem, we attempt to improve the distribution network structure. In this subproblem, stops are closed and opened to search for a better solution. Note that X and R also change simultaneously. There are three types of destruction operations:

[0151] Random Stop Closure: Randomly select a stop from all open stops and close it. All CP customers currently assigned to this stop are removed and placed in the child node pool. In addition, this stop is removed from the vehicle-drone path.

[0152] Worst Open Stop Closure: This destruction operator is similar to the Random Stop Closure operator, but only considers the open stops that serve the fewest CP customers.

[0153] Random docking point opening: Among all closed docking points, one is randomly selected and opened. Then, β CP customers are randomly selected, removed from their assigned docking points, and inserted into the child node pool.

[0154] For the location selection subproblem, the repair operation is as follows:

[0155] Random CP customer assignment to docking point: Assign the CP customer in the child node pool to a random docking point and open it if it is not used yet. Then, in R l Add stops at random locations with a median value of 0.

[0156] Greedy CP Customer Assignment to Stops: This operator is similar to the previous random insertion, but selects the stop that can serve all CP customers in the child node pool at the lowest cost.

[0157] Randomly assign CP customers to open docking points: Each CP customer in the subnode pool is randomly assigned to an open docking point.

[0158] Assign the nearest CP customer to an open docking point: Assign each CP customer in the child node pool to the nearest open docking point.

[0159] Greedy CP customer assignment to open stop insertion: Assign each CP customer in the child node pool to the open stop with the lowest cost.

[0160] (2) Scheduling subproblem

[0161] In the scheduling subproblem, we attempt to improve the vehicle's docking time by reducing the penalty costs incurred by failed pickups. During this process, the dock is kept closed or open. There are three types of destruction operations:

[0162] Random stop duration removal: Among all open stops, β stops are randomly selected and placed into the child node pool.

[0163] Worst Stop Duration Remove: This operator is similar to the previous Remove operator, but only considers open stops that result in the highest penalty costs.

[0164] Greedy docking duration removal: This operator selects only the β open docking points that serve the most CP customers.

[0165] For the scheduling subproblem, there are two repair operations:

[0166] Random dwell duration fix: For stops in a child node pool, generate random dwell times without violating time window constraints.

[0167] Greedy stop duration fix: Maximize the dwell time of stops in the child node pool without violating the time window constraint.

[0168] (3) Path sub-problem

[0169] In the path planning subproblem, we try to improve the order in which vehicles and drones serve nodes to minimize the travel cost. There are five types of destruction operations:

[0170] Random removal: Randomly delete R u β nodes in , and put them into the child node pool.

[0171] Continuous removal: Randomly delete R u β nodes in , and put them into the child node pool.

[0172] Distance-related removal: Randomly delete R u , and delete the β-1 nodes that are closer to the selected node in Euclidean distance. Then, put all the nodes to be deleted into the child node pool.

[0173] Time-dependent removal: Randomly delete R u , and delete β-1 nodes with similar time windows. Then, put all the nodes to be deleted into the child node pool.

[0174] Worst Removal: Calculates the removal cost of each node, which is calculated as the difference between the target value before and after removal. This operator is used to remove β nodes with the highest removal cost and put them into the child node pool.

[0175] For the path planning sub-problem, there are three repair operations. Note that they are only used for nodes delivered by vehicles, where the state can only take the value 0:

[0176] Random insertion: Each node in the child node pool is randomly placed in R u In R l A state is randomly generated in .

[0177] Greedy insertion: For each node in the child node pool, calculate the difference between the target values ​​before and after insertion, and calculate each R uThe insertion cost of each state in . This operator inserts the node with the minimum insertion cost.

[0178] Regretful Insertion: This operator is similar to Greedy Insertion, but while calculating the insertion cost, it is multiplied by a random number in the range [1,2].

[0179] 3.4 Two-stage local search

[0180] The present invention proposes a two-stage local search (2P-LS) algorithm with a certain probability P 2P-LS Improve the current solution S'. In the first phase, the variable neighborhood descent (VND) algorithm is applied, using four specific neighborhood moves to further optimize the paths of vehicles and drones. Subsequently, in the second phase, the assignment and scheduling problem (ASP) is introduced as a new mixed integer programming (MIP) model, which optimizes customer assignments and vehicle dwell time schedules based on the paths established in the first phase. Algorithm 2 describes the 2P-LS framework.

[0181]

[0182] (1) Variable neighborhood descent search

[0183] The VND process is applied to perform the first phase of local search. In each iteration, the four neighborhood structures are called in sequence to generate neighborhood solutions, and then the best feasible solution is selected as the candidate solution.

[0184] The present invention designs the following four neighborhood structures: ① random exchange of nodes; ② random overall exchange; ③ random overall insertion; ④ random state change. The process of neighborhood movement is as follows: Figure 5 shown.

[0185] (2) Mathematical heuristics

[0186] After the VND process, a mathematical model called the assignment and scheduling problem (ASP) was established to reconstruct the optimal CP customer assignment and residence time (Schermer et al., 2019). Through the VND procedure, a solution representing the paths of vehicles and drones can be obtained. Assume is the solution of VND. is represented as a set of open stops. ASP is only used to find the optimal solution of solution S {g ij ,sd i}, whose objective function aims to minimize the compensation and penalty costs. ASP can be described as follows.

[0187] The objective function (36) aims to minimize the compensation paid to CP customers and the penalty cost for the degree of non-coverage, and is expressed as follows:

[0188]

[0189] Constraint (37) ensures that every CP customer is served (covered) by an open stop, as expressed below:

[0190]

[0191] Constraints (38)-(39) set the arrival time of the truck / drone at each node, which is expressed as follows:

[0192]

[0193] Constraints (40)-(41) ensure that the time window will not be violated, and the expressions are as follows:

[0194]

[0195] Constraint (42) states that if the drone performs a trip, the truck must wait for the drone to complete its trip operation, as expressed by:

[0196]

[0197] Constraint (43) ensures that the truck must wait for the dwell time at an open stop; for the drone trip, the expression is as follows:

[0198]

[0199] Constraint (44) sets the lower limit of the earliest arrival time of the UAV, which is expressed as follows:

[0200]

[0201] Constraints (45)-(47) are the range of decision variables, and the expressions are as follows:

[0202]

[0203] .3.5 Selection Mechanism

[0204] The subproblems and the destroy-repair operator pairs are selected based on their weights using a roulette wheel selection principle. This algorithm introduces a new weight update mechanism that is determined based on the quality and diversity of the new solutions obtained by applying the subproblems and the destroy-repair operator pairs. This approach ensures the effectiveness of the algorithm search while also preventing it from falling into local optimal solutions. Specifically, the improvement degree and diversity The selection weights for the subproblems and the destruction-repair operator pairs are calculated in the history iteration It. and The calculation of is as follows:

[0205]

[0206] It j is the number of destruction-repair operator pairs j selected; f(S it ) and f(S it ′) are the current solution S in iteration it it and S it ′The target value of the modified solution; D (i,j) (S it ,S it ′) If arc (i, j)∈A exists in both solutions S it and S it ’, it is equal to 1, otherwise it is 0.

[0207] Let w it,j The weight of the destruction-repair operator pair j in iteration it is updated as follows:

[0208]

[0209] Where η is the weight coefficient, and its value range is between [0,1]. it,j The probability of is calculated as follows:

[0210]

[0211] A similar selection mechanism also works for the selection of subproblems.

[0212] 3.6 Acceptance Mechanism

[0213] A simulated annealing mechanism is used to accept degenerate solutions to avoid falling into local optimal solutions. The probability of accepting a degenerate solution S′ (f(S′)>f(S)) is calculated as follows:

[0214] P=e -(f(S′)-f(S)) / T (52)

[0215] Where T is called the temperature and is set to T0 at the beginning of the algorithm. In each iteration, in order to keep the search convergent, T is reduced by multiplying it by the cooling factor e.

[0216] Example 2:

[0217] refer to Figure 6-Figure 12 Based on the above embodiment 1, a simulation test is disclosed.

[0218] In the present invention, a simulation experiment is carried out on a test case.

[0219] 1. Test Case

[0220] According to the TSPTW standard case description, all distribution areas cover approximately 25 square kilometers, and the distribution centers are nearby (N) or 7 kilometers away (F).

[0221] The TSPTW standard case provides sets of different numbers of customers, including 8, 10, 20, and 50 customers. From the 50-customer case, 60% and 80% of the customers are retained to construct sets of 30 and 40 customers, respectively. Next, these customers are divided into stops and HD customers, and some CP customers are additionally generated. Table 2 shows the number of customers for the specific test cases. CP customers are generated using two methods: random generation (R) and clustering (C). In the first type, the locations of CP customers are independently and uniformly distributed from 0 to 5 kilometers. In the second type, for each CP customer location, an angle is drawn uniformly from [0, 2π] and a distance is drawn from a distribution with a mean of 500 meters and a standard deviation of 50, corresponding to a random stop. Finally, only three time window densities are of interest: a time window with 0 (S), half the number of HD customers (M), and all HD customers (L).

[0222] These cases are labeled HIJKLMN, where H represents the number of stops, I represents the number of HD customers served only by vehicles, J represents the number of HD customers served by both vehicles and drones, K represents the number of CP customers, L represents the distance between the vehicle base and the delivery area (L∈{N,F}), M represents the time window density (M∈{S,M,L}), and N represents the CP customer location type (N∈{R,C}).

[0223] Table 2: Test case scale

[0224]

[0225]

[0226] Among them, HD T Indicates the number of customers who only accept truck delivery; HD T·D Indicates the number of customers who accept delivery by truck or drone.

[0227] Other parameters are set as follows: the vehicle speed is 24 km / h, the drone speed ratio is δ = 1.5, that is, the drone speed is 36 km / h. The truncated normal distribution of CP customers is set to u i =15, σ=20, a=0, b=30, minimum stop time granularity τ=10 minutes. The cost parameters are set as follows: c T=5CNY / km, c D =1CNY / km, v1=1CNY / km, v2=1CNY, k=5CNY.

[0228] 1.2 Parameter setting

[0229] In the experiments of the present invention, the ALNS algorithm parameters were determined through preliminary experiments, aiming to strike a balance between solution quality and computational time. The maximum number of consecutive non-improvement iterations was set to maxNonImprove = 500. The initial temperature T0 was determined so that the probability of accepting a solution that is 30% worse than the initial solution is equal to 0.5, and the cooling factor e = 0.95. The number of historical iterations It = 20, and the balance factor η = 0.7. Finally, the probability of using 2P-LS was set to P 2P-LS =0.2.

[0230] 1.3 Small-scale example results

[0231] In this paper, the performance of the ALNS metaheuristic method is evaluated by comparing it with the optimal solution of MIP. For performance evaluation, the MIP is solved to the optimal solution using the Gurobi solver in Python for a small-scale example, and then the results of ALNS are executed five times.

[0232] Table 3 shows the results of running the ALNS metaheuristic method on 24 examples of a small-scale scenario. The table reports the best objective function value (Best), runtime (t(s)), and the gap (Gap(%)) to the known optimal solution. The results show that Gurobi can only find 22 of the 24 optimal solutions in 382.9 seconds, and the runtime increases significantly with the number of customers. In contrast, ALNS is more robust, with an average execution time of only 11.6 seconds to obtain all optimal solutions. In summary, ALNS demonstrates effectiveness in providing high solution quality and efficient computation time.

[0233] Table 3: Comparison of computational results between Gurobi and ALNS on small-scale examples

[0234]

[0235]

[0236] 1.4 Large-scale example results

[0237] To verify the efficiency of 2P-LS, three versions of 2P-LS were considered: the first phase of local search alone (ALNS-FPLS), the second phase alone (ALNS-SPLS), and no 2P-LS (ALNS-NonLS). Tables 4 and 5 show the computational results obtained by different versions of ALNS on medium- and large-scale examples. In Tables 4 and 5, the Best, Avg., t(s), and Gap(%) columns respectively represent the best objective function value, average objective function value, average solution time (seconds), and the gap to the known optimal objective function value obtained across ten runs. Furthermore, in all case tests, the parameters of ALNS-FPLS, ALNS-SPLS, and ALNS-NonLS were consistent with those of ALNS.

[0238] Table 4: Comparison of running results of ALNS variants and ALNS on medium-scale examples

[0239]

[0240]

[0241] Table 5: Comparison of running results of ALNS variants and ALNS on large-scale examples

[0242]

[0243]

[0244] Tables 4 and 5 show the solution results of ALNS-FPLS, ALNS-SPLS, ALNS-NonLS, and ALNS on medium- and large-scale examples, respectively. The results show that ALNS outperforms ALNS-NonLS, demonstrating the effectiveness of 2P-LS. Furthermore, SPLS outperforms FPLS, as ALNS-SPLS finds the optimal solution in the majority of examples (35 of 48). Furthermore, compared to the average objective function value of ALNS-NonLS, ALNS-SPLS achieves an average improvement of 2.9%, while ALNS-FPLS achieves an average improvement of only 1.1%.

[0245] Figure 6 represents the average objective function value across all delivery scenarios. It can be observed that for the N vs. F scenario, the average target savings is 24.9%, for the S vs. M and L scenarios, the average target savings are 1.3% and 2.7%, respectively, and for the C vs. R scenario, the average target savings is 20.1%. In summary, different scenarios significantly impact last-mile delivery costs.

[0246] 1.5 Delivery Mode Sensitivity

[0247] In order to compare the effects of VMPSP and drone delivery, this paper proposes a vehicle-drone delivery network that only considers door-to-door delivery (TSPTWD) and a vehicle delivery network that only considers door-to-door delivery (TSPTW). Since in TSPTWD and TSPTW, it is assumed that the vehicle does not visit the stop, the probability of all CP customers picking up the goods is 0, that is, the penalty cost is k·|N CP In addition, considering the compensation for providing CP services as the minimum compensation cost value, it is

[0248] Compare the objective function values ​​of TSPTW, TSPTWD and TSPD-VMPSP in the 10-20-20-50 test scale example. Figure 7 The results show that VMPSP and drone delivery effectively reduce total costs across all scenarios. Specifically, compared to TSPTW, TSPD-VMPSP achieves an average objective function savings of 39.2%, while TSPTWD achieves an average objective function savings of 36.7%. Furthermore, TSPTWD alone achieves an average cost reduction of 4.0% over TSPTW. Notably, the impact of VMPSP is even more pronounced in scenarios with clustered CP customer characteristics. In summary, integrating VMPSP and drone delivery strategies is crucial for reducing delivery costs.

[0249] 1.6 Sensitivity Analysis of Flexible Stop Duration

[0250] This paper evaluates the impact of flexible stop duration (Flexible SD) on TSPD-VMPSP and compares it with fixed SD (Fixed SD) of 10, 20 and 30 respectively. The scale of all test cases is 10-20-20-50.

[0251] Figure 8 This indicates that flexible dwell times effectively reduce delivery costs in all cases. Compared to fixed dwell times of 10, 20, and 30, the average objective function savings are 4.8%, 22%, and 35.1%, respectively. This is because flexible dwell times provide a wider range of route and time combinations, avoiding inefficient vehicle idling and thus reducing total costs.

[0252] 1.7 Sensitivity Analysis of Drone Travel

[0253] This paper investigates the impact of allowing single-loop and multi-loop drone operations on the TSPD-VMPSP, comparing it to the TSPD-VMPSP when drone operations are prohibited. Using a 10-20-20-50 test case, the objective function savings are compared when multi-loop and single-loop operations are permitted, compared to when drone operations are prohibited.

[0254] Figure 9 The results show that across all tested case types, allowing both single-trip and multi-trip drone operations effectively reduces total delivery costs, with savings ranging from 0 to 8%. Furthermore, experimental results demonstrate that creating scenarios that favor multi-trip drone operations is feasible. Compared to prohibiting drone trips, allowing multi-trips results in an average objective function savings of 2.1%, while allowing single trips results in an average objective function savings of 1.7%. However, it is worth noting that multi-trip drone operations do not always occur, occurring in only seven cases. Specifically, although theoretically allowing multi-trip drone operations would have a larger feasible solution space, it does not always exist, and in most cases, at most four drone trips occur at the same node.

[0255] 1.8 Sensitivity analysis of time window width

[0256] This paper investigates the impact of the client time window width (|TW|) on TSPD-VMPSP. In previous examples, |TW| was set to 30 minutes, while this paper considers settings of {60, 120, 180} minutes. To analyze the impact of time window width, we selected examples with a time window density of L and covering a range of client numbers from 20 to 100. For each example size, the |TW| values ​​were compared to a baseline of |TW| = 30 minutes.

[0257] Figure 10 The results show that wider customer time windows help reduce total costs, with savings ranging from 0 to 10%. This is because HD customers with wider time windows allow for more flexibility in delivery routes. Consequently, the feasible domain of the problem is larger, reducing the total distance traveled by vehicles and drones, thereby lowering total costs.

[0258] 1.9 Sensitivity Analysis of UAV Flight Distance

[0259] If the UAV has a maximum flight distance L, the following constraints can be added to the MIP in Example 1:

[0260]

[0261] Constraint formulas (53)-(55) ensure that the UAV flight distance does not exceed the maximum flight distance L.

[0262] This paper explores the impact of the maximum flight distance of drones on TSPD-VMPSP. For different delivery scenarios with a test case scale of 10-20-20-50, the maximum flight distance of drones is set to 500-5000.

[0263] Figure 11It means that as the maximum drone flight distance increases, the total cost will continue to decrease. However, when the maximum drone flight distance increases to a certain range, such as 4500 or 5000, the increase in the maximum drone flight distance has almost no effect on the objective function value. On the one hand, this is because some customers' needs stipulate that they must be visited by vehicles, which limits the flexibility of drone delivery. Even if the maximum flight distance of the drone is increased, it cannot affect the objective function value. On the other hand, TSPD-VMPSP limits the drone to serving only one customer at a time, further limiting the application of drone delivery. In this case, as the maximum flight distance of the drone increases, using drone delivery is not necessarily beneficial to customer service. This may cause the drone to fly a longer distance and take longer, and may violate other constraints such as time windows, further increasing the complexity of path scheduling.

[0264] 1.10 Unit Penalty Cost Sensitivity Analysis

[0265] In this paper, we analyze the impact of unit penalty cost on TSPD-VMPSP. Taking the examples 10-20-20-50-FLR and 10-20-20-50-FLC as examples, we consider the changes in the objective function value and the average customer self-pickup failure probability when k varies from 1 to 9.

[0266] Figure 12 This indicates that as the unit penalty cost increases, the objective value increases, while the average customer pickup failure probability decreases. This is because increasing the unit penalty cost causes the vehicle to travel longer routes and have longer parking times. However, for sufficiently large unit penalty costs, such as 7 or 9, there is no effect on the objective function value or the average customer pickup failure probability. This may be because the distance between CP customers and the nearest stop is quite large, and even with the maximum vehicle parking time, there is still a possibility that customers will not be able to pick up their parcels.

[0267] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A vehicle-drone joint delivery method based on mobile docking and self-pickup, characterized by: Here are the steps: Build a delivery mathematical programming model based on the combination of mobile docked pickup vehicles and drone delivery. This model optimizes joint decision-making based on dock opening, customer allocation, truck dwell time, and truck and drone routing, taking into account individual customer differences. Design an initial solution based on a greedy construction heuristic method and obtain the vehicle-UAV path through the solution representation; Design a two-stage local search to optimize customer assignment and vehicle dwell time scheduling.

2. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 1 is characterized in that: To build a mathematical programming model for distribution, the steps are as follows: Customer needs are divided into three categories: drone or vehicle service, drone and vehicle joint service, and pickup at the stop, and a delivery model with the goal of minimizing total cost is established.

3. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 2 is characterized in that: The objective function expression is as follows: in, For trucks in arc Unit operating costs on For trucks in arc 1 when the upward movement occurs, otherwise 0; For trucks in arc Unit operating costs on For drones in arc 1 when the uptrend occurs, otherwise 0; u ij The self-pickup cost assigned to stop j by self-pickup customer i; g ij For customers By stop 1 when providing service, otherwise 0; N CP Collection for self-pickup customers; sd j For trucks at nodes Length of stop.

4. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 1 is characterized in that: The solution representation is constructed by the path component R of the vehicle and drone and the natural number array component X. The steps are as follows: By R u and R l Two arrays form R, R u Whether the nodes in R are visited by vehicles or drones; l It reflects whether the node is served by a vehicle alone, a drone alone, a vehicle and drone cooperative service, or a drone performing the trip service. If R l If the i-th digit (i>1) of is 0, it means that the vehicle and the drone return to the distribution center; X includes stops represented by {1, 2, .., d} and CP customers represented by {n+r+d+1, ..., n+r+d+m}. If the i-th stop in X is a stop and the next stop is the j-th stop in X, then the CP customer from the i+1-th stop in X to the j-1-th stop in X will be provided with self-pickup service.

5. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 1 is characterized in that: The initial solution is constructed by greedy construction heuristics, as follows: For each CP customer i∈N CP Assign to the nearest stop p∈N P , and the set of stops assigned to customers is called the open stop set N P '; Construct a vehicle-only route that serves all HD customers and open stops. Improve the TSPTW path through the 2-opt method; Assign some customers as drone nodes and some as vehicle nodes, and use the greedy partitioning heuristic method to construct the TSPTW path as a TSPTW-D path; Sort the open stops from large to small according to the number of CP customers served, gradually increase the stop time of each stop to its upper limit in sequence, and ensure that the entire route does not violate the time window constraint.

6. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 1 is characterized in that: Design a two-stage local search to optimize customer assignment and vehicle dwell time scheduling. The steps are as follows: 1) Applying the variable neighborhood descent algorithm, four specific neighborhood moves are used to further optimize the paths of vehicles and drones; 2). Introduce the assignment and scheduling problem as a new mixed integer programming model to optimize customer assignment and vehicle dwell time arrangement according to the path established in step 1).

7. The vehicle-drone joint delivery method based on mobile docking and self-pickup according to claim 6 is characterized in that: The allocation and scheduling problem model is constructed in the following steps: Assumptions is the solution of VND, Represented as a collection of open stops; The allocation and scheduling problem model is only used to find the optimal solution of solution S {g ij ,sd i }, whose objective function aims to minimize the compensation cost and penalty cost.

Images