Vehicle path optimization method in multi-access truck-unmanned aerial vehicle collaborative distribution mode

Abstract

This invention belongs to the field of vehicle routing optimization and discloses a vehicle routing optimization method in a multi-access truck-drone collaborative delivery mode. It uses minimizing environmental pollution and minimizing total delivery cost as dual objective functions, and constructs constraints based on a dynamic flight endurance model of the drone. For each non-dominated solution in the first Pareto front, iterative optimization is performed using a mutation operator until a local optimization termination condition is reached, outputting a new solution corresponding to each non-dominated solution. Solutions are selected from the population as parents, and crossover and mutation operators are sequentially executed on the parents to generate offspring. The population, new solutions, and offspring are merged, and the population is updated based on fast non-dominated sorting and congestion distance. If the global optimization termination condition is reached, the Pareto optimal solution is output as the optimal vehicle routing optimization scheme. This invention overcomes the limitations of traditional static models that assume overly idealistic assumptions and reduces the risk of task failure due to power depletion in actual delivery.

Description

Technical Field

[0001] This invention belongs to the field of vehicle routing optimization, specifically relating to a vehicle routing optimization method in a multi-access truck-drone collaborative delivery mode. Background Technology

[0002] With the rapid development of e-commerce and the continuous growth of market demand, logistics systems are facing increasing delivery pressure. However, in complex urban environments with severe traffic congestion, traditional ground vehicle (i.e., truck) delivery is inefficient and accompanied by significant environmental pollution problems. Against this backdrop, the logistics and transportation industry has become one of the major sources of global carbon emissions. In recent years, the issue of green vehicle route optimization has gradually attracted attention from the academic community. Its core objective is to optimize delivery routes to reduce energy consumption and environmental pollution while meeting customer service needs.

[0003] To promote sustainable logistics, the introduction of drones has become an important research direction for optimizing green vehicle routes. Various logistics companies have successively launched drone delivery pilot projects. Although drones have shown potential in reducing environmental pollution, their application in large-scale logistics scenarios is still limited by payload capacity and flight endurance. Therefore, some companies have begun to adopt a truck-drone collaborative delivery model, leveraging the complementary advantages of different transportation modes to compensate for the shortcomings of a single delivery model. At the same time, academia is gradually expanding its research focus to the route optimization problem within the truck-drone collaborative delivery model.

[0004] While truck-drone collaborative delivery has received widespread attention in research on green vehicle route optimization, it still faces several key challenges and limitations. In most studies, a single drone flight serves only one customer, a delivery model known as single-visit delivery. However, single-visit delivery forces drones to frequently return to the truck for pickup, resulting in significant redundant flights. This not only wastes energy and increases the burden on truck scheduling but also exacerbates environmental pollution. In recent years, with the maturation of single-visit drone operations serving multiple customers, multi-visit truck-drone collaborative delivery has become a new research hotspot. This model has been shown to significantly improve last-mile delivery efficiency. However, existing research on multi-visit truck-drone collaborative delivery generally focuses on operational performance indicators such as delivery time and cost, neglecting environmental considerations.

[0005] Furthermore, existing vehicle routing optimization models for multi-access truck-drone collaborative delivery often oversimplify drone energy consumption modeling, typically considering only flight time or flight distance. Flight time-based drone energy consumption models ignore the dynamic changes in payload in multi-access delivery models, while flight distance-based models neglect drone hovering energy consumption. In multi-access delivery, the weight of each package (which is not negligible relative to the drone's own weight) and the hovering time that may occur during truck-drone handover are two key variables for measuring drone energy consumption. Although some studies incorporate drone payload and flight time into drone energy consumption modeling, these studies usually use a constant energy consumption rate, ignoring the differences in energy consumption rates at different flight stages (such as takeoff, level flight, hovering, and landing). This static modeling method is prone to significant prediction bias. Summary of the Invention

[0006] The purpose of this invention is to provide a vehicle route optimization method in a multi-access truck-drone collaborative delivery mode. By explicitly considering the energy consumption rate, load changes, and cumulative flight time of key flight phases (such as takeoff, level flight, hovering, and landing), it overcomes the limitations of overly idealistic assumptions in traditional static models and reduces the risk of mission failure due to power depletion in actual delivery.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A vehicle routing optimization method in a multi-access truck-drone collaborative delivery model includes the following steps:

[0009] The dual objective functions are minimizing environmental pollution and minimizing total delivery cost, and constraints are constructed based on the dynamic flight endurance model of UAVs.

[0010] Initialize the population for the non-dominated sorting genetic algorithm;

[0011] Calculate the biobjective function value for each solution in the population, and perform fast non-dominated sorting and crowding distance calculation to determine the first Pareto front;

[0012] For each nondominated solution in the first Pareto front, iterative optimization is performed using the mutation operator until the local optimization termination condition is met, and the new solution corresponding to each nondominated solution is output.

[0013] Select a solution from the population as the parent generation, and perform the crossover and mutation operators on the parent generation in sequence to generate offspring generation;

[0014] Merge the population, new solutions, and offspring, and update the population based on fast non-dominated sorting and crowding distance;

[0015] If the global optimization termination condition is met, the Pareto optimal solution is output as the optimal vehicle routing optimization scheme; otherwise, the iteration continues.

[0016] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0017] As a preferred embodiment, the dynamic flight endurance model of the UAV is expressed by the following formula:

[0018]

[0019] In the formula, Indicates that the drone has left the node fly to node The amount of electricity consumed The vertical ascent height at the start of drone flight. The average speed during the drone's flight. For the physical power of the drone, This refers to the net weight of the drone. Drone arrival node Effective load capacity at that time This refers to the level flight time of the drone. For drones at nodes Hovering time, , and These are the drone's engine efficiency, transmission efficiency, and charging efficiency, respectively. For drones in the path Total flight time on The power consumed by the internal electronic systems of the drone.

[0020] Preferably, the constraints include:

[0021]

[0022]

[0023] The formula ensures that the drone has sufficient energy throughout its journey, among which For the drone to leave the node The remaining battery power of the drone at that time Indicates that the drone has left the node fly to node The amount of electricity consumed For the drone to leave the node The remaining battery power of the drone at that time As a preset positive number, If the drone is a binary variable, From node fly to node If the value is 1, then the value is 1; otherwise, the value is 0. A collection of trucks and drones with the same configuration. For a binary variable, if the customer If selected as a recycling node, the value is 1; otherwise, the value is 0. Given two variables, if the truck From node Driving towards the node If the value is 1, then the value is 1; otherwise, the value is 0. For the first node set, Includes warehouses and customer nodes Node 0 serves as the starting point for the truck. For the second set of nodes, Includes warehouses and customer nodes , where nodes As a return point for trucks.

[0024] Preferably, the solution is represented as follows:

[0025] The complete chromosome sequence contains the same number of combined paths as the number of trucks. Each combined path contains a drone path for a drone and a truck path for a truck. The numbers in the combined path represent customer nodes or warehouses, and the order of the numbers represents the access order.

[0026] The drone path contains one or more sequentially visited routes, where the first and last numbers of each route are the same as the numbers in the corresponding truck path, and the order of the first and last numbers of the route is the same as the order of the corresponding numbers in the truck path; the truck path contains one route, where the first and last points of each route are warehouses.

[0027] Preferably, the population used to initialize the non-dominated sorting genetic algorithm includes:

[0028] Phase 1: Starting from the warehouse, using the nearest neighbor search algorithm, iteratively select the geographically closest unvisited customer to add to the current path. Once the truck's load capacity is insufficient to add more customers, the vehicle returns to the warehouse, thus forming a closed composite path. By repeating the search process until all customers are visited, the multiple composite paths generated are finally linked together to form a complete chromosome sequence.

[0029] Phase Two: For each customer in each combined route, the feasibility of the drone delivery route is first evaluated based on drone payload capacity constraints and dynamic flight endurance constraints. If drone delivery is feasible, the potential cost savings of assigning the customer to the drone are calculated. If the calculated potential cost savings are non-negative, the corresponding drone route is retained. Through iteration, eligible customers are added to the drone route in turn until the drone's payload capacity or flight endurance limit is reached. Once the drone reaches its payload capacity or flight endurance limit, it returns to the truck to reload the package and replace the battery. After completing the package loading and battery replacement, the drone can be launched again to serve other customers.

[0030] Preferably, the calculation of potential cost savings after a customer is assigned to a drone includes:

[0031] Scenario 1: Consider a combined path containing a visit sequence (1, 2, 3) of three customers, where customers 1, 2, and 3 are served sequentially by trucks. If customer 2, originally served by trucks, is instead served by drones, and the drones have sufficient payload capacity and flight endurance, the cost savings from assigning customer 2 to the drones would be: ,in For trucks from the node arrive The cost of driving For drones from nodes arrive The operating costs;

[0032] Scenario 2: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 1 is served by a drone, and customers 2, 3, and 4 are served by trucks. If customer 3, originally served by a truck and located at the end of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, then the cost savings from assigning customer 3 to the drone would be: ;

[0033] Scenario 3: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 4 is served by a drone, and customers 1, 2, and 3 are served by trucks. If customer 2, originally served by a truck and located at the starting point of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, then the cost savings from assigning customer 2 to the drone would be: .

[0034] Preferably, the mutation operator is randomly selected from among the exchange mutation operator, the insertion mutation operator, and the inversion mutation operator.

[0035] This invention provides a vehicle route optimization method (MV-GVRP) for a multi-access truck-drone collaborative delivery model, aiming to simultaneously reduce environmental pollution and delivery costs. While drones generate almost no direct pollution during flight, the carbon dioxide emissions from the electricity production process—which powers the drones to power their flight—have an environmental impact. This invention combines the indirect carbon emissions from drones with the direct carbon emissions from truck operation, using the total system carbon emissions as a quantitative indicator to assess the environmental impact of the truck-drone collaborative delivery system. Compared with existing technologies, it has the following advantages:

[0036] (1) In view of the current situation that existing research on truck-drone collaborative delivery focuses on optimizing operational efficiency, this invention introduces the multi-access delivery mode into the green vehicle route optimization problem, thereby reducing carbon emissions and delivery costs by reducing redundant flights.

[0037] (2) A dynamic flight endurance model was constructed. In view of the limitations of traditional models that rely mainly on time or distance and thus oversimplify energy consumption estimation, MV-GVRP integrates load changes, cumulative flight time and different energy consumption rates in each flight stage, and more accurately depicts the energy consumption of UAVs in actual logistics scenarios.

[0038] (3) An extended non-dominated sorting genetic algorithm (ENSGA-II) was designed. The algorithm uses a hybrid heuristic initialization to generate initial solutions, utilizes sequential crossover operators and random multi-operator mutation mechanisms to accelerate algorithm convergence, and combines operator refinement strategies to enhance the diversity of non-dominated solutions in multi-access delivery scenarios. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the MV-GVRP model of the present invention;

[0040] Figure 2 This is a flowchart of the vehicle route optimization method in the multi-access truck-drone collaborative delivery mode of the present invention;

[0041] Figure 3 This is a flowchart of the ENSGA-II algorithm of the present invention;

[0042] Figure 4 This is an example diagram of the chromosome of the present invention;

[0043] Figure 5 The diagram shows three possible solutions for replacing trucks with drones according to the present invention.

[0044] Figure 6 This is a schematic diagram illustrating the execution of the OX operator of the present invention;

[0045] Figure 7This is a schematic diagram illustrating the execution of the mutation operator of the present invention;

[0046] Figure 8 This is a comparison chart of C-metric values ​​under different drone service rates in the experiments of this invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0049] Truck-drone collaborative delivery, as a novel delivery model, has demonstrated significant advantages in reducing logistics energy consumption and environmental pollution, becoming a research hotspot for green vehicle route optimization. However, existing studies mostly employ a single-visit delivery model, where drones need to return after completing a single customer service, making it difficult to fully utilize their payload capacity and endurance advantages. Simultaneously, the energy consumption from redundant flights during delivery exacerbates environmental pollution risks. Furthermore, existing flight endurance models typically only estimate drone energy consumption based on flight distance or flight time, failing to reflect the significant impact of dynamic payload changes and differences in delivery operation processes on energy consumption in complex logistics scenarios. Therefore, this invention proposes a novel multi-visit truck-drone collaborative delivery optimization model (MV-GVRP) for the green vehicle route optimization problem considering dynamic flight endurance. This model introduces a multi-visit delivery mode based on the traditional single-visit model to reduce redundant flights and lower delivery costs. Simultaneously, by comprehensively considering payload changes, flight duration, and energy consumption rate differences at different flight stages, it dynamically models the drone's flight endurance to better reflect actual logistics scenarios. To solve MV-GVRP, this invention proposes an extended non-dominated sorting genetic algorithm (ENSGA-II). This algorithm uses a hybrid heuristic initialization method to generate initial solutions and utilizes sequential crossover operators and random multi-operator mutation mechanisms to accelerate algorithm convergence. At the same time, it introduces a combination operator refinement strategy to enhance the diversity of non-dominated solutions.

[0050] Figure 1A schematic diagram of the MV-GVRP model is shown. Multiple identically configured trucks depart from a warehouse, each equipped with a drone capable of multi-access delivery, providing delivery services to customers whose needs and locations are known. The drones can return to the trucks to reload packages and replace batteries for subsequent customers.

[0051] MV-GVRP aims to plan optimal truck-drone collaborative delivery routes while minimizing total system carbon emissions and delivery costs. In this embodiment, the MV-GVRP model is set up as follows: given the characteristics of urban road networks, truck routes use Manhattan distance metrics, while drone flight paths between nodes use Euclidean distance metrics. Drones are fully charged at the start of each delivery mission. Drones can take off from a warehouse or any customer node, but must be recovered by the same truck that launched them, and the recovery location must be a node on that truck's route.

[0052] like Figure 2 As shown, the vehicle route optimization method in the multi-access truck-drone collaborative delivery mode of this embodiment includes the following steps:

[0053] Step 1: Using minimizing environmental pollution and minimizing total delivery cost as dual objective functions, and constructing constraints based on the UAV dynamic flight endurance model, a vehicle route optimization model is obtained.

[0054] Most existing studies assume that the energy consumption rate of drones is constant, but this assumption does not match the energy consumption situation in real-world drone delivery scenarios. Reference 1 ("Energy-Based Long-Range Path Planning for Soaring-Capable Unmanned Aerial Vehicles") proposes a physical power model (…). This was used to calculate the energy consumption of drones. Building on this, Reference 2 ("Comparison of energy demands of drone-based and ground-based parcel delivery services") further advanced refined energy consumption modeling by decomposing flight states. However, the method in Reference 2 has limitations: it only applies to single-visit delivery models, leading to a simplified payload model of a binary switch between "fully loaded departure and empty return," and it assumes a fixed hovering time.

[0055] To address the limitations of single-access energy consumption modeling in Reference 2, this invention proposes a dynamic flight endurance model for multi-access delivery scenarios. The proposed model improves and extends the energy consumption modeling method in Reference 2 by decomposing the UAV flight phases and combining dynamic load changes and uncertain hovering times, making it adaptable to multi-access delivery scenarios. The energy consumption of a certain flight segment during multi-access delivery can be calculated using formula (1). The first part of the formula is an improvement on the single-access flight energy consumption model proposed in Reference 2, used to calculate the energy consumption of the flight phases to accurately characterize the impact of dynamic load changes and uncertain hovering times on UAV energy consumption; the second part directly adopts the modeling method for the energy consumption of internal electronic devices in Reference 2.

[0056] (1)

[0057] in, Indicates that the drone has left the node fly to node The amount of electricity consumed (abbreviated as for ease of description) ), For the drone along the path Weight during flight. Unlike the study in Reference 2 (which assumes a fixed load in single-visit delivery), The dynamics of the drone's payload during multiple-visit delivery processes are depicted. This refers to the net weight of the drone. Drone arrival node Effective load capacity at that time; The speed is assumed to be 0 when hovering, and constant during other flight phases. , This represents the average speed of the drone during its flight. The angle of inclination during flight, and the angle of inclination at takeoff. During landing Level flight and hovering are Here, This refers to the level flight time of the drone. For drones at nodes The hovering time. Unlike the assumption in Reference 2 (fixed hovering time), this time varies depending on whether the drone is recovered at that node. And changes; if recycled, the potential time waiting for the truck to arrive must also be considered. For drones in the path The total flight time, assuming that at the start of each flight, the drone first ascends vertically to 150 meters (i.e., Then it transitions to level flight. The power consumed by the internal electronic systems of the drone. , and These are engine efficiency, transmission efficiency, and charging efficiency, respectively. Regarding the physical power of the drone... For detailed calculations, please refer to reference 1.

[0058] The MV-GVRP model in this embodiment includes two main optimization objectives: minimizing environmental pollution ( ) and minimizing total delivery cost ( As shown in formulas (2) and (3). To quantify environmental pollution, this embodiment calculates the total carbon emissions generated by the drone and truck system during the delivery process.

[0059] (2)

[0060] (3)

[0061] in, The amount of carbon dioxide emissions generated by power plants during the electricity production process to meet the electricity requirements of drones per unit flight distance; This refers to the amount of carbon dioxide emissions produced per unit distance traveled by a truck.

[0062] The constraints of the MV-GVRP model are defined as follows:

[0063] (4)

[0064] (5)

[0065] (6)

[0066] (7)

[0067] (8)

[0068] (9)

[0069] (10)

[0070] (11)

[0071] (12)

[0072] (13)

[0073] (14)

[0074] (15)

[0075] (16)

[0076] (17)

[0077] (18)

[0078] (19)

[0079] (20)

[0080] (twenty one)

[0081] (twenty two)

[0082] Formula (4) ensures that each customer is served only once by truck or drone. Formulas (5) and (6) ensure that each truck departs from and returns to the warehouse at most once. Formulas (7) and (8) ensure that the number of times drones and trucks enter and leave the warehouse at each node is consistent. Formulas (9) and (10) ensure that the number of times the drones and trucks enter and leave the warehouse at each node is consistent. drones or the first For each truck customer, access must be made by the corresponding drone or truck. Formulas (11) and (12) ensure the reasonableness of traffic flow when the customer node is used as a drone launch or recovery node, i.e., the drone must take off from the selected launch node and eventually drive into the selected recovery node. Formulas (13) and (14) ensure the feasibility of the drone's arrival time throughout the entire journey, i.e., the time when the drone arrives at the next node is no earlier than the time when it departs from the current node (or the service ends) and flies to that node. Formula (15) is the arrival time constraint for the truck's journey, i.e., the time when the truck arrives at the next node is no earlier than the time when it departs from the current node and drives to that node. Formula (16) is the departure time constraint for the truck's journey, i.e., the departure time of the truck must be later than its service end time or the time when the drone is recovered. Formula (17) ensures that the drone can complete the delivery and return to the warehouse within the maximum working time limit. Formula (18) describes the payload update mechanism of the drone throughout the entire journey, ensuring that the reduction of its effective payload after serving the customer is consistent with the delivery task. Formulas (19) and (20) ensure that the drone has sufficient energy throughout the journey. Formulas (21) and (22) ensure that the drone and truck load do not exceed the maximum load limit throughout the journey.

[0083] in, For the drone to leave the node The remaining battery power of the drone at that time Indicates that the drone has left the node fly to node The amount of electricity consumed For the drone to leave the node The remaining battery power of the drone at that time If the drone is a binary variable, From node fly to node If the value is 1, then the value is 1; otherwise, the value is 0. A collection of trucks and drones with the same configuration. For a binary variable, if the customer If selected as a recycling node, the value is 1; otherwise, the value is 0. Given two variables, if the truck From node Driving towards the node If the value is 1, then the value is 1; otherwise, the value is 0. For the first node set, Includes warehouses and customer nodes Node 0 serves as the starting point for the truck. For the second set of nodes, Includes warehouses and customer nodes , where nodes As a return point for trucks. For the set of arcs, ; For the first The demand of each user ; For trucks at the node and Manhattan distance between known nodes and nodes The positions are respectively and ,but ; For drones at nodes and Euclidean distance between, given nodes and nodes The positions are respectively and ,but ; This is the maximum load capacity of the truck; This represents the maximum payload capacity of the drone. This refers to the net weight of the drone; Cost per unit distance traveled by a truck; The cost per unit distance traveled by a drone; The service time of the drone at the node; The service time of the truck at the node; The time required for truck preparation and drone launch; The time required to recover the drone and replace its battery; This is the maximum working time for the truck; The average speed of the truck during its journey; It is a sufficiently large positive number; For a binary variable, if the customer by drone If the service is accessed and served, the value is 1; otherwise, it is 0. For a binary variable, if the customer by truck If the service is accessed and served, the value is 1; otherwise, it is 0. For a binary variable, if the customer If selected as the transmitting node, the value is 0; otherwise, it is 0. For a binary variable, if the customer If selected as a recycling node, the value is 1; otherwise, it is 0. For the drone to reach the node Effective load capacity at that time; For the drone to reach the node The time of the hour; For the truck to arrive at the node The time of the hour; For drones at nodes The time it was taken back ; For the drone to leave the node Time; For the truck to leave the node The time.

[0084] Step 2: Use a non-dominated sorting genetic algorithm to solve the vehicle routing optimization model and output the optimal vehicle routing optimization scheme.

[0085] The MV-GVRP model is an NP-hard problem. Due to its high computational complexity, exact algorithms face significant challenges when handling large-scale examples. To solve this multi-objective problem, this embodiment employs the NSGA-II framework. As a widely used algorithm, NSGA-II utilizes non-dominated sorting to classify solutions and maintains diversity through a crowding distance mechanism, thereby effectively approximating the Pareto front.

[0086] This embodiment extends NSGA-II in the following three aspects to solve the MV-GVRP model: 1) Designing a hybrid heuristic initialization method to generate high-quality initial solutions; 2) Employing sequential crossover (OX) operators and random multi-operator mutation mechanisms to accelerate algorithm convergence; 3) Applying a combination operator refinement strategy to enhance the diversity of non-dominated solutions in multi-access delivery scenarios. Figure 3 The framework of ENSGA-II was shown.

[0087] Step 2.1: Initialize the population for the non-dominated sorting genetic algorithm.

[0088] ENSGA-II is essentially a genetic algorithm. To enable it to effectively solve the MV-GVRP model, this embodiment constructs a novel chromosome encoding mechanism, mapping complex vehicle path solutions into an integer sequence representing the customer access order. This chromosome consists of a series of integers, where regular integers represent customers and the special marker 0 represents warehouses. Specifically, the solution is represented as follows: The complete chromosome sequence contains the same number of combined paths as the number of trucks. Each combined path contains a drone path and a truck path, where the numbers in the combined paths represent customer nodes or warehouses, and the order of the numbers indicates the access order. A drone path contains one or more sequentially accessed routes, where the first and last numbers of each route are the same as the numbers in the corresponding truck path, and the order of the first and last numbers is the same as the order of the corresponding numbers in the truck path. A truck path contains a single route, where the first and last points are warehouses.

[0089] Figure 4 A schematic chromosome containing 2 trucks and 14 customers was shown, which is related to... Figure 1 This corresponds to the MV-GVRP model in [the text].

[0090] A complete chromosome sequence, such as (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0), encodes the overall access sequence for all customers. In this sequence, 0 represents a warehouse, and warehouse nodes act as separators, dividing the sequence into multiple segments. Each segment represents a combined path that includes both truck and drone services. For example, (0, 1, 2, 3, 4, 5, 6, 7, 0) defines combined path 1, while (0, 8, 9, 10, 11, 12, 13, 14, 0) defines combined path 2.

[0091] After determining the combined routes, this embodiment applies a cost-saving strategy to construct the drone delivery sequence, thereby generating drone routes and truck routes. For example, (0, 1, 3, 4), (5, 6, 7), and (8, 10, 11, 12, 14) define drone routes, which are three drone routes, while (0, 2, 4, 5, 7, 0) and (0, 8, 9, 13, 14, 0) define truck routes, which are two truck routes.

[0092] To generate a high-quality initial solution, this embodiment designs a hybrid heuristic initialization method that integrates the nearest neighbor search algorithm and a cost-saving strategy. The method consists of two stages: the first stage constructs a combined path based on the nearest neighbor search algorithm; the second stage, based on the combined path generated in the first stage, further determines the specific driving paths of the drone and the truck based on the cost-saving strategy.

[0093] Phase 1: Constructing combined paths based on the nearest neighbor search algorithm.

[0094] To ensure the algorithm generates a high-quality initial solution, a reasonable combined path must first be constructed. This is because the final truck-drone collaborative solution is further generated based on this combined path, which forms the foundation for constructing the initial solution. If the base combined path is randomly generated, the routes are often chaotic and involve significant detours, resulting in the inability to generate a high-quality initial solution. Therefore, this embodiment employs nearest neighbor search to construct a compact and ordered combined path, ensuring the quality of the initial solution from the outset.

[0095] Starting from warehouse (0), the algorithm iteratively selects the geographically closest unvisited customers to join the current path using the nearest neighbor search algorithm. Once the truck's load capacity is insufficient to add more customers, the vehicle returns to the warehouse, thus forming a closed composite path segment. By repeating this process until all customers are visited, the generated multiple path segments are eventually concatenated to form a complete chromosome sequence. This algorithm can quickly construct feasible solutions covering all customers, providing high-quality initial solutions for subsequent algorithm evolution.

[0096] Phase 2: Determining drone and truck routes based on cost-saving strategies.

[0097] To construct a high-quality collaborative initial solution based on combined paths, this embodiment designs a cost-saving strategy to determine delivery routes for drones and trucks. The core idea of ​​this strategy originates from the core principle of the Clarke-Wright cost-saving algorithm, which optimizes system operating costs by identifying redistribution schemes with cost-saving potential. Unlike traditional cost-saving algorithms that achieve cost savings by merging vehicle routes, this embodiment, given a combined path, evaluates the cost savings of shifting some customers from truck delivery to services provided by drones launched and retrieved from truck nodes, thereby achieving collaborative delivery between trucks and drones.

[0098] In the proposed cost-saving strategy, each customer on the combined route is repeatedly examined and their suitability for drone delivery is evaluated. For each customer, the feasibility of the drone delivery route is first assessed based on drone payload capacity constraints and dynamic flight endurance constraints. If drone delivery is feasible, the potential cost savings of assigning that customer to a drone are calculated. Figure 5 As shown, this embodiment evaluates three drone alternative scenarios.

[0099] Scenario 1: Consider a combined path containing a visit sequence (1, 2, 3) of three customers, where customers 1, 2, and 3 are served sequentially by trucks. If the intermediate customer (customer 2), originally served by trucks, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, the cost savings from assigning customer 2 to the drone would be: ,in For trucks from the node arrive The cost of driving For drones from nodes arrive The operating costs.

[0100] Scenario 2: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 1 is served by a drone, and customers 2, 3, and 4 are served by trucks. If customer 3, originally served by a truck and located at the end of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, the cost savings from assigning customer 3 to the drone would be: .

[0101] Scenario 3: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 4 is served by a drone, and customers 1, 2, and 3 are served by trucks. If customer 2, originally served by a truck and located at the starting point of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, the cost savings from assigning customer 2 to the drone would be: .

[0102] If the calculated cost savings are non-negative, the corresponding drone path is retained. Eligible customers are added to the drone path sequentially until the drone's payload capacity or flight endurance limit is reached. Once the drone reaches its payload capacity or flight endurance limit, it returns to the truck to reload packages and replace the battery. After package loading and battery replacement, the drone can launch again to serve other customers.

[0103] Step 2.2: Calculate the biobjective function value for each solution in the population, and perform fast non-dominated sorting and crowding distance calculation to determine the first Pareto front. The fast non-dominated sorting and crowding distance calculation are the same as in the conventional NSGA-II algorithm, and will not be described in detail in this embodiment.

[0104] Step 2.3: For each non-dominated solution in the first Pareto front, perform iterative optimization using the mutation operator until the local optimization termination condition is met, and output the new solution corresponding to each non-dominated solution.

[0105] To improve solution quality and accelerate algorithm convergence, this embodiment selects the first Pareto front in the current population as the refining target. The first Pareto front consists of all non-dominated solutions in the current population that are not dominated by other solutions, representing a set of candidate solutions with optimal trade-offs under multi-objective considerations. This embodiment applies a combined operator refining strategy, incorporating exchange, insertion, and inversion mutation operators, to the first Pareto front to explore the diverse neighborhoods of elite solutions.

[0106] For each non-dominated solution in the first Pareto front, a combinatorial refinement strategy is applied iteratively (each iteration randomly selects one from the exchange, insertion, and inversion mutation operators) until no further improvement is found (e.g., no better solution appears after multiple iterations) or a predefined iteration limit is reached. Newly generated solutions are accepted only if they improve at least one objective without degrading the performance of others. Through this acceptance criterion, solutions in the first Pareto front are progressively updated and strengthened, thereby continuously improving the overall quality of the solutions and accelerating the convergence speed of the algorithm while maintaining the non-dominance of the solution set. All newly obtained solutions are combined to form a solution set G.

[0107] Step 2.4: Select a solution from the population as the parent generation, and perform the crossover and mutation operators on the parent generation in sequence to generate offspring.

[0108] To systematically improve the diversity of non-dominated solutions and suppress premature convergence, ENSGA-II adopts a hybrid genetic strategy that combines sequential crossover (OX) operators with random multi-operator mutation strategies.

[0109] During the crossover or mutation phase, the algorithm performs genetic operations on the complete chromosome sequence by ignoring the warehouse: during the operation, the warehouse node (0) is temporarily ignored, and crossover and mutation are performed only on the customer sequence. After the genetic operation is completed, the warehouse node is reinserted into the offspring sequence according to the truck load capacity constraint to ensure the feasibility of the delivery route. This method simplifies the genetic operation while ensuring the feasibility of the solution.

[0110] In the crossover phase, the sequential crossover (OX) operator is used. This operator first selects a continuous subsequence from parent generation 1 and copies it to the corresponding position in the offspring. Then, the remaining chromosome sequence from parent generation 2, after removing this subsequence, is filled into the empty positions in the offspring according to its original relative order, thus generating a new individual. This method effectively preserves the beneficial local order structure in the parent solution, thereby accelerating the search for high-quality paths. A schematic diagram of the OX operator is shown below. Figure 6 As shown.

[0111] During the mutation phase, this embodiment employs a random mutation strategy, which combines random selection among exchange, insertion, and inversion mutation operators. This strategy effectively prevents premature convergence of the algorithm and maintains controllable genetic diversity. The mutation operation is as follows: Figure 7 As shown, the exchange mutation operator randomly selects two chromosomes from the parent generation and swaps their positions; the insertion mutation operator randomly selects one chromosome from the parent generation and inserts it into a randomly selected new position; the inversion mutation operator randomly selects two pairs of chromosomes from the parent generation and swaps the positions of each pair. The exchange, insertion, and inversion mutation operators in step 2.3 are performed similarly.

[0112] The selection of parents is based on rapid non-dominated sorting and crowding distance calculations, prioritizing the best individuals to breed the next generation. This selection is dynamic and determined through a tournament process, with no fixed selection ratio. For each parent, crossover and mutation are performed, with a crossover rate of 0.8 and a mutation rate of 0.05.

[0113] Step 2.5: Merge the population, new solutions, and offspring, and update the population based on fast non-dominated sorting and crowding distance.

[0114] Step 2.6: If the global optimization termination condition is met (e.g., the maximum number of iterations is reached), output the Pareto optimal solution as the optimal vehicle path optimization scheme; otherwise, continue iterating.

[0115] In one embodiment, parameter sensitivity analysis was performed on the ENSGA-II algorithm, and its performance in solving the MV-GVRP model was evaluated by comparison with other benchmark multi-objective algorithms. All experiments were performed using Python on a personal computer running a 64-bit operating system, equipped with an AMD Ryzen 5 5600U processor (integrated Radeon Graphics) with a clock speed of 2.301 GHz, and 16.0 GB of memory.

[0116] (1) Experimental design:

[0117] Given the relatively recent research on the MV-GVRP model and the lack of directly usable standardized benchmark examples, this experiment randomly generated a set of benchmark examples to simulate real-world delivery scenarios. In designing this set of examples, three core dimensions were comprehensively considered: customer size, delivery range, and drone service capability. Specific parameters were set as follows: the number of customers was set to 40, 80, 120, and 160; the delivery area was set to squares with sides of 40km, 60km, and 80km; and the drone service rate was set to 30%, 50%, and 70% to simulate the real-world constraint that drones cannot cover all customers. All benchmark examples were named according to combinations of these three parameters. For example, "40-40-30" represents a example containing 40 customers within a 40km × 40km square area with a drone service rate of 30%.

[0118] Based on the above design, a total of 36 different benchmark examples were generated, covering various parameter combinations. In the experiments, ENSGA-II was compared with classic multi-objective optimization algorithms, including NSGA-II (a non-dominated sorting genetic algorithm with an elitist strategy), SPEA2 (an improved strength Pareto evolutionary algorithm), and MOEA / D (a decomposition-based multi-objective evolutionary algorithm). To enhance statistical robustness, each algorithm was run independently 20 times on each example, and the average performance metric was used for statistical evaluation. The parameters used in the MV-GVRP model are shown in Table 1.

[0119] Table 1. Parameters used in the MV-GVRP model

[0120]

[0121] (2) Performance indicators:

[0122] This experiment evaluated the effectiveness of ENSGA-II using numerical experiments. The following four performance metrics were used for evaluation: hypervolume (HV), R², coverage (C-metric), and CPU time.

[0123] Hypervolume (HV) is a comprehensive metric used to simultaneously evaluate the convergence and diversity of a solution set. Its calculation principle is to quantify the volume (or hypervolume) of the target spatial region enclosed between the solution set and a preset reference point (1.05, 1.05). A larger HV value means a wider spatial coverage of the solution set and a better overall solution quality.

[0124] The R² metric (R²) uses a uniformly distributed set of weight vectors (representing different preference directions) to evaluate the convergence of an approximate Pareto front to an ideal front. Specifically, the R² value is the average of the minimum Tchebyshev utility values ​​of the solution set across each weight vector. A lower R² value indicates that the solution set approximates the ideal front, and the algorithm exhibits better convergence.

[0125] Coverage (C-metric), as a pairwise comparison metric, measures the dominance of one solution set over another. The value of C(A, B) represents the degree to which solution set B is covered (dominated) by solution set A. A larger coverage value means that A has a significant advantage over B in terms of convergence and distribution.

[0126] CPU time (in seconds) refers to the actual running time required for an algorithm from initialization to meeting the termination condition, directly reflecting the algorithm's computational efficiency and time complexity. To ensure fairness in the comparison, all experiments were performed in a completely consistent computing environment.

[0127] (3) Parameter sensitivity analysis:

[0128] Given the significant impact of key parameters on ENSGA-II performance, this experiment conducted a parameter sensitivity analysis. To ensure both representativeness and computational efficiency, this experiment selected a typical example (120-60-50%) with moderate scale and complexity as the test benchmark.

[0129] The experiment primarily examined two variables: crossover rate and mutation rate. Referring to standard settings for evolutionary algorithms and recommended values ​​from relevant literature, this experiment set the crossover rate to 0.6, 0.7, and 0.8, and the mutation rate to 0.01, 0.05, and 0.10, generating nine combinations through a full factorial design. Each configuration was run independently 20 times (maximum 200 iterations). The analysis results are detailed in Table 2, with data presented in the format "HV / computation time (seconds)".

[0130] Table 2. Results of parameter sensitivity analysis

[0131]

[0132] Experimental results show that the combination of a mutation rate of 0.05 and a crossover rate of 0.8 achieved the highest HV value (0.99), indicating the best solution quality. Although this combination did not have the shortest time (101.63 seconds), its HV value was significantly higher than other combinations. Based on this, subsequent experiments set the mutation probability to 0.05 and the crossover probability to 0.8.

[0133] (4) Performance analysis:

[0134] To evaluate the overall performance of ENSGA-II on MV-GVRP, this experiment used 36 simulated datasets for comparative testing, comparing it with three classic multi-objective optimization algorithms. All algorithms were run independently 20 times under uniform conditions, and performance metrics were obtained by averaging the results of each run. The average performance metrics of each algorithm are shown in Tables 3 (inclusive) to 5 (inclusive). Figure 8 As shown, “E”, “N”, “S” and “M” represent ENSGA-II, NSGA-II, SPEA2 and MOEA / D respectively, and the optimal value is indicated in bold; “↓”: the lower the index, the better the algorithm; “↑”: the higher the index, the better the algorithm.

[0135] Tables 3 (inclusive) to 5 (inclusive) show that in most examples, ENSGA-II outperforms NSGA-II, SPEA2, and MOEA / D in terms of HV, indicating that ENSGA-II has advantages in both solution set diversity preservation and convergence performance. ENSGA-II's consistently low R² value confirms its good convergence performance, demonstrating its ability to more accurately balance the relationships between optimal objectives. Although ENSGA-II does not achieve the shortest computation time, its average CPU time remains within an acceptable range, achieving a balance between computational efficiency and solution quality. The results also show that the advantages of ENSGA-II become increasingly significant as the scale of the examples increases.

[0136] Table 3. Average performance indicators at a 30% drone service rate

[0137]

[0138] Continued from Table 3

[0139]

[0140] Table 4. Average performance indicators at 50% drone service rate

[0141]

[0142] Continued from Table 4

[0143]

[0144] Table 5. Average performance indicators at 80% drone service rate

[0145]

[0146] Continued from Table 5

[0147]

[0148] To evaluate the dominance and robustness of ENSGA-II, this experiment plotted C-metric box plots under different drone service rates. Figure 8 By comparing the cross-coverage distribution of ENSGA-II with three other classic multi-objective optimization algorithms (NSGA-II, SPEA2, and MOEA / D), it can be found that the median C-metric of ENSGA-II consistently remains at a high level. This means that the solutions found by ENSGA-II not only have higher solution set quality but also maintain good performance stability under different service rates.

[0149] (5) Statistical significance test:

[0150] To determine whether the observed advantage of ENSGA-II in solving MV-GVRP compared to other classical multi-objective optimization algorithms stems from chance, this experiment employed the Wilcoxon signed-rank test for statistical significance. Given that HV can comprehensively quantify the convergence and diversity of the solution set (the core objective of the algorithm proposed in this invention), this index was chosen for verification. This experiment performed paired one-sided tests on the HV values ​​of ENSGA-II and each comparative algorithm in 36 sets of examples (alternative hypothesis: ENSGA-II is superior to the comparative algorithms). Due to the involvement of multiple algorithm comparisons, Bonferroni correction was used to control the overall significance level (α = 0.0167). Statistical results show that ENSGA-II achieved significantly better HV values ​​in all comparisons (p-value < 0.001), and the corresponding effect size was relatively large (see Table 6, where the optimal value is indicated in bold; "↓": lower index, better algorithm; "↑": higher index, better algorithm). However, in terms of overall results, ENSGA-II showed superior HV levels in most cases, and its advantage was not only statistically significant, but also had clear practical significance in terms of effect size.

[0151] Table 6. Wilcoxon test results (p-values) for HV value comparison.

[0152]

[0153] To address the issue of green vehicle routing, this invention proposes a multi-access truck-drone collaborative delivery method that considers dynamic endurance. This method overcomes the limitations of the traditional single-access mode, allowing drones to serve multiple customers in a single flight. Furthermore, it comprehensively considers load variations, cumulative flight time, and energy consumption differences at various flight stages (such as hovering and takeoff / landing) in energy consumption estimation, thereby significantly improving the feasibility and accuracy of route planning in real-world logistics scenarios.

[0154] To solve this NP-hard problem, this invention proposes an extended non-dominated sorting genetic algorithm (ENSGA-II), which integrates a hybrid heuristic initialization and combinatorial operator refinement strategy. Experimental results based on 36 benchmark examples show that ENSGA-II outperforms classic algorithms such as NSGA-II, SPEA2, and MOEA / D in both HV and R² metrics, demonstrating that it can obtain Pareto solution sets with better convergence and more diverse distributions. Wilcoxon signed-rank test and effect size analysis further confirm that the performance advantage of ENSGA-II is statistically significant. Furthermore, C-metric analysis shows that ENSGA-II exhibits strong robustness and dominance under different UAV service rate configurations.

[0155] In another embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a vehicle routing optimization method in a multi-access truck-drone collaborative delivery mode.

[0156] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0157] In another embodiment, the present invention provides a computer device including a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of a vehicle routing optimization method in a multi-access truck-drone collaborative delivery mode.

[0158] The memory and processor are electrically connected directly or indirectly to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more communication buses or signal lines. The memory stores a computer program that can run on the processor, which implements the method of the present invention by running the computer program stored in the memory.

[0159] The memory may be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The memory stores the program, and the processor executes the program upon receiving an execution instruction.

[0160] The processor may be an integrated circuit chip with data processing capabilities. The aforementioned processor can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor.

[0161] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0162] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for vehicle path optimization in a multi-access truck-drone collaborative delivery mode, characterized in that, Includes the following steps: The dual objective functions are minimizing environmental pollution and minimizing total delivery cost, and constraints are constructed based on the dynamic flight endurance model of UAVs. Initialize the population for the non-dominated sorting genetic algorithm; Calculate the biobjective function value for each solution in the population, and perform fast non-dominated sorting and crowding distance calculation to determine the first Pareto front; For each nondominated solution in the first Pareto front, iterative optimization is performed using the mutation operator until the local optimization termination condition is met, and the new solution corresponding to each nondominated solution is output. Select a solution from the population as the parent generation, and perform the crossover and mutation operators on the parent generation in sequence to generate offspring generation; Merge the population, new solutions, and offspring, and update the population based on fast non-dominated sorting and crowding distance; If the global optimization termination condition is met, the Pareto optimal solution is output as the optimal vehicle routing optimization scheme; otherwise, the iteration continues.

2. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 1, characterized in that, The dynamic flight endurance model for the UAV is expressed by the following formula: In the formula, Indicates that the drone has left the node fly to node The amount of electricity consumed The vertical ascent height at the start of drone flight. The average speed during the drone's flight. For the physical power of the drone, This refers to the net weight of the drone. Drone arrival node Effective load capacity at that time This refers to the level flight time of the drone. For drones at nodes Hovering time, , and These are the drone's engine efficiency, transmission efficiency, and charging efficiency, respectively. For drones in the path Total flight time on The power consumed by the internal electronic systems of the drone.

3. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 1, characterized in that, The constraints include: The formula ensures that the drone has sufficient energy throughout its journey, among which For the drone to leave the node The remaining battery power of the drone at that time Indicates that the drone has left the node fly to node The amount of electricity consumed For the drone to leave the node The remaining battery power of the drone at that time As a preset positive number, If the drone is a binary variable, From node fly to node If the value is 1, then the value is 1; otherwise, the value is 0. A collection of trucks and drones with the same configuration. For a binary variable, if the customer If selected as a recycling node, the value is 1; otherwise, the value is 0. Given two variables, if the truck From node Driving towards the node If the value is 1, then the value is 1; otherwise, the value is 0. For the first node set, Includes warehouses and customer nodes Node 0 serves as the starting point for the truck. For the second set of nodes, Includes warehouses and customer nodes , where nodes As a return point for trucks.

4. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 1, characterized in that, The solution is represented as follows: The complete chromosome sequence contains the same number of combined paths as the number of trucks. Each combined path contains a drone path for a drone and a truck path for a truck. The numbers in the combined path represent customer nodes or warehouses, and the order of the numbers represents the access order. The drone path contains one or more sequentially visited routes, where the first and last numbers of each route are the same as the numbers in the corresponding truck path, and the order of the first and last numbers of the route is the same as the order of the corresponding numbers in the truck path; the truck path contains one route, where the first and last points of each route are warehouses.

5. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 1, characterized in that, The population used to initialize the non-dominated sorting genetic algorithm includes: Phase 1: Starting from the warehouse, using the nearest neighbor search algorithm, iteratively select the geographically closest unvisited customer to add to the current path. Once the truck's load capacity is insufficient to add more customers, the vehicle returns to the warehouse, thus forming a closed composite path. By repeating the search process until all customers are visited, the multiple composite paths generated are finally linked together to form a complete chromosome sequence. Phase Two: For each customer in each combined route, the feasibility of the drone delivery route is first evaluated based on drone payload capacity constraints and dynamic flight endurance constraints. If drone delivery is feasible, the potential cost savings of assigning the customer to the drone are calculated. If the calculated potential cost savings are non-negative, the corresponding drone route is retained. Through iteration, eligible customers are added to the drone route in turn until the drone's payload capacity or flight endurance limit is reached. Once the drone reaches its payload capacity or flight endurance limit, it returns to the truck to reload the package and replace the battery. After completing the package loading and battery replacement, the drone can be launched again to serve other customers.

6. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 5, characterized in that, The calculation of potential cost savings after assigning a customer to a drone includes: Scenario 1: Consider a combined path containing a visit sequence (1, 2, 3) of three customers, where customers 1, 2, and 3 are served sequentially by trucks. If customer 2, originally served by trucks, is instead served by drones, and the drones have sufficient payload capacity and flight endurance, the cost savings from assigning customer 2 to the drones would be: ,in For trucks from the node arrive The cost of driving For drones from nodes arrive The cost of driving; Scenario 2: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 1 is served by a drone, and customers 2, 3, and 4 are served by trucks. If customer 3, originally served by a truck and located at the end of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, then the cost savings from assigning customer 3 to the drone would be: ; Scenario 3: Consider a combined path containing a visit sequence (1, 2, 3, 4) of four customers, where customer 4 is served by a drone, and customers 1, 2, and 3 are served by trucks. If customer 2, originally served by a truck and located at the starting point of the drone's flight path, is instead served by a drone, and the drone has sufficient payload capacity and flight endurance, then the cost savings from assigning customer 2 to the drone would be: .

7. The vehicle route optimization method in the multi-access truck-drone collaborative delivery mode according to claim 1, characterized in that, The mutation operator is randomly selected from among the exchange mutation operator, the insertion mutation operator, and the inversion mutation operator.

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