Robust optimization method for unmanned aerial vehicle-truck collaborative distribution

Abstract

The invention discloses a robust optimization method for unmanned aerial vehicle-truck collaborative distribution, and aims to solve the scheduling problem of unmanned aerial vehicle-truck collaborative distribution in a traffic uncertainty environment. The scheduling process comprises the following steps of: 1, dynamically determining an alternative driving path of a truck and task allocation of an unmanned aerial vehicle according to geographic distribution and real-time traffic data required by a customer; secondly, a distance matrix reflecting the distance between the distribution points is calculated; thirdly, according to the cost of the truck and the unmanned aerial vehicle, a robust optimization objective function is constructed to minimize the total distribution cost; 4, constructing related constraint conditions; and 5, solving the constructed robust optimization model by adopting a genetic algorithm. Through simulation verification, the distribution scheme can still realize cooperative distribution of the unmanned aerial vehicle and the truck under the condition of traffic disturbance, and the influence of uncertainty on the distribution system is effectively relieved. The method overcomes the limitation that a traditional distribution theory is difficult to adapt to an unmanned aerial vehicle and truck collaborative distribution scene, and has important theoretical value and practical significance.

Description

Technical Field

[0001] This invention relates to logistics distribution scheduling methods, and in particular to a robust optimization method for drone-truck collaborative delivery, belonging to the field of logistics engineering. Background Technology

[0002] With the booming development of e-commerce and the increasing demand for logistics, optimizing the efficiency and cost of last-mile delivery has become an important research direction in the logistics industry. Traditional delivery methods mainly rely on trucks for point-to-point goods transportation; however, due to limitations in road traffic conditions, geographical environment, and accessibility in remote areas, delivery efficiency is often low. In recent years, the rapid development of drone technology has provided new possibilities for logistics delivery. Drones can bypass ground traffic restrictions and quickly cover remote or hard-to-reach areas, but their range is limited and their payload capacity is low, making it impossible to independently complete large-scale delivery tasks. Therefore, the collaborative model of truck and drone joint delivery has gradually attracted attention, which utilizes trucks as mobile platforms to carry drones, achieving efficient delivery through reasonable task allocation and route planning.

[0003] In existing research, the route planning problem for truck-drone joint delivery is typically addressed in deterministic environments, using methods such as exact algorithms (e.g., mixed-integer programming) and heuristic algorithms (e.g., genetic algorithms). However, real-world delivery scenarios involve various uncertainties, such as fluctuating truck speeds due to traffic conditions or weather changes, and drone ranges affected by wind speed. These uncertainties can lead to significant deviations in delivery time and cost. Furthermore, existing methods lack robustness in ensuring full coverage of all delivery points, and some demand points may be overlooked due to optimization objectives biased towards total cost or time. Therefore, there is an urgent need for a delivery method that can optimize scheduling schemes under uncertain environments while ensuring full coverage. Currently, there is limited theoretical research on drone-truck collaborative delivery both domestically and internationally, and existing last-mile delivery theories are ill-suited to the drone-truck collaborative delivery scenario. Therefore, providing a drone-truck collaborative delivery method has significant theoretical and practical value. Summary of the Invention

[0004] Technical Problem: To provide a robust optimization method for drone-truck collaborative delivery, aiming to solve the problems of low delivery efficiency and inability to ensure full coverage of all delivery points in the context of uncertainty in existing technologies.

[0005] Technical solution: A robust optimization method for drone-truck collaborative delivery, comprising the following steps:

[0006] (1) Calculate the distance matrix between each customer point based on the distance between the customer point and the distribution center.

[0007] (2) Construct a cost function related to drone-truck collaborative delivery;

[0008] (3) Construct constraints related to drone-truck collaborative delivery;

[0009] (4) Construct a robust model for collaborative delivery between drones and trucks under uncertain ground traffic conditions;

[0010] (5) A robust model for collaborative delivery between drones and trucks was constructed using an improved genetic algorithm;

[0011] Specifically, in step (1), the formula for the distance between each customer point is as follows:

[0012]

[0013] Where, x i y i The x and y coordinates of customer point i are represented by x. j y j Let V represent the x and y coordinates of customer point j, and let V represent the set of all customer points. ij This represents the distance between customer points i and j.

[0014] Furthermore, in step (2), the costs associated with drone-truck collaborative delivery include fixed costs, truck delivery costs, and drone delivery costs, as detailed below:

[0015]

[0016] Among them, C total x represents the total delivery cost of drone and truck collaborative delivery. ij Let ∈{0,1} represent the route decision variables for the truck, i.e., whether the truck travels along path ij; y ij ∈{0,1} represents the path decision variable of the drone, i.e., whether the drone traverses path ij; v d With v t These represent the operating speeds of the drone and the truck, respectively; c d With c t These represent the unit time cost of drones and trucks, respectively; F represents the fixed cost incurred in each delivery cycle.

[0017] Furthermore, in step (3), the constraints related to the collaborative delivery between drones and trucks are as follows:

[0018] (3.1) All customer points were visited once:

[0019]

[0020] (3.2) Both the truck and the drone depart from the distribution center and eventually return to the distribution center, where x ji The variables representing the truck's route decision are whether the truck travels along path ji and y. ji This represents the path decision variable for the drone, i.e., whether the drone traverses path ji:

[0021]

[0022] (3.3) The launch and recovery nodes of the drones must be coordinated with the trucks, where x ik x ki Let ik and ki represent the decision variables for the truck on the corresponding paths:

[0023] y ij ≤x ik

[0024] y ji ≤x ki

[0025] (3.4) The delivery distance and delivery volume of the drone in each small delivery cycle shall not exceed the drone's own range D. max With load limit Q max , where w j The demand for customer point j:

[0026]

[0027]

[0028] (3.5) Eliminate truck sub-circuit, U i U j V represents the order in which nodes i and j are visited, and V represents the set of all client points.

[0029] U i -U j +|V|·x ij ≤|V|-1

[0030] (3.6) Drone access order restriction, i.e., the access order of the take-off point on the truck route is earlier than that of the rendezvous point, where y ik y ki Let ik and ki represent the decision variables of the drone on the corresponding paths:

[0031]

[0032] (3.7) Path continuity constraints for trucks and drones:

[0033]

[0034] Furthermore, in step (4), the truck running speed, which was originally a fixed value, is defined as a variable. Let U be the set of uncertainties to which it belongs. If the road conditions are poor during the truck's journey to customer point i, then v t It will be lower than the normal speed v nominal However, it will not fall below the lower speed limit v. min The decrease in speed will lead to an increase in delivery time. Therefore, the robust model is constructed as follows: (4.1) Construct the objective function of the robust model:

[0035]

[0036] (4.2) By comparing the robust model with the original model, the uncertainty increment ΔC is obtained. truck The objective function is to maximize the uncertainty increment maxΔC. truck , where w ij For decision variables, consider whether path ij changes under deterministic and uncertain conditions:

[0037]

[0038] (4.3) Introduce auxiliary decision variable z ij Γ is used to indicate whether the path is affected, leading to worst-case traffic conditions. An uncertain budget variable Γ and a dual variable λ are introduced to transform the original robust model into a dual model:

[0039]

[0040]

[0041] Furthermore, in step (5), an improved genetic algorithm is used to solve the problem, and the objective function is:

[0042]

[0043] Where minC total This represents the optimal objective value of the objective function, which is the minimum value of delivery cost and fixed cost under the current delivery plan.

[0044] Beneficial Effects: Compared with existing technologies, this invention, for the first time in last-mile logistics delivery scenarios, proposes a robust delivery model based on a "drone-truck" collaborative delivery mode, designed to address uncertainties in ground traffic. Since drones can operate independently of ground traffic conditions, provide delivery services over a certain distance, and replenish power and cargo via trucks, compared to traditional vehicle transportation or heterogeneous delivery under fixed traffic conditions, the robust delivery model better adapts to actual delivery scenarios. It exhibits high robustness to changes in traffic conditions, and the robust optimization method effectively addresses traffic disturbances, ensuring the stability and feasibility of the delivery plan under worst-case scenarios. Real-world testing shows that this invention, when applied to delivery in rural areas and other situations with inadequate transportation infrastructure, effectively solves the problem of delivery plans being difficult to implement due to unstable road traffic conditions. Attached Figure Description

[0045] Figure 1 This is a flowchart of the implementation process for drone-assisted truck delivery scheduling;

[0046] Figure 2 This is a schematic diagram of a drone-assisted truck delivery service model. The drone departs from the distribution center with the truck, separates at a certain truck service node, autonomously travels to the drone service node, and autonomously travels to the next truck service node to meet up with the truck after completing the service.

[0047] Figure 3 This is a diagram illustrating the adjustment of a drone-assisted truck delivery solution under road traffic disturbances. When severe traffic disturbances occur in a certain area, the original delivery solution may not be feasible. Therefore, drones are assigned to deliver goods to customers in that area, and the overall delivery solution is adjusted accordingly.

[0048] Figure 4 This is a schematic diagram of the final delivery plan obtained by the embodiment of the present invention. The solid blue line is the truck delivery route, and the dashed lines of different colors represent the various sub-delivery routes of the drones. Both depart from the delivery center represented by the pentagram at the same time, serve all customer points, and return to the delivery center at the same time.

[0049] Figure 5 This is a schematic diagram of a two-stage method for solving the drone-assisted truck delivery model. Detailed Implementation

[0050] The technical solution of the present invention will be described more comprehensively and in detail below with reference to the accompanying drawings and embodiments.

[0051] This invention is based on the Solomon standard example, with a dataset created by the American Transportation Association. It utilizes the RC101 dataset to construct an implementation example suitable for "drone-truck" collaborative delivery route optimization scenarios. The original example includes several customer point coordinates and corresponding demand and service time windows. For example... Figure 2 As shown, consider the following rural logistics delivery scenario: A truck and a drone are used to collaboratively deliver goods. Initially, the drone is mounted on the truck and departs from the distribution center. Upon reaching a customer location, the drone is released to autonomously deliver to the next customer location, while the truck also departs for another customer location. After completing their respective deliveries, both the drone and the truck will rendezvous at the next customer location until they have completed all scheduled deliveries and return together to the original distribution center.

[0052] The "drone-truck" collaborative delivery process is as follows: Figure 1 As shown, firstly, cluster analysis is performed based on the geographical distribution of customer points; secondly, the distance matrix between each customer point is determined based on the cluster distribution; thirdly, a cost function related to "drone-truck" collaborative delivery is constructed based on relevant cost factors; fourthly, constraints related to path optimization are constructed based on the distance matrix and the relevant limitations of drones and trucks; fifthly, a two-stage method is used to solve the constructed collaborative delivery model. Figure 5 The following provides a detailed explanation of each step.

[0053] Step 1: Perform cluster analysis based on the geographical distribution of customer locations.

[0054] From the RC101 example, 26 customer locations were selected, with number 1 being the distribution center and the rest being customer locations. All coordinates were assigned to a 100*100 rectangular area, resulting in the following table showing the corresponding coordinates and requirements:

[0055] Table 1 Customer Location Coordinates and Corresponding Requirements

[0056]

[0057] According to the cluster analysis described in step (1) of the invention, the customer points are divided into 5 clusters.

[0058] Step 2: Calculate the distance matrix based on the distance between each cluster center and the customer point.

[0059] Step 3: Construct a cost function related to "drone-truck" collaborative delivery based on relevant cost factors.

[0060] Construct the objective function according to the method in step (3) of the invention.

[0061] Step 4: Construct constraints related to "drone-truck" collaborative delivery

[0062] Take the service capacity of a single UAV as c = 50; construct the objective function according to the method in step (4) of the invention.

[0063] Step 5: Solve the constructed "drone-truck" collaborative delivery model using a two-stage method.

[0064] According to the method in step (4) of the invention, the model is divided into a main problem of delivery sequence arrangement and a sub-problem of customer point allocation. The experimental environment is AMD Ryzen 5 5600 CPU@4.60GHz RAM:32G, and the solution is performed using the Python 3.11 programming language. The "drone-truck" collaborative delivery solution is obtained as follows: Figure 4 As shown. Calculations show that this delivery plan, under traffic disruption conditions (... Figure 3 Even with this alternative, the delivery plan can still be successfully coordinated, and the cost of the delivery plan is lower than that of the original delivery plan, which can effectively mitigate the impact of uncertainty on the delivery system.

[0065] Please note to all technical personnel: Although the present invention has been described according to the specific embodiments above, the inventive concept of the present invention is not limited to this invention. Any modifications that utilize the inventive concept will be included within the scope of protection of this patent.

Claims

1. A robust optimization method for drone-truck collaborative delivery, characterized in that, Includes the following steps: Step (1) Calculate the distance matrix between each customer location and the distribution center location; Step (2) Construct the cost function related to drone-truck collaborative delivery; Step (3) Construct the constraints related to drone-truck collaborative delivery; Step (4) Construct a robust model for collaborative delivery between drones and trucks under uncertain ground traffic conditions; Step (5) uses a two-stage method to solve the robust model of drone and truck collaborative delivery.

2. The robust optimization method for drone-truck collaborative delivery according to claim 1, characterized in that, The distance formula between customer points in step (1) is as follows: Where, x i y i The x and y coordinates of customer point i are represented by x. j y j Let V represent the x and y coordinates of customer point j, and let V represent the set of all customer points. ij This represents the distance between customer points i and j.

3. The robust optimization method for drone-truck collaborative delivery according to claim 2, characterized in that, The costs associated with drone-truck collaborative delivery in step (2) include fixed costs, truck delivery costs, and drone delivery costs, as detailed below: Among them, C total This represents the total delivery cost of drone and truck collaborative delivery; x ij Let ∈{0,1} represent the route decision variables for the truck, i.e., whether the truck travels along path ij; y ij ∈{0,1} represents the path decision variable of the drone, i.e., whether the drone traverses path ij; v d With v t These represent the operating speeds of the drone and the truck, respectively; c d With c t F represents the unit time cost of drones and trucks, respectively; F represents the fixed cost incurred in each delivery cycle.

4. A robust optimization method for drone-truck collaborative delivery according to claim 3, characterized in that, In step (3), the constraints related to drone-truck collaborative delivery are as follows: (3.1) All customer points were visited once: (3.2) Both the truck and the drone depart from the distribution center and eventually return to the distribution center, where x ji The variables representing the truck's route decision are whether the truck travels along path ji and y. ji This represents the path decision variable for the drone, i.e., whether the drone traverses path ji: (3.3) The launch and recovery nodes of the drones must be coordinated with the trucks, where x ik x ki Let ik and ki represent the decision variables for the truck on the corresponding paths: and ij ≤x ik and ji ≤x ki (3.4) The delivery distance and delivery volume of the drone in each small delivery cycle shall not exceed the drone's own range D. max With load limit Q max , where w j The demand for customer point j: (3.5) Eliminate truck sub-circuit, U i U j V represents the order in which nodes i and j are visited, and V represents the set of all client points. U i -U j +|V|·x ij ≤|V|-1 (3.6) Drone access order restriction, i.e., the access order of the take-off point on the truck route is earlier than that of the rendezvous point, where y ik y ki Let ik and ki represent the decision variables of the drone on the corresponding paths: (3.7) Path continuity constraints for trucks and drones:

5. A robust optimization method for drone-truck collaborative delivery according to claim 4, characterized in that, In step (4), a robust model for collaborative delivery between drones and trucks under uncertain ground traffic conditions is constructed, and the truck speed, which is originally a fixed value, is defined as a variable. Let U be the set of uncertainties to which it belongs. If the road conditions are poor during the truck's journey to customer point i, then v t It will be lower than the normal speed v nominal However, it will not fall below the lower speed limit v. min Since a decrease in speed will lead to an increase in delivery time, a robust model is constructed as follows: (4.1) Construct the objective function of the robust model: (4.2) By comparing the robust model with the original model, the uncertainty increment ΔC is obtained. truck The objective function is to maximize the uncertainty increment maxΔC. truck , where w ij For decision variables, consider whether path ij changes under deterministic and uncertain conditions: (4.3) Introduce auxiliary decision variable z ij This is used to indicate whether the path is affected, leading to worst-case traffic conditions; an uncertain budget variable Γ and a dual variable λ are introduced to transform the original robust model into a dual model:

6. A robust optimization method for drone-truck collaborative delivery according to claim 5, characterized in that, In step (5), an improved genetic algorithm is used to solve the problem, and the objective function is: Where minC total This represents the optimal objective value of the objective function, which is the minimum value of delivery cost and fixed cost under the current delivery plan.

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