| In modern logistics distribution,as a new type of transportation,drone has attracted the attention of many logistics enterprises.As a new distribution mode,cooperative distribution of vehicles and drones is proposed.This distribution mode can combine the advantages of traditional vehicle distribution and drone distribution to achieve high efficiency and cost-effectiveness of logistics distribution.Therefore,it is of great significance for the development of modern logistics industry and the improvement of logistics transportation efficiency to study the joint distribution path optimization of vehicles and drones.Firstly,this paper briefly introduces the concept of vehicle routing problem(VRP)and the related algorithms for solving VRP,focusing on the analysis of the key content and solution structure of clustering algorithm,neighborhood search algorithm and variable neighborhood search algorithm.At the same time,the paper provides the theoretical basis for the solution of the Traveling Salesman Problem with Drones(TSPD)and the Multi-truck and multi-drones vehicle routing problem(MTMDVRP),the construction of different function models and the design of different algorithms.Secondly,aiming at the TSP-D path optimization,aiming at the minimum total service time,the mathematical model of joint distribution between single vehicle and drone is established.A hybrid neighborhood search algorithm is proposed for the model.The experimental results show that the hybrid neighborhood search algorithm combined with simple heuristic algorithm can better solve the path optimization problem of single vehicle and single drone joint distribution.Then,on the basis of TSP-D path optimization problem,it expands the number of customers points and becomes a vehicle routing problem with drone(VRP-D).The MTMDVRP route optimization problem is analyzed in detail,and the mathematical model with the shortest total delivery time as the objective function is established.A hybrid variable neighborhood search algorithm combined with adaptive K-means clustering search algorithm is designed to solve the model.By analyzing the role of adaptive K-means clustering search algorithm in the model,the role of variable neighborhood search operation in solving the model,and through different parameter settings,the effectiveness of the algorithm is further analyzed.The experimental results show that the hybrid variable neighborhood search algorithm combined with adaptive Kmeans clustering search algorithm can solve the MTMDVRP path optimization problem well.Finally,the traditional sensitivity analysis method and the nonlinear single factor sensitivity analysis method are introduced respectively.The sensitivity analysis of the time factor in the objective function is carried out,and the influence degree of each influence factor on the objective function model is obtained.The results show that the influence degree of objective function value from large to small is drone maximum flight time,drone flight speed load influence factor,drone flight speed,drone launch time and recovery time.Therefore,in the actual transportation process,we need to focus on the impact of drone performance on path optimization. |