Research On Improved Whale Algorithm For Vehicle Routing Problem With Time Windows

With the strong development of China's economy and e-commerce industry,the logistics industry has also acquired a broad market.Nevertheless,China's current logistics industry is still in the initial stage of development,with low logistics service efficiency and high transportation costs.How to plan the delivery route in a scientific and reasonable way and realize the efficient and low-cost logistics operation is the focus of current scholars' research.This paper mainly solves the vehicle routing problem with time windows(VRPTW),and seeks the minimum value of total cost by taking the vehicle load weight and the time windows as main constraints conditions.Since the VRPTW belongs to the NP-Hard problem,solving with traditional heuristic and precise algorithms,the calculation time will increase exponentially with the expansion of the problem size,making it difficult to obtain a better solution in a limited time.Therefore,it is urgent to find new methods to effectively solve complex VRPTW.Swarm intelligence optimization algorithms are new algorithms that simulate biological evolution or foraging behaviors,such as WOA,BA,etc.These algorithms are committed to obtaining approximate optimal solutions in a reasonable time,and have fast convergence speed,strong search capabilities.Therefore,swarm intelligence optimization algorithms are increasingly applied to solve VRPTW.This article focuses on the improved whale algorithm for solving VRPTW.The specific research contents are as follows:1.Aiming at the shortcoming that the whale optimization algorithm solves the VRPTW,which leads to the reduction of population diversity,a discrete whale algorithm based on K-means(K-DWOA)is proposed to solve VRPTW.In K-DWOA,customers are divided into different distribution areas according to their positions under the limit of the maximum vehicle load,this approach improves the quality of the initial population and speeds up the convergence of the algorithm.In order to better meets the requirements for solving VRPTW,and at the same time to improve the local search ability of the algorithm,this paper uses random exchange,inversion and insertion strategies to redefine the update rules of the whale optimization algorithm.Finally,simulation experiments are performed through the Solomon test data,the effectiveness and feasibility of the proposed algorithm are verified by comparative experiments.2.On the basis of K-DWOA,by introducing the greedy selection strategy,the improved discrete whale algorithm based on the greedy selection principle is proposed(GS-IDWOA).This algorithm introduces the waiting time factor and heuristic information factor to design the calculation formula of the transition probability,which is used to select the appropriate path to better control the moving direction of the whale in the search space.In order to improve the solution accuracy of the algorithm,by comparing the size of the transition probability between customer to select the appropriate insertion,inversion,and exchange position,so that the whale can move closer to the optimal solution position;in addition,in order to expanding the search space of the algorithm and improving the ability of the algorithm to jump out of the local optimum,The neighborhood search strategy combining random exchange search,2-opt and 3-opt was introduced to the optimal solution obtained during each iteration.Finally,simulation experiments are performed through the Solomon test data,the efficiency and stability of the proposed algorithm are verified by comparative experiments.