Optimization Research On Time-dependent Vehicle Routing Problem With Simultaneous Pickup And Delivery And Soft Time Windows

Vehicle Routing Problem has always been one of the hotspots in the field of operations research,and it is the key to effectively reduce logistics costs.Considering the emergence of more and more logistics activities such as return maintenance and recovery in real life,the research on Vehicle Routing Problem with Simultaneous Pickup and Delivery which integrates the forward logistics and reverse logistics has also received increasing attention.In the existing Vehicle Routing Problem with Simultaneous Pickup and Delivery,it is generally assumed that the vehicle traveling speed is constant,or the average traveling speed is constant.However,in real life,due to people's commuting,weather conditions,road maintenance and other factors,the speed of the vehicle at different time periods or different road types will vary according to the travel time,resulting in the traveling cost of two nodes is different.Therefore,it has certain theoretical basis and practical significant to study the time-dependent Vehicle Routing Problem with Simultaneous Pickup and Delivery.In order to better reflect the timeliness and accord with the reality,based on the existing time-dependent Vehicle Routing Problem,the acceleration of the vehicle speed is considered in order to make the vehicle speed change smoothly.In this paper,a mathematical model of time-dependent VRPSPD problem with soft-time window constraints is constructed,and a hybrid particle swarm optimization algorithm embedded with adaptive perturbation mechanism is designed to solve the time-dependent Vehicle Routing Problem with Simultaneous Pickup and Delivery.In the mechanism,the variable neighborhood descent search is taken as the main body,and the structures of intra-rout and inter-rout neighborhood are defined.The roulette rules with the path gravity center as the selection probability and the adaptive neighborhood selection strategy are designed to give full play to the advantages of both.In order to verify the feasibility of the algorithm,the existing examples are extended,and the time-dependent functions of four different scenarios are combined to compare and analyze the particle swarm optimization algorithm with or without perturbation mechanism,as well as the comparison of the running results with or without accelerated speed.It is concluded that the perturbation mechanism is beneficial to the particle swarm optimization algorithm to jump out of the optimal solution,and traveling cost is different in different scenarios,and the influence degree of accelerated speed is different.Therefore,according to the actual situation,reasonable travel arrangement can effectively reduce the cost.