Research On Optimization Algorithm For Multi-Depot Vehicle Routing Problem With Fuzzy Time Window

With the continuous and stable development of China’s economy,the economic volume is getting bigger and bigger,and the logistics scale will be further expanded.While expanding,there are also many problems.Due to the unreasonable route planning,the transportation cost will increase,the delivery will be overtime,and the customers will complain,and it will also have a certain impact on the traffic of the entire city.Therefore,reasonable planning of vehicle distribution paths,reduction of transportation costs and labor costs of enterprises,improvement of customer service quality,and enhancement of customers’ dependence on enterprises have become the focus of current research.Based on the traditional vehicle routing problem,this paper considers the distance cost of vehicles and the cost of customer satisfaction,and proposes a vehicle routing problem for multiple distribution centers based on fuzzy time windows(MDVRPFTW)for the vehicle driving problem of multiple distribution centers.).The MDVRPFTW problem belongs to the NP-Hard problem,which uses traditional heuristic algorithms and exact algorithms.With the increase of the scale of the problem,its operation speed will increase exponentially,and it is difficult to find a better solution in a limited time.In order to effectively solve the MDVRPFTW problem,swarm intelligence optimization algorithms provide new ideas,such as whale algorithm,fish swarm algorithm,seagull algorithm,sparrow search algorithm,gray wolf algorithm and so on.When solving different types of vehicle routing problems,each intelligent optimization algorithm has different advantages,disadvantages and degrees of suitability.Therefore,the focus of this paper is to study the improved multiverse algorithm for solving the MDVRPFTW model.The details are as follows:1.When solving the MDVRPFTW problem,the traditional multiverse algorithm itself is easy to fall into the local optimal solution,which seriously affects the final solution accuracy.Aiming at this problem,a Discrete Multi-Verse Optimizer(DMVO)is proposed to solve the MDVRPFTW problem.In DMVO,the update strategy of the multiverse is improved.First,three atomic operations are defined,including insertion,exchange,and reversal.Using atomic operations in the redefinition of black hole/white hole transfer and the redefinition of moving to the optimal universe,the improved update method can not only reduce the premature convergence of the algorithm,but also enhance the ability of the algorithm to jump out of the local optimum.It can also ensure that the individual universe is optimized around the current optimal universe.Finally,the Solomon data set is used to compare the DMVO algorithm with several other algorithms,and the results show the feasibility of the DMVO algorithm.2.Based on the DMVO algorithm,inspired by the genetic crossover operator,a cross-mapping strategy is introduced,and an improved discrete multiverse algorithm(CM-IDMVO)based on cross-mapping is proposed.The algorithm redefines the update strategy of black hole/white hole transfer and movement to the optimal universe,and adopts a combination of one-point move operator,2-exchange operator,point-arc exchange operator,and 2-opt operator.Domain search strategy,as an atomic operation of paths in the MDVRPFTW problem.Then,the CM-IDMVO algorithm is compared with the DMVO,SA,WOA,SOA,PSO,MFO and GWO algorithms on the Solomon data set and the extended data set.The experimental results show that the CM-IDMVO algorithm not only shows excellent performance in the vehicle routing problem model of multi-distribution centers with single fuzzy time window,but also verifies the feasibility of the algorithm in the vehicle routing problem model of multi-distribution centers with multiple fuzzy time windows.and effectiveness.