Research And Application Of Multi-Objective Optimization Algorithms In Vehicle Routing Problem With Time Windows

With the continuous development of smart cities and intelligent transportation,the vehicle routing problem(VRP)has received widespread attention as a core issue.The main goal of the vehicle routing problem is to optimize the sequence of vehicle distribution by combining the actual distribution situation with reasonable planning to minimize logistics costs.However,due to its NP-Hard nature,it is difficult to obtain optimal solutions within a limited time using traditional heuristic and exact algorithms.Therefore,there is an urgent need to develop new effective methods to solve complex vehicle routing problems.This paper primarily focuses on addressing the vehicle routing problem with time windows for single/multi-objectives.The main work of this paper is as follows:(1)To overcome the limitations of traditional intelligent optimization algorithms in solving the single-objective vehicle path problem with time windows,such as susceptibility to local optima,low convergence accuracy,and low convergence diversity,this paper utilizes the powerful global optimization capabilities and fast convergence speed of the Grasshopper Optimization Algorithm(GOA)with few parameters.To address the shortcoming of GOA’s inability to accurately search the local area,this paper adopts the concept of dynamic compression factor,where the compression factor size is adjusted according to the iteration changes to balance the parameters during the iteration process.To address the issue of GOA easily falling into local optima,this paper introduces the idea of a simulated annealing algorithm and utilizes the Metropolis acceptance criterion to accept inferior solutions with a certain probability,allowing the algorithm to jump out of local optima.Experimental results demonstrate the effectiveness of the proposed hybrid grasshopper optimization algorithm for solving single-objective vehicle routing problem with time windows.(2)To improve the realism of vehicle routing planning,this paper proposes a multiobjective model for vehicle routing problem with time windows,with the number of vehicles,travel distance,working time,waiting time,and delay time as the objectives.However,solving a multi-objective problem poses computational difficulties and requires balancing convergence and diversity of the optimization algorithm.Therefore,a two-stage algorithm framework is proposed.In the first stage,the EC-NSGA-II algorithm is enhanced by incorporating global and local optimization concepts from particle swarm algorithms,enabling better search for extreme solutions,and local search algorithms to improve convergence.In the second stage,a multi-objective optimization framework based on non-dominated rankingand local search is employed to improve the algorithm’s search capability,and a novel local search method with multi-neighborhood operators is introduced to address the problem of falling into local optima with the original local search method.Experimental results demonstrate the effectiveness of the proposed two-stage hybrid multi-objective optimization algorithm for solving multi-objective vehicle routing problem with time windows.