Research And Application Of Multi-objective Vehicle Routing Optimization With Time Window Constraint

With the rapid development of the economy and urbanization,logistics activities dramatically increased in people’s daily life and production processes.The need for efficient and reasonable logistics delivery solutions was becoming increasingly urgent,while environmental problems caused by logistics activities also received more attention from scholars,especially with the country’s promotion of a green economy.Vehicle routing optimization problem was fundamental to logistics activities,aiming to minimize transportation costs by planning the most efficient and reasonable vehicle driving routes.Its related theory and algorithms have invaluable value for real-life applications.However,in the process of logistics distribution,traffic congestion often occurs.How to meet customer needs in a complex situation,minimize transportation costs and reduce environmental pollution has become a subject of widespread concern and practical significance.The main research contents and innovative points of this paper include:(1)Constructing a Time Dependent Green Vehicle Route Problem with Time Window(TDGVRPTW)model in a time-dependent environment.Existing models for vehicle routing optimization problems with time window constraints considered few realistic conditions and often only focused on time window constraints.Moreover,existing models considered single optimization objectives that could not reflect the requirements of practical distribution processes for path planning well.To address these issues,this paper proposed a TDGVRPTW model that considers three objectives simultaneously,including total transportation costs,total travel time,and the number of vehicles.The model also considered constraints such as capacity,time windows,road congestion,and cost factors such as carbon emissions,making it more consistent with actual situations than previous models.(2)An improved multi-objective differential evolution algorithm was proposed to solve the TDGVRPTW problem.As the number of optimization objectives for vehicle routing optimization problems increases,it becomes increasingly challenging to obtain high-quality solutions through algorithms.To obtain better solution sets,this paper proposed an improved differential evolution algorithm to solve the TDGVRPTW.The improvements mainly focused on initialization,mutation operators,and selection strategies.In the initialization stage,reverse Tent chaotic initialization was proposed to generate more uniformly distributed initial populations and expand the search scope of the algorithm.During the evolutionary process,a hybrid mutation strategy and repair operator were designed.The hybrid mutation strategy integrated two popular differential evolution operators,while the repair operator repaired outof-range individuals to prevent offspring populations from clustering on the boundary of the solution space.In the selection stage,an adaptive selection strategy was designed to retain potential solutions.This strategy balanced population diversity and convergence well.The effectiveness of the proposed improvement algorithm was verified through theoretical analysis and comparative experiments on the Solomon benchmark dataset and real MOVRPTW instances.(3)A dynamic constraint multi-objective optimization algorithm based on the cooperative co-evolution framework was proposed to solve the TDGVRPTW.VRP problems have complex constraints,and existing VRP algorithms often impose strict restrictions based on constraints to meet problem requirements,failing to fully utilize the role of constraint information in solving problems.Therefore,based on the idea of simple tasks assisting complex task solving in multitask optimization,a collaborative constraint multi-objective evolutionary algorithm was designed to solve the TDGVRPTW.The algorithm treated the complete TDGVRPTW as a complex task and introduced a shift crowding distance calculation that simultaneously considered the distribution and convergence information of individuals in the selection process,which balanced the convergence and diversity of the population well.Meanwhile,a dynamic constraint selection strategy was designed to implement simple tasks,considering the impact of partial constraint conditions on the population.The two populations exchanged information through offspring populations.Comparative experiments were conducted on constraint multiobjective test function sets,Solomon benchmark datasets,and real MOVRPTW instances,and the experimental results showed that the constraint multi-objective optimization algorithm based on the cooperative co-evolution framework had good comprehensive performance.