Evolutionary Multi-Objective Optimization For Vehicle Routing Problemwith Simultaneous Delivery And Pickup In Logistics

The vehicle routing problem is a core issue in modern logistics systems,with the main goal of determining a set of vehicle routes to efficiently transport goods to their destination.However,with the continuous development of logistics business and changing customer demands,a single vehicle routing plan is no longer sufficient to meet the demands of modern logistics.Vehicle Routing Problem with Simultaneous Delivery and Pickup(VRPSDP)not only considers the transportation routes of goods from the distribution center to customers,but also takes into account customer collection requirements and the recycling needs of reverse logistics.As a result,the problem becomes more complex and practical.Due to its NP-hard nature,it is difficult to solve using traditional algorithms,and hybrid evolutionary optimization algorithms play an important role in solving this problem,with positive value in both theoretical and practical applications.A hybrid evolutionary algorithm combining a multi-region mixed-sampling strategy for global search and a local search based on individual route sequence differences is proposed to solve the Vehicle Routing Problem with Simultaneous Delivery and Pickup and time windows(VRPSDPTW)for a single vehicle model.First,a reasonable mathematical model is constructed for the problem,and the global search strategy is used to quickly converge the algorithm to the Pareto front.Then,the local search strategy is employed to further improve the quality of individuals and enhance the algorithm’s local search ability.The proposed algorithm is evaluated on a standard test dataset for the VRPSDPTW,and the results show that the proposed method significantly improves the convergence performance and produces solutions with good distribution.a hybrid evolutionary algorithm with multiple stages and time slots is proposed to solve the VRPSDPTW for multiple vehicle models.A vehicle type vector is introduced,and individuals are represented in the form of dual chromosome vectors.The original hybrid algorithm is split into three stages.In the first stage,a multi-region sampling strategy is employed to enable the population to quickly approach the Pareto front from multiple directions.In the second stage,a strategy based on the differences between individual route sequences is used to accelerate the convergence speed of individuals.In the third stage,the direction of the strategy based on differences between individual route sequences is changed,and individuals are guided to search in the local area of the Pareto front.Experiments show that this algorithm can better handle VRPSDPTW with multiple vehicle types.The hybrid evolutionary algorithm proposed in this study combines a global search based on a multi-region sampling strategy and a local search based on differences between individual route sequences,balancing the algorithm’s search and exploration capabilities.Experimental results show that the proposed algorithm and strategies can better handle the VRPSDPTW and provide valuable experience and insights for solving other complex multi-objective optimization problems using hybrid evolutionary algorithms.