A multi-start variable neighborhood search for multi-objective location routing problem with simultaneous pickup and delivery

In order to minimize the total cost and maximum gap among each tour in a location-routing problem with simultaneous pickup and delivery (LRPSPD), a LRPSPD bi-objective model, which considers the vehicle capacity and travel distance constrains simultaneously, is established. Multiple ant colonies are used to construct the initial solutions. The initial solutions are associated with each other by multiple pheromones and are taken as multi-starts of bi-objective variable neighborhood search algorithm. Four types of neighborhood structures are established for the variable neighborhood search. The pheromones are updated according to the latest optimal neighborhood solutions, so that there are positive influence relationships not only among multiple initial solutions generated by ants, but also between initial solutions and solutions generated by variable neighborhood search. The proposed multi-start variable neighborhood search (MSVNS) approach is then used to solve 128 instances, which are classified in 4 sets in the literature and obtain the approximate Pareto solutions. The results demonstrate the significance of considering the maximum gap among each tour as a minimized objective in some instances, which have scattered nodes and demands distribution. Compare the solutions with lowest cost (absolute preference to minimize the costs) from Pareto solutions with previous results from literature which minimize the total costs only. The comparison results indicate that the procedure can be operated in extremely short running time and the Pareto solutions acquired by the algorithm provide good tradeoff between two objectives and yield a competitive solution of the cost-minimizing objective. © 2022 South China University of Technology. All rights reserved.