Lagrange Heuristic Algorithm Incorporated with Decomposition Strategy for Green Multi-depot Heterogeneous-Fleet Vehicle Routing Problem

Linhao Xu, Bin Qian, Rong Hu, Nai-Kang Yu, Huai-Ping Jin

Abstract: Aiming at the green multi-depot heterogeneous-fleet vehicle routing problem (GMDHFVRP), a mixed integer programming model (MIP) was established to minimize the total cost, and a Lagrange heuristic algorithm incorporated with decomposition strategy (LHA_DS) was proposed to solve it. First, the original problem is decomposed into a number of vehicle sub-problems by relaxing the complex constraints. At the same time, the distance-based K-means clustering method is used to allocate service customer sets for each parking lot, and the surrogate subgradient method is used to solve the sub-problems to update the lagrange multiplier; Secondly, in order to obtain a better initial feasible solution, a repair strategy based on greedy idea is designed to repair the problem relaxation solution to obtain a better solution, and a neighborhood search method to determine the operation order is designed to optimize the feasible solution. Finally, the effectiveness of LHA_DS in solving GMDHFVRP is verified by simulation experiments.