A Hybrid GRASP+VND Heuristic for the Two-Echelon Vehicle Routing Problem Arising in City Logistics

Abstract

The two-echelon vehicle routing problem (2E-VRP) is a variant of the classical vehicle routing problem (VRP) arising in two-level transportation systems such as those encountered in the context of city logistics. In the 2E-VRP, freight from a depot is compulsorily delivered through intermediate depots, named satellites. The first echelons are routes that distribute freight from depot to satellites, and the second are those from satellites to customers. This problem is solved by a hybrid heuristic which is composed of a greedy randomized adaptive search procedure (GRASP) with a route-first cluster-second procedure embedded and a variable neighborhood descent (VND), called GRASP+VND hereafter. Firstly, an extended split algorithm in the GRASP continuously splits randomly generated permutations of all customers and assigns customers to satellites reasonably until a feasible assignment appears, and a complete 2E-VRP feasible solution is obtained by solving the first echelon problem subsequently and, secondly, a VND phase attempts to improve this solution until no more improvements can be found. The process above is iterated until the maximum number of iterations is reached. Computational tests conducted on three sets of benchmark instances from the literature show that our algorithm is both effective and efficient and outperforms the best existing heuristics for the 2E-VRP.