A two-phase hybrid heuristic for the two-echelon vehicle routing problem

The Two-Echelon Vehicle Routing Problem (2E-VRP) is a novel variant of Vehicle Routing Problem (VRP), in which freight from a depot is compulsorily delivered through intermediate depots, called satellites. The first echelon is from depot to satellites, while the second from satellites to customers. Solution to 2E-VRP is challenging and limited. In this paper a two-phase hybrid heuristic is proposed for 2E-VRP, which is composed of a greedy randomized adaptive search procedure (GRASP) and a variable neighborhood descent (VND), called GRASP+VND in the sequel. The GRASP+VND solves 2E-VRP in a bottom-up manner according to the nature of this problem. Firstly, a GRASP that utilizes an extended split algorithm repeatedly operates on randomly generated permutations of all customers and assigns them to satellites until a feasible assignment appears, the complete initial feasible solution is obtained by solving the first echelon problem subsequently. Secondly, a VND works on the solution until no improvements can be found in any neighborhoods applied. The preceding process is iterated until the termination condition is satisfied. Computational tests on 39 benchmark instances from the literature verify the effectiveness and efficiency of the proposed algorithm and that it outperforms two existing heuristics for 2E-VRP.