A Hybrid GRASPxVNS Algorithm with Effective Depot Reduction Mechanism for the Capacitated Location Routing Problem

In this paper, we propose a new hybrid heuristic to solve the Location Routing Problem with capacitated depots and capacitated vehicles. The heuristic combines a Greedy Randomized Adaptive Search Procedure to determine the depot locations to be established and a Variable Neighborhood Search to optimize the vehicle routes originating at the opened depots. Furthermore, we enhance the heuristic by a powerful depot reduction mechanism. In numerical studies performed on the benchmark sets available from the literature, our GRASPxVNS heuristic outperforms all state-of-the-art heuristics in terms of solution quality and computing time. In addition, our algorithm is able to find 22 new best solutions on the large instance sets. Technical Report 01/2011 IT-based Logistics, Goethe University Frankfurt