Decomposition Strategies for Vehicle Routing Heuristics

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterization of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: We discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight their strengths and weaknesses, and derive a set of desirable properties. Through an extensive numerical campaign, we investigate the impact of decompositions within two algorithms for the capacitated vehicle routing problem: the Adaptive Large Neighborhood Search of Pisinger and Ropke (2007) and the Hybrid Genetic Search of Vidal et al. (2012). We evaluate the quality of popular decomposition techniques from the literature and propose new strategies. We find that route based decomposition methods, which define subproblems by means of the customers contained in selected subsets of the routes of a given solution, generally appear superior to path-based methods, which merge groups of customers to obtain smaller subproblems. The newly proposed decomposition barycenter clustering achieves the overall best performance and leads to significant gains compared with using the algorithms without decomposition.