Creating Very Large Scale Neighborhoods out of Smaller Ones by Compounding Moves: a Study on the Vehicle Routing Problem

Neighborhood search algorithms are a wide class of improvement algorithms where at each iteration an improving solution is found by searching the “neighborhood” of the current solution. This paper discusses neighborhood search algorithms where the size of the neighborhood is “very large” with respect to the size of the input data. For large problem instances, it is impractical to search these neighborhoods explicitly, and one must either search a small portion of the neighborhood or else develop efficient algorithms for searching the neighborhood implicitly. We concentrate on a very large scale neighborhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts, swaps, and insertions. We demonstrate that the search for an improving neighbor can be done by finding a negative cost path on an auxiliary graph. In this paper we study CIM algorithms for the vehicle routing problem with capacity and distance constraints. We present results of the computational study which indicates that the CIM algorithms for the capacitated vehicle routing problem are competitive with the current state of the art heuristics. (Very-large scale neighborhood search; Vehicle routing problem; Heuristics)