A multi-arm bandit neighbourhood search for routing and scheduling problems

Abstract Local search based meta-heuristics such as variable neighbourhood search have achieved remarkable success in solving complex combinatorial problems. Local search techniques are becoming increasingly popular and are used in a wide variety of meta-heuristics, such as genetic algorithms. Typically, local search iteratively improves a solution by making a series of small moves. Traditionally these methods do not employ any learning mechanism. We treat the selection of a local search neighbourhood as a dynamic multi- armed bandit (D-MAB) problem where learning techniques for solving the D-MAB can be used to guide the local search process. We present a D-MAB neighbourhood search (D-MABNS) which can be embedded within any meta- heuristic or hyperheuristic framework. Given a set of neighbourhoods, the aim of D-MABNS is to adapt the search sequence, testing promising solutions rst. We demonstrate the eectiveness of D-MABNS on two vehicle routing and scheduling problems, the real-world geographically distributed mainte- nance problem (GDMP) and the periodic vehicle routing problem (PVRP). We present comparisons to benchmark instances and give a detailed analysis of parameters, performance and behaviour. Keywords Meta-heuristic Local search Vehicle routing