A hybrid algorithm for the static bike-sharing re-positioning problem based on an effective clustering strategy

Abstract This paper studies the bike-sharing re-positioning problem (BSRP) frequently encountered in modern bike-sharing systems that are widely deployed around the world. To cope with customer demand fluctuations and improve service level, BSRP aims to identify the optimal vehicle routes to visit bike-sharing stations in order to balance their inventories, picking up excess bikes from surplus stations and adding needed bikes to insufficient stations, with the objective of minimizing total traveling cost and inventory cost. The mathematical model of the studied problem is first given, detailing the considerations of multiple depots available for re-positioning vehicles and the extra objective of inventory cost minimization. An effective clustering strategy is then proposed to put bike-sharing stations into self-sufficient groups, which is shown to be able to greatly decompose the problem complexity for large-scale instances. A destroy-and-repair algorithm is developed to improve the clusters, and an adaptive variable neighborhood search algorithm is designed to conduct intra-cluster and inter-cluster vehicle routing optimization. Performance of the hybrid algorithm is validated on three sets of benchmark instances, and compared with CPLEX as well as state-of-the-art algorithms from the literature, which demonstrates that the proposed algorithm is highly competitive in solving BSRPs.