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.

本文研究了在全球广泛部署的现代自行车共享系统中经常遇到的自行车共享重新定位问题（BSRP）。为了应对客户需求波动并提高服务水平，BSRP旨在确定访问共享单车站的最佳车辆路线，以平衡其库存，从多余的站点取回多余的自行车以及将所需的自行车添加到不足的站点，目的是使总旅行成本和库存成本最小化。首先给出了所研究问题的数学模型，详细介绍了可用于重新定位车辆的多个仓库的考虑因素以及最小化库存成本的额外目标。然后提出了一种有效的集群策略，将自行车共享站点划分为自给自足的群体，它被证明能够极大地分解大型实例的问题复杂性。开发了销毁修复算法以改善集群，并设计了自适应可变邻域搜索算法来进行集群内和集群间车辆路线优化。在三组基准实例上验证了混合算法的性能，并将其与CPLEX以及文献中的最新算法进行了比较，这表明所提出的算法在解决BSRP方面具有很高的竞争力。