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In bicycle sharing systems, many vehicles restore bicycles to ports. To construct the shortest tour of these vehicles, in a previous work, we formulated the multiple-vehicle bike sharing system routing problem (mBSSRP) and demonstrated that an optimal solution can be obtained for small-sized instances through a general-purpose mixed-integer linear programming solver. However, for large-sized instances, the optimal solution could not be found in a reasonable time frame. Therefore, to find near-optimal solutions for the mBSSRPs in a short time, in this study, we develop a method with a searching strategy, which explores both the feasible and infeasible solution spaces. To investigate the performance of the proposed method, we solve benchmark problems of mBSSRP. In addition, we compare the proposed method with the method exploring only the feasible solution space, in terms of performance. The results of the numerical experiments demonstrate that the proposed method can reach optimal solutions for almost all small-sized mBSSRP instances and that searching both the feasible and infeasible solution spaces yields good feasible solutions both for small-sized and large-sized instances.

Strategy for Exploring Feasible and Infeasible Solution Spaces to Solve a Multiple-Vehicle Bike Sharing System Routing Problem