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

Takafumi Matsuura,Tohru Ikeguchi,Honami Tsushima

doi:10.3390/app11167749

Takafumi Matsuura, Tohru Ikeguchi + Show 1 more

Open Access

https://doi.org/10.3390/app11167749

Copy DOI

Abstract

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.

Highlights

In recent years, bicycle sharing systems (BSSs) have been implemented in many cities around the world to ease traffic jams in town centers, to reduce CO2 emissions and to improve public health [1]
If an optimal solution was not obtained within 12 h, the best solution obtained within that period was output
If the CPU time was less than 43,200 [s] (=12 [h]), an optimal solution was obtained by the Gurobi optimizer

Summary

Introduction

Bicycle sharing systems (BSSs) have been implemented in many cities around the world to ease traffic jams in town centers, to reduce CO2 emissions and to improve public health [1]. In BSSs, when many bicycles are used, the number of bicycles at each port becomes unbalanced, because almost all users conduct round trips and one-way trips To overcome this problem, capacitated vehicles restore the required number of bicycles to the rental ports. Many researchers have investigated the optimum rebalancing of the bicycles with BSSs. Chemla et al (2013) [2] proposed a branch-and-cut-algorithm for finding an optimal solution to the static rebalancing problem using a single vehicle with up to 100 ports. Chemla et al (2013) [2] proposed a branch-and-cut-algorithm for finding an optimal solution to the static rebalancing problem using a single vehicle with up to 100 ports The results of their numerical experiments demonstrated that their method is very efficient up to 60 ports [2]. They reported that for up to 50 ports, their proposed method performed better than their previous method [3]

Methods

Results

Conclusion