Factors affecting the final solution of the bike-sharing rebalancing problem under heuristic algorithms

The bike-sharing rebalancing problem (BRP) belongs to a class of one-commodity pickup and delivery vehicle route problems (1-PDVRPs) which often must be solved using heuristic algorithms due to the large problem size. However, an open question is which factors affect the quality of the final solutions for the BRP with heuristic algorithms, and how they affect the solution quality. This study proposed six initial solution construction methods and two heuristic algorithms, and applied 32 instances to explore this question in greater depth. The results showed that problem size and the algorithms' searching capacity are the most important factors affecting the quality of final solutions. Furthermore, the influence of the quality and diversity of initial solutions cannot be ignored. The quality of final solutions is negatively correlated with problem size, and positively correlated with the algorithms' searching capacity, and the quality and diversity of initial solutions. The influence of the quality and diversity of initial solutions on the quality of final solutions is positively correlated with problem size. For algorithms with insufficient (powerful) searching capacity, the influence of the quality (diversity) of initial solutions is more significant than that of their diversity (quality). High-quality and rich-diversity initial solutions are very helpful for algorithms to find high-quality final solutions. In addition, the CPU time of heuristic algorithms is generally positively correlated with their searching capacity. These findings have certain universal applicability and reference value for solving the 1-PDVRPs with similar solution structures using heuristic algorithms.