Learning to Select Customized Valid Cuts for Joint Pricing and Routing for 'Co-bus'

With the development of cities, public transportation problems such as traffic congestion, inconvenient transfers, and insufficient capability during peak periods are getting worse. In response to these problems, a novel operational mode that is inspired by the sharing economy has gained considerable attention, integrating private vehicles into traditional public transportation systems (referred to as "Cooperative-bus", "Co-bus" as an abbreviation). In this mode, pricing plays a crucial role in determining the service capacity of social resources, but traditional research rarely considers this aspect. Therefore, this study aims to design pricing strategies and vehicle routing plans simultaneously to fill the gap between supply and demand. To address this issue, we establish a mixed integer programming (MIP) model for pricing and routing and propose a series of customized valid cuts to enhance the computation efficiency of the branch and bound algorithm. Since the valid cuts improve the relaxation boundaries while increasing the number of constraints, the efficiency does not necessarily increase with the increase of the number of cuts. In order to obtain the optimal cut combination in different cases, we employ Machine Learning techniques and simultaneously customize statistical features. Numerical experiments demonstrate the superiority of adaptive valid cut selection, with our predictive model achieving a remarkable 96.43% accuracy.