Mixed-integer second-order cone programming model for bus route clustering problem

Bus route clustering problem (BRCP) concerns the assignment of bus routes to different boarding locations of a bus station with the objective of minimizing passenger waiting time. In this study, we formulate the BRCP as a mixed-integer second-order cone program (MISOCP). Simulations are conducted, in which the MISOCP model is applied to a major bus station in Hong Kong based on the network of actual bus routes. Experiments are tested for large size instances under different scenarios. Results show that the complexity of the BRCP is highly dependent on the overlapping degree of bus networks, while other factors, including the number of bus routes, destinations, and boarding locations have a joint effect; the influence is instance-specific based on different overlapping topologies of bus route networks.