Cooperatively coevolutionary optimization design of limited-stop services and operating frequencies for transit networks

The objective of the limited-stop service design and frequency setting problem (LSDFSP) is to realize the operation of a transit route with a set of elaborate service patterns and corresponding frequencies that can minimize the total social cost of the users and operators. In practice, these different patterns and frequencies involve a trade-off between the user and operator requirements, and this aspect cannot be fully clarified by a single-objective optimization problem. Therefore, in this study, the LSDFSP is considered at the network level and formulated as a multi-objective optimization problem with competing objectives of minimizing the user and operator costs. The cooperative coevolutionary multi-objective evolutionary algorithm is redesigned to collaboratively optimize the service patterns and frequencies. A prioritization method is proposed to separately incorporate different types of unsatisfied demand as critical indicators, prompting the algorithm to dig deeper into valuable genes and evolve more feasible solutions. The proposed algorithm is tested on a small network and a real intricate network. It is noted that higher frequencies increased the fleet size and decreased the users’ waiting time and in-vehicle time. Furthermore, skipping more stations reduced the fleet size and users’ in-vehicle time, while increasing the users’ waiting time and number of transfers. The computational results indicated that the proposed algorithm can suitably incorporate the trade-offs and generate an accurate set of Pareto-optimal solutions