A cooperative coevolutionary optimization design of urban transit network and operating frequencies

Abstract The transit network design and frequency setting problem (TNDFSP) is a complex combinatorial optimization problem. Generally, the nature of multiobjective in TNDFSP has not attracted enough attention, and the frequency setting is directly embedded as a subproblem to generate a unique set of frequencies for a given transit network, ignoring trade-off solutions among multiple objectives with different sets of frequencies. In this study, the problem is formulated as a multiobjective model with two conflicting objectives of minimizing passengers’ and operators’ costs. Moreover, we establish two populations to simultaneously optimize networks and frequencies. Also a cooperative coevolutionary multiobjective evolutionary algorithm (CCMOEA) is developed to collaboratively coevolve these two populations along multiple objectives. Unsatisfied demand is embedded into the individual prioritization process, and infeasible individuals can be retained instead of being replaced arbitrarily, driving the evolution to gradually generate more feasible solutions. The proposed CCMOEA is tested on the well-known Mandl’s benchmark. The results show that our algorithm can efficiently produce a comprehensive set of high-quality trade-off solutions. These solutions perform well with lower waiting time, competitive in-vehicle travel time and number of transfers, resulting in lower user costs than previously published results in the same fleet size.