An artificial fish swarm optimization algorithm for the urban transit routing problem

The Urban Transit Routing Problem (UTRP) is an NP-hard discrete problem that deals with the design of routes for public transport systems. It is a highly complex, multiply constrained problem, while the evaluation of candidate route sets can prove both challenging and time-consuming, with many potential solutions rejected on the grounds of infeasibility. Due to its difficulty, metaheuristic methods, such us swarm intelligence algorithms, are considered highly suitable for the UTRP. The suitability of these methods heavily relies on the correct adaptation of the chosen method for a discrete-space problem, the initialization procedure, and the solution evaluation method. In this context, this study proposes an artificial fish swarm optimization algorithm for the efficient solution of the UTRP, presenting a novel discrete-space adaptation of the former. The results are subsequently compared to 14 other algorithms, including evolutionary, swarm intelligence and hyper-heuristic implementations, using Mandl's widely used and accepted benchmark. Comparison of the produced solutions with published results on Mandl's benchmark network, shows that the developed algorithm yields superior results to the existing techniques, yielding very high shares of direct trip coverage, which is vital for transit systems to attract riders and contribute to urban sustainability. A new indicator for operator cost calculation is also developed and integrated into our analysis, offering insights on the trade-offs between user and operator costs. Differences in generated solutions, influenced by the weighting factor value, can result in variations of up to 13% in direct trip coverage and 1.5 minutes in average travel time.