The Urban Transit Routing Problem (UTRP) comprises an NP-hard problem that deals with the construction of route networks for public transit networks. It is a highly complex and multiply constrained problem, in which the assessment of candidate route networks can be both time consuming and challenging. Except for that, a multitude of potential solutions are usually rejected due to infeasibility. Because of this difficulty, soft computing algorithms can be very effective for its efficient solution. The success of these methods, however, depends mainly on the quality of the representation of candidate solutions, on the efficiency of the initialization procedure and on the suitability of the modification operators used. An optimization algorithm, based on particle swarm optimization, is designed and presented in the current contribution, aiming at the efficient solution of UTRP. Apart from the development of the optimization algorithm, emphasis is also given on appropriate representation of candidate solutions, the route networks in other words, and the respective evaluation procedure. The latter procedure considers not only the quality of service offered to each passenger, but also the costs of the operator. Results are compared on the basis of Mandl's benchmark problem of a Swiss bus network, which is probably the only widely investigated and accepted benchmark problem in the relevant literature. Comparison of the obtained results with other results published in the literature shows that the performance of the proposed soft computing algorithm is quite competitive compared to existing techniques. 
Solving the Urban Transit Routing Problem using a particle swarm optimization based algorithm