Designing bus line plans for realistic cases - the Utrecht case study

This paper presents an approach to design better line plans for realistic cases. The planning problem is modelled as a realistic instance of the Transit Network Design and Frequency Setting Problem (TNDFSP). It incorporates additional assumptions taken from practice such as discrete frequencies, a subset of allowed terminal nodes and circular lines. A bi-objective memetic algorithm minimizes the average travel time (ATT) of the passengers and the fleet size. The method to generate the TNDFSP instance from real data is described in detail. Moreover, a new metric is proposed to compare different transit networks. In order to illustrate the approach, it is applied to the area of Utrecht, The Netherlands. The results show that the current network is modelled accurately and that the algorithm successfully generates alternative bus line plans within reasonable CPU time. It returns a subset of non-dominated solutions from which a compromise solution can be selected for practice. There are solutions with the same fleet size as the current solution, but a 6% lower ATT, or solutions with the same ATT, but a fleet size which is 19% smaller. Compared to the current network, the algorithm finds that it is convenient to substantially reduce the number of lines and to leave a small portion of demand unsatisfied. This paper also presents extensive experiments to test the impact of different assumptions about demand, bus capacity and minimum frequency.