New Mathematical Modeling to Optimize the Frequency of Bus Routes

The public transport system must be structured to ensure the constancy of activities, the maintenance of demand, and financial stability, in which the frequency of service plays a crucial role. This paper introduces a new mathematical model and two optimization techniques to improve bus route frequency. The objective is to minimize social, operational, and environmental costs. The model comprises a mixed-integer nonlinear formulation, and the optimization techniques involve linearization and a heuristic approach, which is based on sequentially solving relaxed mixed-integer subproblems and fixing integer variables throughout the process. As a case study, we consider the bus routes connecting the central and oceanic regions of Niterói, Brazil. The results indicate that the combined approach has good application in real-world scenarios, positively contributing to sustainable mobility by making the best fleet allocation based on existing demand.