A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem

In this study, we propose a novel multi-objective nonlinear mixed-integer mathematical programming model for the transit network design and frequency setting problem that aims at designing the routes and determining the frequencies of the routes to satisfy passenger demand in a transit network. The proposed model incorporates the features of real-life transit network systems and reflects the views of both passengers and the transit agency by considering the in-vehicle travel time, transfers, waiting times at the boarding and transfer stops, overcrowding and under-utilization of vehicles, and vehicle fleet size. Unlike previous studies that simplify several aspects of the transit network design and frequency setting problem, the proposed model is the first to determine routes and their frequencies simultaneously from scratch, i.e., without using line and frequency pools while considering the aforementioned issues, such as transfers and waiting. We solve the proposed model using Gurobi. We provide the results of what-if analyses conducted using a real-world public bus transport network in the city of Kayseri in Türkiye. We also present the results of computational tests implemented to validate and verify the model using Mandl benchmark instances from the literature. The results indicate that the model produces better solutions than the state-of-the-art algorithms in the literature and that the model can be used by public transit planners as a decision aid.