A two-stage linear programming model for efficient optimization of public transport network design

Public transport is essential for sustainable mobility, and optimized network design is crucial for making it competitive with other modes. While several network optimization methods exist, their practical use is limited due to assumptions, simplifications, and limited scope. This paper proposes a two-stage sequential linear programming approach for the transit network design and frequency setting problem that significantly cuts down computation times, enabling the solution of more comprehensive models. The first stage routes passengers along shortest paths, selects infrastructure to operate, and sets minimum aggregated frequencies. The second stage determines line designs and sets frequencies to minimize waiting times and transfers for passengers. We also introduce symmetry-breaking constraints to further speed up the optimization process. We evaluate the model performance using Mandl’s network by comparing it with a simultaneous optimization model in multiple scenarios (balancing operator and passenger objectives). Results show that the sequential optimization model runs over 180 times faster for operator-focused scenarios, while passenger-focused scenarios do not yet achieve the predicted computational efficiency. The sequential optimization model shows losses of 0.3-7.0-% optimality compared to the simultaneous optimization model. Overall, the model shows potential in significantly reducing the complexity of the transit network design problem.