Transportation Network Design Under Passenger Choice

The transportation network design problem has been extensively studied in the literature, with most prior research assuming that passenger demand is exogenously determined. However, in practical scenarios, demand is inherently influenced by service quality, which is significantly shaped by the network design itself. Accounting for this endogenous relationship introduces substantial complexity to the problem. In this work, we introduce a practically relevant class of mixed-integer non-convex optimization problems for network design, unified by shared mathematical properties that serve as the foundation of this study. We present a general compact formulation for this class of problems and evaluate three solution approaches: Adaptive Discretization, Exponential Cone Programming, and a convex reformulation augmented with sparsity. Through extensive computational experiments on both simulated and real-world networks, we demonstrate that all three methods achieve optimal or near-optimal solutions for small-scale problems. Among these, convex sparsity-based reformulation stands out for its scalability, exploiting the sparse structure of the matrices characteristic of transportation network design problems. This approach delivers solutions within an optimality gap of 5 % in all instances tested and outperforms other methods in terms of computational efficiency for larger problem sizes.