A non-smooth model for signalized road network design problems

A signalized road network is considered where the set of link capacity expansions and signal setting variables are simultaneously determined. This paper addresses a new optimization scheme for a signalized road network design problem (SRNDP). A SRNDP can be formulated as a mathematical program with equilibrium constraints (MPEC) where user equilibrium is expressed as a variational inequality problem. Due to non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth model is established. A bundle subgradient projection (BSP) method is presented with global convergence. Numerical calculations are conducted on a real data city road network and large-scale grid networks where promising results are obtained.