Bi-level optimization in transportation analysis

This paper presented a unified description of the transportation bi-level optimization problems with user equilibirium constraints. Specifically, the network link capacity expansion problem, the road toll pricing problem and the optimal signal timing problem are discussed. The traditional bi-level model formulation of these problems is transformed into a single-level continuously differentiable problem using a marginal function approach. An efficient partially penalized method is used to solve the resulting single-level differentiable optimization problems. The methods are illustrated with simple analytical examples. The marginal function approach proves to be very promising in dealing with the transportation bi-level optimization problems with user equilibrium constraints.