Traffic equilibrium problem with route-specific costs: formulation and algorithms

Using a new gap function recently proposed by Facchinei and Soares [Facchinei, F., Soares, J., 1995. Testing a new class of algorithms for nonlinear complementarity problems. In: Giannessi, F., Maugeri, A. (Eds.), Variational Inequalities and Network Equilibrium Problems. Plenum Press, New York], we convert the nonlinear complementarity problem (NCP) formulation for the traffic equilibrium problem to an equivalent unconstrained optimization. This equivalent formulation uses both route flows and the minimum origin-destination travel costs as the decision variables. Two unique features of this formulation are that: (i) it can model the traffic assignment problem with a general route cost structure; (ii) it is smooth, unconstrained, and that every stationary point of the minimization corresponds to a global minimum. These properties permit a number of efficient algorithms for its solution. Two solution approaches are developed to solve the proposed formulation. Numerical results using a route-specific cost structure are provided and compared with the classic traffic equilibrium problem, which assumes an additive route cost function.