A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs

This paper considers solving a special case of the nonadditive traffic equilibrium problem presented by Gabriel and Bernstein in which the cost incurred on each path is made up of the sum of the arc travel times plus a path-specific cost for traveling on that path. A self-adaptive projection and contraction method is suggested to solve the path-specific cost traffic equilibrium problem, which is formulated as a nonlinear complementarity problem. The computational effort required per iteration is very modest. It consists of only two function evaluations and a simple projection on the nonnegative orthant. A self-adaptive technique is embedded in the projection and contraction method to find suitable scaling factor without the need to do a line search. The method is simple and has the ability to handle a general monotone mapping F. Numerical results are provided to demonstrate the features of the projection and contraction method.