A Modified Levenberg-Marquardt (L-M) Algorithm for Traffic Equilibrium Problem with Nonadditive Route Costs

The traditional traffic equilibrium problem (TEP) is mainly based on the additivity assumption that the route cost is simply the sum of the link costs on that route. However, there are many situations where this assumption on the route costs is inappropriate, and thus we have to explicitly formulate and solve the TEP in the route space instead of link space. In this paper, we firstly reformulate the TEP with nonadditive route cost function to a nonlinear complementarity problem (NCP), and then the NCP is converted to an equivalent least square problem (LSP) with a new NCP function; then we propose a modified Levenberg- Marquardt algorithm to solve the LSP, and also, the quadratic convergence and the equivalent condition of the proposed L-M algorithm are proved under some assumptions. Finally, a numerical example is presented in the paper. As the results shown, the proposed method has the capability to converge to a high level accuracy with reasonable computational efforts.