Feasible and Descent Direction Method for Continuous Equilibrium Network Design Problem

In this study, we firstly express the stochastic user equilibrium traffic assignment problem in asymmetric traffic network as variation inequality model and then formulate ntinuous network design problem as mathematical program with equilibrium constraints. When path flow travel cost function is continuous, differentiable and strong monotone, the solution of variational inequality follows logit assignment principle and is unique. So mathematical program with equilibrium constraints can be written as an implicit optimization problem and the gradient of objective function is received by sensitivity analysis. A feasible and descent direction method is addressed where the direction can be computed with the sign of gradient and the step size can be calculated by operation of comparison. Finally, numerical experiments are conducted and calculation results show high efficiency of the proposed method in solving asymmetric equilibrium network design problem.