Complementarity-based equilibrium computation methods for traffic flow management in intelligent transportation networks

Abstract

The intelligent transportation system needs a robust mathematical approach to compute equilibrium in the presence of intricate interactions between traffic flows, congestion effects, and network constraints. In this paper, proposes a novel equilibrium computation methodology based on complementarity, which formulates traffic flow management into a nonlinear complementarity problem and reformulates the problem using a variational inequality formulation. The approach uses monotone operator theory in establishing the equilibrium existence, uniqueness, convergence, and perturbation stability properties under the assumptions of continuity, strong monotonicity, and Lipschitz condition. A merit function is used based on the Fisher-Burmeister function to convert complementarity conditions to a smooth residual minimization problem and develop an iterative algorithm using a projection technique to solve the equilibrium problem efficiently. To provide theoretical results that show that the proposed method has linear convergence to the unique solution of the problem and bounded sensitivity to operator disturbance. Numerical simulations for large-scale transportation network problem instances show the better efficiency of the algorithm than Frank-Wolfe, Gradient Projection, and Extragradient methods in computing the equilibrium point with less equilibrium gap, complementarity residual, and faster convergence speed.