Multi-Criteria traffic network equilibrium problems with flexible demands and capacity constraints of arcs

Abstract

This paper mainly deals with a multi-criteria traffic network equilibrium problem with flexible demands and capacity constraints of arcs. A multi-objective minimum cost flow problem with flexible demands is firstly introduced. A set of (weak) vector minimum cost flows is obtained by using an inexact multi-objective augmented Lagrangian method. Since (weak) vector minimum cost flows may not be a (weak) vector equilibrium flows, we pay attention to constructing equivalent optimization problems for weak vector equilibrium flows and vector equilibrium flows in terms of an activation function ReLU and a vector version of the Heaviside step function, respectively. In addition, numerical methods based on smoothing the objective functions are proposed to generalize the set of the (weak) vector equilibrium flows. Finally, extensive numerical examples are given to illustrate excellence of our algorithms compared with existing algorithms. It is shown that the proposed smoothing method is more efficient and can find more vector equilibrium flows.