Formulating multi-class user equilibrium using mixed-integer linear programming

Abstract

We introduce an approach to formulate and solve the multi-class user equilibrium traffic assignment as a mixed-integer linear programming (MILP) problem. Compared to simulation approaches, the analytical MILP formulation makes the solution of network assignment problems more tractable. When applied in a multi-class context, it obviates the need to assume a symmetrical influence between classes and thereby allows richer traffic behavior to be taken into account. Also, it integrates naturally in optimization problems such as maintenance planning and traffic management. We develop the model and apply it for the Sioux Falls network, showing that it outperforms the traditional Beckmann-based and MSA approaches in smaller-scale problems. Further research opportunities lie in developing extensions of MILP-based assignment, with different variants of user equilibrium or dynamic assignment, and in improving the model and solution algorithms to allow large-scale application.