Tolerance-based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem

Abstract

The column generation (CG) algorithm has been widely applied to traffic assignment problems due to its capability of circumventing path enumeration. Incorporating bounded rationality (BR) and dynamics, this paper proposes four tolerance-based strategies for extending the CG algorithm to the bounded rational dynamic user equilibrium model (BR-DUE): (i) a tolerance-based minimum disutility path search strategy is developed to allow travelers seeking satisfactory paths; (ii) a self-adjusted convergence threshold strategy is applied for fast convergence at the intermediate iterations; (iii) a varied temporal resolution scheme, combining exploration and exploitation, is suggested to assign flows to narrow time regions rather than to the whole time horizon; and (iv) a path search skipping strategy is introduced by comparing the lower bound of travel disutility and the minimum disutility between the OD pairs. With these strategies, an efficient tolerance-based column generation (TBCG) algorithm for BR-DUE is developed. Numerical examples are provided to demonstrate that the TBCG algorithm leads to significant computation time reductions without the expense of solution quality, of which the speedup factors are around two compared with using the original CG algorithm.