Tolerance-based column generation for boundedly rational dynamic activity-travel assignment in large-scale networks

Boundedly rational dynamic activity-travel assignment (BR-DATA) endogenously integrates activity-travel scheduling and dynamic traffic assignment to determine the interaction between land use transport supplies and activity-travel demands of boundedly rational travelers. The combinatorial explosion of activity-travel patterns (ATPs) involving multi-dimensional choice facets poses severe challenges to the model applicability in large networks. This study refines a tolerance-based column generation (TBCG) algorithm for solving BR-DATA problems in multi-state supernetworks without ATP enumeration. The refined TBCG algorithm employs spatial-temporal exploration to allocate activity-travel flows only to potential ATPs in the intermediate assignment process. The spatial-temporal exploitation intensifies ATP generation and network loading, which results in fewer iterations and ultimately substantial speedups compared with the original column generation algorithm. We prove that the TBCG algorithm is capable of finding solutions that satisfy the BR-DATA user equilibrium conditions. A series of numerical examples demonstrate that the TBCG algorithm has a speedup factor larger than two whilst producing approximately the same BR-DATA solutions as the original column generation algorithm.