This study reviews existing computational methods to calculate simulation-based dynamic network equilibrium. We consider a trip-based multi-modal approach for the dynamic network loading. Mode and path choices are carried out at the same level; therefore, travel times depend on the travel path and the mode attributes of travelers. This study develops a multi-class model with several parameters per class. Two different categories of algorithms (heuristic and meta-heuristic) are considered in order to solve the discrete DTA problem. Finally, we analyze the equilibrium in a large-scale multi-modal DTA test case (Lyon 6th + Villeurbanne) in order to investigate the performance of different optimization approaches to solve trip-based DTA. The results show that, in a multimodal and heterogeneous setting, the meta-heuristic methods provide better solutions than the heuristic methods in terms of optimality and computation time. These improvements are even more significant than in a homogeneous setting.