Dynamic Traffic Assignment (DTA) refers to the procedure of assigning trips to paths in a given transportation system considering the Origin-Destination pair (OD) flow demand and the network dynamic traffic states. This problem can be represented as a fixed-point problem. In a large-scale and trip-based setting, it is not possible to guarantee that fixed point algorithms converge towards the optimal. From a computational point of view, the main drawback of these methods for addressing DTA on large-scale networks is that they cannot be parallelized. This is because the existing algorithms need to know the last iteration results to determine the next best path flow for the next iteration. The goal of this study is to overcome the drawbacks of serial algorithms by using meta-heuristic algorithms that are known to be parallelizable. This study proposes two new solution methods: the new extension of the Simulated Annealing and adaptive Genetic Algorithm. With parallel simulation, the algorithm is going to run more simulations in comparison with existing methods, but it is expected to carry out a better exploration of the solution space and consequently achieve better solutions in terms of closeness to the optimal solution and computation time in comparison with classic methods.