The aim of this study is to solve the large?scale dynamic traffic assignment (DTA) model using a simulation?based framework, which is computationally a challenging problem. Many studies have been performed on developing an efficient algorithm to solve DTA. Most of the existing algorithms are based on path?swapping descent direction methods. From the computational standpoint, the main drawback of these methods is that they cannot be parallelized. This is because the existing algorithms need to know the results of the last iteration to determine the next best path flow for the next iteration. Thus, their performance depends on the single initial or intermediate solution, which means they exploit a solution that satisfies the equilibrium conditions more than explore the solution space for the optimal solution. More specifically, the goal of this study is to overcome the drawbacks of serial algorithms by using meta?heuristic algorithms known to be parallelizable and that have never been applied to the simulation?based DTA problem. This study proposes two new solution methods: a new extension of the simulated annealing and an adapted genetic algorithm. With parallel simulation, the algorithm runs more simulations in comparison with existing methods, but the algorithm explores the solution space better and therefore obtains better solutions in terms of closeness to the optimal solution and computation time compared to classical methods.