Material handling is a widely used process in manufacturing and is generally considered a non-value-added process. The Dynamic Facility Layout Problem (DFLP) considered in this paper minimizes the total material handling and re-arrangement cost. In this study, an integrated DFLP model with unequal facility areas, assignment of material handling devices (MHD), and flexible bay structure (FBS) is considered, and it is aimed to propose fast solution approaches. Two different solution methods are proposed for the problem, which are the genetic algorithm and the simulated annealing algorithm, respectively. In both methods, a non-linear mathematical model solution was used to calculate the fitness values. Thus, the solutions in the feasible solution space are utilized. The proposed solution approaches were applied to solve four problems published in the literature. The computational experiments have validated the effectiveness of the algorithms and the quality of solutions produced.