This paper proposes a novel hybrid algorithm in which simulated annealing algorithm starts with a population of good initial solutions constructed by combining ant colony, clonal selection, and robust layout design approaches. The proposed algorithm can be used to solve a dynamic (multi-period) facility layout problem in both deterministic and stochastic cases. In the stochastic environment, product demands are assumed to be normally distributed random variables with known probability density function that changes from period to period at random. In addition, a quadratic assignment-based mathematical model, which is used in the proposed hybrid algorithm, is developed to design a robust layout for the stochastic dynamic layout problem. Finally, the performance of the proposed algorithm is evaluated by solving a large number of randomly generated test problems and some test problems from the literature in stochastic and deterministic cases respectively. The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time points of view.