The main aim of this study is to propose an efficient meta-heuristic algorithm for topology optimization of geometrically nonlinear single layer domes by serially integration of computational advantages of firefly algorithm (FA) and particle swarm optimization (PSO). During the optimization process, the optimum number of rings, the optimum height of crown and tubular section of the member groups are determined considering geometric nonlinear behaviour of the domes. In the proposed algorithm, termed as FA-PSO, in the first stage an optimization process is accomplished using FA to explore the design space then, in the second stage, a local search is performed using PSO around the best solution found by FA. The optimum designs obtained by the proposed algorithm are compared with those reported in the literature and it is demonstrated that the FA-PSO converges to better solutions spending less computational cost emphasizing on the efficiency of the proposed algorithm.