Optimum design in civil structures like domes and vaults is a very old and ongoing research field. These structures are preferably designed to transport loads via membrane action. In this paper, we have considered a reinforced concrete dome and vault, where the bending moment and strain energy were used as objective function to be minimized using genetic algorithm, and model reduction method by proper orthogonal decomposition based on the results of finite element analysis of gradually changed design parameters. The proposed approach results are of a high accuracy compared to finite element based optimization.