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An efficient methodology is proposed to find optimal shape of arch dams on the basis of constrained natural frequencies. The optimization is carried out by virtual sub population (VSP) evolutionary algorithm employing real values of design variables. In order to reduce the computational cost of the optimization process, the arch dam natural frequencies are predicted by properly trained back propagation (BP) and wavelet back propagation (WBP) neural networks. The WBP network provides better generalization compared with the standard BP network. The numerical results demonstrate the computational merits of the proposed methodology for optimum design of arch dams.