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A hybrid meta-heuristic optimization method is introduced to efficiently find the optimal shape of concrete gravity dams including dam-water-foundation rock interaction subjected to earthquake loading. The hybrid meta-heuristic optimization method is based on a hybrid of gravitational search algorithm (GSA) and particle swarm optimization (PSO), which is called GSA-PSO. The operation of GSA-PSO includes three phases. In the first phase, a preliminary optimization is accomplished using GSA as local search. In the second phase, an optimal initial swarm is produced using the optimum result of GSA. Finally, PSO is employed to find the optimum design using the optimal initial swarm. In order to reduce the computational cost of dam analysis subject to earthquake loading, weighted least squares support vector machine (WLS-SVM) is employed to accurately predict dynamic responses of gravity dams. Numerical results demonstrate the high performance of the hybrid meta-heuristic optimization for optimal shape design of concrete gravity dams. The solutions obtained by GSA-PSO are compared with those of GSA and PSO. It is revealed that GSA-PSO converges to a superior solution compared to GSA and PSO, and has a lower computation cost.

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This study focuses on the shape optimization of concrete gravity dams considering dam–water–foundation interaction and nonlinear effects subject to earthquake. The concrete gravity dam is considered as a two–dimensional structure involving the geometry and material nonlinearity effects. For the description of the nonlinear behavior of concrete material under earthquake loads, the Drucker–Prager model based on the associated flow rule is adopted in this study. The optimum design of concrete gravity dams is achieved by the hybrid of an improved gravitational search algorithm (IGSA) and the orthogonal crossover (OC), called IGSA–OC. In order to reduce the computational cost of optimization process, the support vector machine approach is employed to approximate the dam response instead of directly evaluating it by a time–consuming finite element analysis. To demonstrate the nonlinear behavior of concrete material in the optimum design of concrete gravity dams, the shape optimization of a real dam is presented and compared with that of dam considering linear effect.

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The paper deals with the reliability–based design optimization (RBDO) of concrete gravity dams subjected to earthquake load using subset simulation. The optimization problem is formulated such that the optimal shape of concrete gravity dam described by a number of variables is found by minimizing the total cost of concrete gravity dam for the given target reliability. In order to achieve this purpose, a framework is presented whereby subset simulation is integrated with a hybrid optimization method to solve the RBDO approach of concrete gravity dam. Subset simulation with Markov Chain Monte Carlo (MCMC) sampling is utilized to estimate accurately the failure probability of dams with a minimum number of samples. In this study, the concrete gravity dam is treated as a two–dimensional structure involving the material nonlinearity effects and dam–reservoir–foundation interaction. An efficient metamodel in conjunction with subset simulation–MCMC is provided to reduce the computational cost of dynamic analysis of dam–reservoir–foundation system. The results demonstrate that the RBDO approach is more appropriate than the deterministic optimum approach for the optimal shape design of concrete gravity dams.