This paper presents an efficient optimization procedure to find the optimal shapes of double curvature  arch  dams  considering  fluid–structure  interaction  subject  to  earthquake  loading. The optimization is carried out using a combination of the magnetic charged system search, big bang-big crunch algorithm and artificial neural network methods. Performing the finite element  analysis  during  the  optimization  process  is  time  consuming.  Back  propagation neural  network  is  utilized  to  reduce  the  computational  burden.  A  real-world  arch  dam  is considered as a numerical example to demonstrate the efficiency of the proposed method. The numerical results reveal the computational advantages of the new method for optimal 
design of arch dams.

For optimization of real-world arch dams, it is unavoidable to consider two or more conflicting objectives. This paper employs two multi-objective differential evolution algorithms (MoDE) in combination of a parallel working MATLAB-APDL code to obtain a set of Pareto solutions for optimal shape of arch dams. Full dam-reservoir interaction subjected to seismic loading is considered. A benchmark arch dam is then examined as the numerical example. The numerical results are compared to show the performance of the MoDE methods.