Keywords: arch dam, earthquake loading, optimum design, simultaneous perturbation stochastic approximation, genetic algorithm.

It was found that some methods such as simultaneous perturbation stochastic approximation (SPSA) are computationally efficient for gradient approximations. This method can predict gradient approximation that requires only two measurements of the objective function regardless of the dimensions of the optimisation problem. This feature allows for a significant reduction in cost of optimisation, especially in problems with a large number of variables to be optimized [1,2]. On the other hand, evolutionary algorithms are a robust tool to find proper design optimisation in comparison with gradient based methods. Due to the significant computational effort required by the GA, a combination of SPSA and GA can result in an appropriate optimisation method.

Optimal design of arch dams, with frequency constraints, has been performed in reference [3]. In this study, an efficient method is presented to find optimal shape of arch dams subject to earthquake loading utilizing a combination of SPSA and genetic algorithm methods. This new method is called simultaneous perturbation genetic algorithm (SPGA). Operation of SPGA includes three phases. In the first phase, a preliminary optimisation is achieved using SPSA. In the second phase, an optimal initial population is generated using the first phase results. The optimum design found by SPSA is copied many times to create the main part of the initial population. The rest individuals are selected on the random basis. This method of initial population generation is inspired by reference [4] In the last phase, the GA is employed to find an optimum design using the optimal initial population generated in the second phase.

The response spectrum analysis of arch dam is performed according to the Iranian code. The arch dam cost is considered as objective function.

The numerical results reveal the robustness and high performance of the suggested method for optimum design of arch dams. Also, It is observed that the SPGA is converged to better optimum design than the SPSA and GA.

In the full length paper, the arch dam model and the utilized SPGA method are explained in detail.

1

Spall J.C., "An Overview of the Simultaneous Perturbation Method for Efficient Optimisation", Johns Hopkings APL Technical Digest, 19(4):482-492, 1998.

2

Spall J.C., Introduction to Stochastic Search and Optimisation: Estimation, Simulation and Control. John Wiley and Sons, Inc., 2003. doi:10.1002/0471722138

3

J. Salajegheh, E. Salajegheh, S. Gholizadeh and S.M. Seyedpoor, "Optimum Design of Arch Dams with Frequency Constraints Using Wavelet Neural Networks", in Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil- Comp Press, Stirlingshire, United Kingdom, paper 60, 2006. doi:10.4203/ccp.84.60

4

Salajegheh E, Gholizadeh S., "Optimum design of structures by an improved genetic algorithm and neural networks", Advances in Engineering Software, 36(11-12):757-767, 2005. doi:10.1016/j.advengsoft.2005.03.022

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