Papers by Keyword: Simultaneous Perturbation Stochastic Approximation

Abstract: The aim of this paper is to study the implementation of an efficient and reliable methodology for shape optimization problems where the objective function and constraints are not known explicitly and are dependent on the Finite Element Analysis (FEA). It is based on the Simultaneous Perturbation Stochastic Approximation (SPSA) method for solving unconstrained continuous optimization problems. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems, the constraints are handled using exterior point penalty functions within an algorithm that combines SPSA and exact penalty transformations. This paper presents a new structural optimization methodology that combines shape optimization, geometric modeling, FEA and PSPSA method to successfully optimize structural optimization problems. Several tests have been performed on some well known benchmark functions to demonstrate the robustness and high performance of the suggested methodology. In addition, an illustrative two-dimensional structural problem has been solved in a very efficient way. The numerical results demonstrate the robustness and high performance of the suggested methodology for structural optimization problems.

Abstract: In structural design optimization, numerical techniques are increasingly used. In typical structural optimization problems there may be many locally minimum configurations. For that reason, the application of a global method, which may escape from the locally minimum points, remain essential. In this paper, a new hybrid simulated annealing algorithm for global optimization with constraints is proposed. We have developed a new algorithm called Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the Basic Simulated Annealing algorithm ( BSA) that gives the region containing the global solution of an objective function. In addition, the stochastic method Simultaneous Perturbation Stochastic Approximation (SPSA), for solving unconstrained optimization problems, is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The proposed method is applicable for any problem where the topology of the structure is not fixed, it is simple and capable of handling problems subject to any number of nonlinear constraints. Extensive tests on the ASA as a global optimization method are presented, its performance as a viable optimization method is demonstrated by applying it first to a series of benchmark functions with 2 - 30 dimensions and then it is used in structural design to demonstrate its applicability and efficiency. It is found that the best results are obtained by ASA compared to those provided by the commercial software ANSYS.