Global optimization method for design problems

Abstract

In structural design optimization method, 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, remains 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 Penalty Simultaneous Perturbation Stochastic Approximation algorithm (ASAPSPSA) that uses Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the traditional simulated annealing algorithm that gives 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 hybridization of both techniques ASA and PSPSA provides a powerful hybrid heuristic optimization method; the proposed method is applicable to 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 ASAPSPSA 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 - 50 dimensions and then it is used in structural design to demonstrate its applicability and efficiency.