A Global Stochastic Optimization Method for Large Scale Problems

¹ Laboratory of study and research in applied mathematics, Mohammed V University EMI, BP. 765, Ibn Sina avenue, Agdal Rabat, Morocco
² Laboratory of mechanics of Rouen, national institute for applied sciences, Rouen BP 08, university avenue 76801 St Etienne du Rouvray Cedex, France

^* Corresponding author: E-mail: welalem@yahoo.fr

Abstract

In this paper, a new hybrid simulated annealing algorithm for constrained global optimization is proposed. We have developed a stochastic algorithm called ASAPSPSA that uses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to the basic simulated annealing algorithm (SA) that gives the region containing the global solution of an objective function. In addition, Simultaneous Perturbation Stochastic Approximation (SPSA) method, 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 combination of both techniques ASA and PSPSA provides a powerful hybrid optimization method. The proposed method has a good balance between exploration and exploitation with very fast computation speed, its performance as a viable large scale optimization method is demonstrated by testing it on a number of benchmark functions with 2 - 500 dimensions. In addition, applicability of the algorithm on structural design was tested and successful results were obtained