Geodesic
A Global Stochastic Optimization Method for Large Scale Problems
W. El Alem1, 2 ; A. El Hami2 ; R. Ellaia1
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
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 97-102.

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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
DOI : 10.1051/mmnp/20105716

W. El Alem 1, 2 ; A. El Hami 2 ; R. Ellaia 1

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 
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W. El Alem; A. El Hami; R. Ellaia. A Global Stochastic Optimization Method for Large Scale Problems. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 97-102. doi : 10.1051/mmnp/20105716. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105716/

[1] M. S. Arumugam, M. V. C. Rao, A. W. C. Tan A novel and effective particle swarm optimization like algorithm with extrapolation technique Applied Soft Computing 2009 308 320

[2] A. Georgieva, I. Jordanov Global optimization based on novel heuristics, low-discrepancy sequences and genetic algorithms European Journal of Operational Research 2009 413 422

[3] W. Gong, Z. Cai, L. Jiang Enhancing the performance of differential evolution using orthogonal design method Applied Mathematics and Computation 2008 56 69

[4] Z. Huang, X. Miao, P. Wang A revised cut-peak function method for box constrained continuous global optimization Applied Mathematics and Computation 2007 224 233

[5] D. G. Luenberger. Introduction to linear and nonlinear programming. Addison Wesley, 1973.

[6] S. Sitarz Ant algorithms and simulated annealing for multicriteria dynamic programming Computers and Operations Research 2009 433 441

[7] J. C. Spall Multivariate stochastic approximation using a simultaneous perturbation gradient approximation IEEE Transactions on Automatic Control 1992 332 341

[8] J. C. Spall Adaptive stochastic approximation by the simultaneous perturbation method IEEE Transactions on Automatic Control 2000 1839 1853

[9] PJM. Van Laarhoven, EHL. Aarts. Simulated annealing: theory and applications. Dordrecht: D. Reidel Publishing Company, Kluwer, 1987.

[10] L. Wang, K. Chen, Y. S. Ong (Eds). Advances in Natural Computation. Part III, Springer Science Business Publisher, Changsha, China, 2005.

[11] C. Wang, Y. Yang, J. Li A new filled function method for unconstrained global optimization Journal of Computational and Applied Mathematics 2009 68 79

[12] Y. J. Wang, J. S. Zhang An efficient algorithm for large scale global optimization of continuous functions Journal of Computational and Applied Mathematics 2007 1015 1026

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