Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T02:08:49.330Z Has data issue: false hasContentIssue false
  • English
  • Français

A Global Stochastic Optimization Method for Large ScaleProblems

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
W. El Alem ,
A. El Hami  and
R. Ellaia
W. El Alem*
Affiliation:
Laboratory of study and research in applied mathematics, Mohammed V University EMI, BP. 765, Ibn Sina avenue, Agdal Rabat, Morocco Laboratory of mechanics of Rouen, national institute for applied sciences, Rouen BP 08, university avenue 76801 St Etienne du Rouvray Cedex, France
A. El Hami
Affiliation:
Laboratory of mechanics of Rouen, national institute for applied sciences, Rouen BP 08, university avenue 76801 St Etienne du Rouvray Cedex, France
R. Ellaia
Affiliation:
Laboratory of study and research in applied mathematics, Mohammed V University EMI, BP. 765, Ibn Sina avenue, Agdal Rabat, Morocco
*
* Corresponding author: E-mail:[email protected]
Get access

Abstract

In this paper, a new hybrid simulated annealing algorithm for constrained globaloptimization is proposed. We have developed a stochastic algorithm called ASAPSPSA thatuses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to thebasic simulated annealing algorithm (SA) that gives the region containing the globalsolution of an objective function. In addition, Simultaneous Perturbation StochasticApproximation (SPSA) method, for solving unconstrained optimization problems, is used torefine the solution. We also propose Penalty SPSA (PSPSA) for solving constrainedoptimization problems. The constraints are handled using exterior point penalty functions.The combination of both techniques ASA and PSPSA provides a powerful hybrid optimizationmethod. The proposed method has a good balance between exploration and exploitation withvery fast computation speed, its performance as a viable large scale optimization methodis 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 successfulresults were obtained

Keywords

global optimizationstructural optimizationsimultaneous perturbation stochastic approximation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 97 - 102
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arumugam, M. S., Rao, M. V. C., Tan, A. W. C.. A novel and effective particle swarm optimization like algorithm with extrapolation technique . Applied Soft Computing, 9 (2009), No. 1, 308–320.CrossRefGoogle Scholar
Georgieva, A., Jordanov, I.. Global optimization based on novel heuristics, low-discrepancy sequences and genetic algorithms . European Journal of Operational Research, 196 (2009), 413-422.CrossRefGoogle Scholar
Gong, W., Cai, Z., Jiang, L.. Enhancing the performance of differential evolution using orthogonal design method . Applied Mathematics and Computation, 206 (2008), No. 1, 56–69.CrossRefGoogle Scholar
Huang, Z., Miao, X., Wang, P.. A revised cut-peak function method for box constrained continuous global optimization . Applied Mathematics and Computation 194 (2007), No. 1, 224–233.CrossRefGoogle Scholar
D. G. Luenberger. Introduction to linear and nonlinear programming. Addison Wesley, 1973.
Sitarz, S.. Ant algorithms and simulated annealing for multicriteria dynamic programming . Computers and Operations Research, 36 (2009), No. 2, 433–441.CrossRefGoogle Scholar
Spall, J. C.. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation . IEEE Transactions on Automatic Control, 37 (1992), No. 3, 332–341.CrossRefGoogle Scholar
Spall, J. C.. Adaptive stochastic approximation by the simultaneous perturbation method . IEEE Transactions on Automatic Control, 45 (2000), No. 10, 1839–1853.CrossRefGoogle Scholar
PJM. Van Laarhoven, EHL. Aarts. Simulated annealing: theory and applications. Dordrecht: D. Reidel Publishing Company, Kluwer, 1987.
L. Wang, K. Chen, Y. S. Ong (Eds). Advances in Natural Computation. Part III, Springer Science & Business Publisher, Changsha, China, 2005.
Wang, C., Yang, Y., Li, J.. A new filled function method for unconstrained global optimization . Journal of Computational and Applied Mathematics, 225 (2009), No. 1, 68–79.CrossRefGoogle Scholar
Wang, Y. J., Zhang, J. S.. An efficient algorithm for large scale global optimization of continuous functions . Journal of Computational and Applied Mathematics, 206 (2007), No. 2, 1015–1026.CrossRefGoogle Scholar