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Computational Statistics & Data Analysis
Volume 52, Issue 1, 15 September 2007, Pages 133-149
 
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doi:10.1016/j.csda.2006.12.011    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2006 Elsevier B.V. All rights reserved.

Synthesis of the β-distribution as an aid to stochastic global optimization

M.M. AliCorresponding Author Contact Information, a, E-mail The Corresponding Author

aSchool of Computational and Applied Mathematics, Witwatersrand University, Johannesburg, South Africa

Available online 2 January 2007.

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Abstract

The β-distribution is used as a point generation scheme in global optimization. Two population set-based global optimization algorithms are considered. These are the differential evolution (DE) and the controlled random search (CRS) algorithms. The point generation schemes of DE and CRS are hybridized with the β random variate. The hybridization uses a probabilistic combination of the point generation by the β-distribution and the point generation by DE or CRS. Numerical experiments are carried out using both test and practical problems. Numerical results suggest that the resulting algorithms are superior to their respective original counterpart.

Keywords: Global optimization; Population set; β-Distribution; Continuous variable; Probabilistic adaptation; Hybrid

Article Outline

1. Introduction
2. Brief descriptions of CRS and DE
2.1. The CRS algorithm
2.2. The DE algorithm
3. The self-adjusting β-density
3.1. Use of the β-distribution in CRS2 and DE
3.2. Implementation of β-distribution
4. Probabilistic combination of point generation schemes
4.1. CRS2C: a joint scheme in CRS2
4.2. DEC: a joint scheme in DE
5. Practical problem
5.1. The pig-liver likelihood (PL) function
6. Numerical results
6.1. Parameter value selection
6.2. Comparison
6.3. Comparison using PL function
6.4. Probabilistic adaptation
7. Conclusion
Acknowledgements
Appendix A. Proof of Lemma 1
Appendix B. Proof of Lemma 2
References





 
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