Abstract
In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known DIRECT (DIviding RECTangles) method called SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented.
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Notes
Other examples can be found in [7, 11, 31, 36] and on the web site http://www.geatbx.com/docu/fcnindex-01.html.
All the experiments were executed on a computer with a 2.00 GHz Intel Pentium Core 2 Duo CPU with 4GB of RAM.
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Acknowledgments
The authors would like to thank Prof. Sanjo Zlobec (McGill University, Montreal, Canada) and Prof. Dragan Jukić and Prof. Kristian Sabo (University of Osijek, Croatia) for their useful comments and remarks. We are also thankful to anonymous referees and journal editors for their careful reading of the paper and insightful comments that helped us improve the paper. This work is supported by the Ministry of Science, Education and Sports, Republic of Croatia, through research grants 235-2352818-1034 and 165-0361621-2000.
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Grbić, R., Nyarko, E.K. & Scitovski, R. A modification of the DIRECT method for Lipschitz global optimization for a symmetric function. J Glob Optim 57, 1193–1212 (2013). https://doi.org/10.1007/s10898-012-0020-3
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DOI: https://doi.org/10.1007/s10898-012-0020-3