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A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

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2010
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Journal Article

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Woon, Siew Fang and Rehbock, Volker. 2010. A critical review of discrete filled function methods in solving nonlinear discrete optimization problems. Applied Mathematics and Computations. 217 (1): pp. 25-41.
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Applied Mathematics and Computations
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Department of Mathematics and Statistics
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NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in AppliedMathematics and Computations, 217, 1, 2010 DOI 10.1016/j.amc.2010.05.009

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Abstract

Many real life problems can be modeled as nonlinear discrete optimization problems. Such problems often have multiple local minima and thus require global optimization methods. Due to high complexity of these problems, heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems. One of the more recent global optimization tools is known as the discrete filled function method. Nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given. Some of the most promising filled functions are tested on various benchmark problems. Numerical results are given for comparison.