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A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems

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Abstract

There is a need for a methodology to fairly compare and present evaluation study results of stochastic global optimization algorithms. This need raises two important questions of (i) an appropriate set of benchmark test problems that the algorithms may be tested upon and (ii) a methodology to compactly and completely present the results. To address the first question, we compiled a collection of test problems, some are better known than others. Although the compilation is not exhaustive, it provides an easily accessible collection of standard test problems for continuous global optimization. Five different stochastic global optimization algorithms have been tested on these problems and a performance profile plot based on the improvement of objective function values is constructed to investigate the macroscopic behavior of the algorithms. The paper also investigates the microscopic behavior of the algorithms through quartile sequential plots, and contrasts the information gained from these two kinds of plots. The effect of the length of run is explored by using three maximum numbers of function evaluations and it is shown to significantly impact the behavior of the algorithms.

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Authors and Affiliations

  1. School of Computational and Applied Mathematics, Witwatersrand University, Private Bag-3, Wits-2050, Johannesburg, South Africa

    M. Montaz Ali

  2. Industrial Engineering, University of Washington, Box 352650, Seattle, WA, 98195-2650, USA

    Charoenchai Khompatraporn & Zelda B. Zabinsky

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  1. M. Montaz Ali
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  2. Charoenchai Khompatraporn
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  3. Zelda B. Zabinsky
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Correspondence to M. Montaz Ali.

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Ali, M.M., Khompatraporn, C. & Zabinsky, Z.B. A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems. J Glob Optim 31, 635–672 (2005). https://doi.org/10.1007/s10898-004-9972-2

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  • DOI: https://doi.org/10.1007/s10898-004-9972-2

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