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The Hyperbell Algorithm for Global Optimization: A Random Walk Using Cauchy Densities

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Abstract

This article presents a new algorithm, called the’’Hyperbell Algorithm‘‘, that searches for the global extrema ofnumerical functions of numerical variables. The algorithm relies on theprinciple of a monotone improving random walk whose steps aregenerated around the current position according to a gradually scaleddown Cauchy distribution. The convergence of the algorithm is provenand its rate of convergence is discussed. Its performance is tested onsome ’’hard‘‘ test functions and compared to that of other recentalgorithms and possible variants. An experimental study of complexityis also provided, and simple tuning procedures for applications areproposed.

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Authors and Affiliations

  1. CREPCO (URA CNRS 182), Université, de Provence 29 avenue Robert Schuman, F-13621, Aix-en-Provence Cedex 1, France

    Pierre Courrieu

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  1. Pierre Courrieu
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Courrieu, P. The Hyperbell Algorithm for Global Optimization: A Random Walk Using Cauchy Densities. Journal of Global Optimization 10, 37–55 (1997). https://doi.org/10.1023/A:1008230212303

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  • DOI: https://doi.org/10.1023/A:1008230212303

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