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Spherical Distributions Used in Evolutionary Algorithms

Author

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  • Alexandru Agapie

    (Department of Applied Mathematics, Faculty of Economic Cybernetics, Statistics and Informatics, Bucharest University of Economic Studies, Calea Dorobantilor 15-17, 010552 Bucharest, Romania
    “Gheorghe Mihoc—Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania)

Abstract

Performance of evolutionary algorithms in real space is evaluated by local measures such as success probability and expected progress. In high-dimensional landscapes, most algorithms rely on the normal multi-variate, easy to assemble from independent, identically distributed components. This paper analyzes a different distribution, also spherical, yet with dependent components and compact support: uniform in the sphere. Under a simple setting of the parameters, two algorithms are compared on a quadratic fitness function. The success probability and the expected progress of the algorithm with uniform distribution are proved to dominate their normal mutation counterparts by order n ! ! .

Suggested Citation

  • Alexandru Agapie, 2021. "Spherical Distributions Used in Evolutionary Algorithms," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3098-:d:692346
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    References listed on IDEAS

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    1. D B Dunson & J E Johndrow, 2020. "The Hastings algorithm at fifty," Biometrika, Biometrika Trust, vol. 107(1), pages 1-23.
    2. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    3. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Alexandru Agapie, 2022. "Evolution Strategies under the 1/5 Success Rule," Mathematics, MDPI, vol. 11(1), pages 1-20, December.

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