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An evolutionary algorithm using spherical inversions

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Abstract

This paper introduces an evolutionary algorithm which uses reflections and spherical inversions for global continuous optimization. Two new geometric search operators are included in the design of the algorithm: the inversion search operator and the reflection search operator. The inversion search operator computes inverse points with respect to hyperspheres, and the reflection search operator redistributes the individuals on the search space of the fitness function. The nonlinear geometric nature of the inversion search operator furnishes more “aggressive” search and exploitation capabilities for the algorithm. The performance of the algorithm is analyzed through a benchmark of 28 functions. Statistical tests show the competitive performance of the algorithm in comparison with current leading (geometric) algorithms such as particle swarm optimization and four differential evolution strategies.

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Acknowledgements

This research is partially supported by a Grant of National Council of Science and Technology of Mexico CONACYT (256126). The first author would like to thank the University of Exeter for its hospitality. The third author would like to thank the International Centre for Theoretical Physics (ICTP) and the Institut Des Hautes Etudes Scientifiques (IHES) for their hospitality and support.

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Authors and Affiliations

  1. Information Technologies Laboratory, Technological Institute of Irapuato (ITESI), Irapuato, Guanajuato, Mexico

    Juan Pablo Serrano-Rubio

  2. Computer Science Department, Center for Research in Mathematics (CIMAT), Guanajuato, Guanajuato, Mexico

    Arturo Hernández-Aguirre

  3. Mathematics Department, Center for Research in Mathematics (CIMAT), Guanajuato, Guanajuato, Mexico

    Rafael Herrera-Guzmán

  4. School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, EX4 4QF, UK

    Juan Pablo Serrano-Rubio

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  1. Juan Pablo Serrano-Rubio
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  2. Arturo Hernández-Aguirre
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  3. Rafael Herrera-Guzmán
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Correspondence to Juan Pablo Serrano-Rubio.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

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Serrano-Rubio, J.P., Hernández-Aguirre, A. & Herrera-Guzmán, R. An evolutionary algorithm using spherical inversions. Soft Comput 22, 1993–2014 (2018). https://doi.org/10.1007/s00500-016-2461-y

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