Soft Computing

, Volume 22, Issue 6, pp 1993–2014 | Cite as

An evolutionary algorithm using spherical inversions

  • Juan Pablo Serrano-Rubio
  • Arturo Hernández-Aguirre
  • Rafael Herrera-Guzmán
Methodologies and Application


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.


Geometric search operators Evolutionary algorithm Continuous optimization 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Juan Pablo Serrano-Rubio
    • 1
    • 4
  • Arturo Hernández-Aguirre
    • 2
  • Rafael Herrera-Guzmán
    • 3
  1. 1.Information Technologies LaboratoryTechnological Institute of Irapuato (ITESI)IrapuatoMexico
  2. 2.Computer Science DepartmentCenter for Research in Mathematics (CIMAT)GuanajuatoMexico
  3. 3.Mathematics DepartmentCenter for Research in Mathematics (CIMAT)GuanajuatoMexico
  4. 4.School of Engineering, Computer Science and MathematicsUniversity of ExeterExeterUK

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