An evolutionary algorithm using spherical inversions

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.