Hierarchic Genetic Search with $$\alpha $$-Stable Mutation

Abstract

The paper analyzes the performance improvement imposed by the application of \(\alpha \)-stable probability distributions to the mutation operator of the Hierarchic Genetic Strategy (HGS), in solving ill-conditioned, multimodal global optimization problems in continuous domains. The performed experiments range from standard benchmarks (Rastrigin and multi-peak Gaussian) to an advanced inverse parametric problem of the logging measurement inversion, associated with the oil and gas resource investigation. The obtained results show that the application of \(\alpha \)-stable mutation can first of all decrease the total computational cost. The second advantage over the HGS with the standard, normal mutation consists in finding much more well-fitted individuals at the highest-accuracy HGS level located in attraction basins of local and global fitness minimizers. It might allow us to find more minimizers by performing local convex searches started from that points. It also delivers more information about the attraction basins of the minimizers, which can be helpful in their stability analysis.