Stable Mutations for Evolutionary Algorithms

Description

This book presents a set of theoretical and experimental results that describe the features of the wide family of α-stable distributions (the normal distribution also belongs to this class) and their various applications in the mutation operator of evolutionary algorithms based on real-number representation of the individuals, and, above all, equip these algorithms with features that enrich their effectiveness in solving multi-modal, multi-dimensional global optimization problems. The overall conclusion of the research presented is that the appropriate choice of probabilistic model of the mutation operator for an optimization problem is crucial. Mutation is one of the most important operations in stochastic global optimization algorithms in the n-dimensional real space. It determines the method of search space exploration and exploitation. Most applications of these algorithms employ the normal mutation as a mutation operator. This choice is justified by the central limit theorem but is associated with a set of important limitations. Application of α-stable distributions allows more flexible evolutionary models to be obtained than those with the normal distribution. The book presents theoretical analysis and simulation experiments, which were selected and constructed to expose the most important features of the examined mutation techniques based on α-stable distributions. It allows readers to develop a deeper understanding of evolutionary processes with stable mutations and encourages them to apply these techniques to real-world engineering problems. Front Matter ....Pages i-xiv Introduction (Andrzej Obuchowicz)....Pages 1-8 Foundations of Evolutionary Algorithms (Andrzej Obuchowicz)....Pages 9-22 Stable Distributions (Andrzej Obuchowicz)....Pages 23-48 Non-isotropic Stable Mutation (Andrzej Obuchowicz)....Pages 49-76 Isotropic Stable Mutation (Andrzej Obuchowicz)....Pages 77-106 Stable Mutation with the Discrete Spectral Measure (Andrzej Obuchowicz)....Pages 107-121 Isotropic Mutation Based on an \(\alpha \)-Stable Generator (Andrzej Obuchowicz)....Pages 123-134 Mutation Based on Directional Distributions (Andrzej Obuchowicz)....Pages 135-154 Conclusions (Andrzej Obuchowicz)....Pages 155-158 Back Matter ....Pages 159-164