Analysis of allele distribution dynamics in different genetic algorithms

Abstract

This chapter exemplarily points out how essential genetic information evolves during the runs of certain selected variants of a genetic algorithm. The discussed algorithmic enhancements to a standard genetic algorithm are motivated by Holland's schema theory and the according building block hypothesis. The discussed offspring selection and the relevant alleles preserving genetic algorithm certify the survival of essential genetic information by supporting the survival of relevant alleles rather than the survival of above average chromosomes. This is achieved by defining the survival probability of a new child chromosome depending on the child's fitness in comparison to the fitness values of its own parents. By this means the survival and expansion of essential building block information information is supported also for problem representations and algorithmic settings which do not fulfill the theoretical requirements of the schema theory. The properties of these GA variants are analyzed empirically. The selected analysis method assumes the knowledge of the unique globally optimal solution and is therefore restricted to rather theoretical considerations. The main aim of this chapter is to motivate and discuss the most important properties of the discussed algorithm variants in a rather intuitive way. Aspects for meaningful and practically more relevant generalizations as well as more sophisticated experimental analyses are indicated. © 2012 Springer-Verlag Berlin Heidelberg.