Schemata Theory for the Real Coding and Arithmetical Operators

Abstract

The Schemata Theory analyzes the effect of the selection process, mutation and crossover over the number of individuals that belong to a given schema, within generations. This analysis considers, in its original form, the binary coding and operators. In this article, we present an analogous study, focusing on the real number coding and arithmetical operators. Unfortunately, the conventional schema definition is tightly dependent on discrete alphabets. Therefore, following a generalization of the concept of schema, we present a particular definition that suits better the continuous domain. Using this new definition, we reach an expression simila