Epistasis for real encoding in genetic algorithms

Epistasis is a well known tool introduced by Davidor (1991) to understand and predict the performance of a genetic algorithm using binary encoding. The meaning of variance of epistasis is analyzed using Walsh basis; it is established that this variance can be viewed as a measure of the quality of a linear approximation. Variance of epistasis is therefore easier to estimate using the well known context of polynomial approximation regarding Euclidian distance. This approach also leads to the extension of variance of epistasis to real encoding without considering the notion of schema. Following this new definition, numerical analysis tools can also be applied to compute efficiently this generalized variance of epistasis