An analysis of mutative σ-self-adaptation on linear fitness functions

This paper investigates σ-self-adaptation for real valued evolutionary algorithms on linear fitness functions. We identify the step-size logarithm log σ as a key quantity to understand strategy behavior. Knowing the bias of mutation, recombination, and selection on log σ is sufficient to explain σ-dynamics and strategy behavior in many cases, even from previously reported results on non-linear and/or noisy fitness func-tions. On a linear fitness function, if intermediate multi-recombination is applied on the object parameters, the i-th best and the i-th worst individual have the same σ-distribution. Consequently, the correlation between fitness and step-size σ is zero. Assuming additionally that σ-changes due to mutation and recombination are unbi-ased, then σ-self-adaptation enlarges σ if and only if µ < λ/2, given (µ, λ)-truncation selection. Experiments show the relevance of the given assumptions