Limitations of Mutative sigma-Self-Adaptation
on Linear Fitness Functions
Nikolaus Hansen
This paper investigates sigma-self-adaptation for real valued
evolutionary algorithms on linear fitness functions. We identify
log(sigma) as key quantity to understand strategy behavior.
Identifying the bias of mutation, recombination, and selection on
log(sigma) is sufficient to explain strategy behavior in many cases,
even in a non-linear or noisy environment. 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 sigma-distribution. Consequently, the correlation between
fitness and step-size is zero. Assuming additionally that
sigma-changes due to mutation and recombination are unbiased, and
(mu,lambda)-truncation selection, where mu=lambda/2, then
sigma-self-adaptation is unable to enlarge the step-size. Experiments
show the relevance of the given assumptions.
In Evolutionary Computation, 14(3), 2006.
http://www.mitpressjournals.org/toc/evco/14/3