Bias in Standard Self-Adaptive Evolution Strategies

The mutation strength
$(\sigma)$
adaptation of a multi-recombinative self-adapting Evolution Strategy is investigated on the Rastrigin test function by theoretical and experimental means. Sampling
$\sigma$
from a log-normal distribution reveals the occurrence of an undesired steady-state under high multimodal-ity, which halts the
$\sigma$
-adaptation and prevents convergence. It is shown that an inherent bias is the reason for this steady-state when sampling log-normal mutations. Therefore, sampling from a normal distribution is introduced as an alternative. Normal sampling does not exhibit the steady-state behavior and it is more stable optimizing functions under high multimodality.