On the log-normal self-adaptation of the mutation rate in binary search spaces

This paper discusses the adoption of self-adaptation for Evolutionary Algorithms operating in binary spaces using a direct encoding of the mutation rate. In particular, it focuses on the log-normal update rule for adapting the mutation rate, incorporated in a (mu, lambda)-strategy. Although it is well known that this update rule requires a lower boundary of the mutation rate to prevent it from collapsing to zero, the naive approach of enforcing a fixed lower boundary has undesirable side-effects. This paper studies the dynamics of the fixed lower boundary approach in depth and proposes a simple alternative for dealing with the lower boundary issue.