Performance of the $(\mu /\mu _{I},\lambda )\hbox{-}\sigma {\rm SA}$-ES on a Class of PDQFs
Hans-Georg Beyer, Steffen Finck · IEEE Transactions on Evolutionary Computation · 2009
This paper investigates the behavior of$(\mu /\mu _{I},\lambda )\hbox{-}\sigma {\rm SA}$-ES on a class of positive definite quadratic forms. After introducing the fitness environment and the strategy, the self-adaptation mechanism is analyzed with the help of the self-adaptation response function. Afterward, the steady state of the strategy is analyzed. The dynamical equations for the expectation of the mutation strength$\sigma $and the localization parameter$\zeta $will be derived. Building on that, the progress rate$\varphi $is analyzed and tuned by means of the learning parameter$\tau $. An approximate formula for$\tau _{\rm opt}$, yielding locally maximal progress, is presented. Finally, the performance of the$\sigma {\rm SA}$-rule is compared with the performance of the cumulative step size adaptation rule, and a rough approximation for the expected runtime is presented.