  Theoretical analyses of evolution strategies are indispensable for gaining a
deep understanding of their inner workings. For constrained problems, rather
simple problems are of interest in the current research. This work presents a
theoretical analysis of a multi-recombinative evolution strategy with
cumulative step size adaptation applied to a conically constrained linear
optimization problem. The state of the strategy is modeled by random variables
and a stochastic iterative mapping is introduced. For the analytical treatment,
fluctuations are neglected and the mean value iterative system is considered.
Non-linear difference equations are derived based on one-generation progress
rates. Based on that, expressions for the steady state of the mean value
iterative system are derived. By comparison with real algorithm runs, it is
shown that for the considered assumptions, the theoretical derivations are able
to predict the dynamics and the steady state values of the real runs.
