Active-set approaches are commonly used in algorithms for constrained numerical optimization. We propose that active-set techniques can beneficially be employed for evolutionary black-box optimization with explicit constraints and present an active-set evolution strategy. We experimentally evaluate its performance relative to those of several algorithms for constrained optimization and find that the active-set evolution strategy compares favourably for the problem set under consideration.

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. Nonlinear 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.