On the behaviour of the (1, λ)-es for a conically constrained problem
Dirk V. Arnold · 2013
We consider a conically constrained optimisation problem where the optimal solution lies at the apex of the cone and study the behaviour of a (1,λ)-ES that handles constraints by resampling infeasible candidate solutions. Expressions that describe the strategy's single-step behaviour are derived. Assuming that the mutation strength is adapted in a scale-invariant manner, a simple zeroth-order model is used to determine the speed of convergence of the strategy. We then derive expressions that approximately characterise the step size and convergence rate attained when using cumulative step size adaptation and compare the values with optimal ones.