title: On the behaviour of the (1, λ)-ES for conically constrained linear problems.
abstract: We study the behaviour of a [Formula: see text]-ES that handles constraints by resampling infeasible candidate solutions for linear optimization problems with a conically constrained feasible region. The analysis generalizes prior work in that no particular orientation of the cone relative to the gradient of the objective function is assumed. 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 characterize the average step size and convergence rate attained when using cumulative step size adaptation and compare the values with optimal ones.
authors.affiliation: Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2 dirk@cs.dal.ca.
authors.forename: Dirk V
authors.initials: DV
authors.lastname: Arnold
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003205:Computing Methodologies; D008432:Mathematical Computing; D008962:Models, Theoretical
keywords: Evolution strategies; constraint handling; cumulative step size adaptation