Towards an Augmented Lagrangian Constraint Handling Approach for the (1+1)-ES

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We consider the problem of devising an approach for handling inequality constraints in evolution strategies that allows converging linearly to optimal solutions on sphere functions with a single linear constraint. An analysis of the single-step behaviour of the (1+1)-ES shows that the task of balancing improvements in the objective with those in the constraint function is quite delicate, and that adaptive approaches need to be carefully designed in order to avoid failure. Based on the understanding gained, we propose a simple augmented Lagrangian approach and experimentally demonstrate good performance on a broad range of sphere functions as well as on moderately ill-conditioned ellipsoids with a single linear constraint.