Augmented Lagrangian Constraint Handling for CMA-ES---Case of a Single Linear Constraint

Asma Atamna 1 Anne Auger 1 Nikolaus Hansen 1
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : We consider the problem of minimizing a function f subject to a single inequality constraint g(x) <= 0, in a black-box scenario. We present a co-variance matrix adaptation evolution strategy using an adaptive augmented La-grangian method to handle the constraint. We show that our algorithm is an instance of a general framework that allows to build an adaptive constraint handling algorithm from a general randomized adaptive algorithm for unconstrained optimization. We assess the performance of our algorithm on a set of linearly constrained functions, including convex quadratic and ill-conditioned functions, and observe linear convergence to the optimum.
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Asma Atamna, Anne Auger, Nikolaus Hansen. Augmented Lagrangian Constraint Handling for CMA-ES---Case of a Single Linear Constraint. Proceedings of the 14th International Conference on Parallel Problem Solving from Nature, Sep 2016, Edinburgh, United Kingdom. pp.181 - 191, ⟨10.1007/978-3-319-45823-6_17⟩. ⟨hal-01390386⟩

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