Modeling an augmented Lagrangian for improved blackbox constrained optimization

By Sébastien Le Digabel, Robert B. Gramacy, Genetha Anne Gray, Herbert K. H. Lee, Pritam Ranjan, Garth Weels, Stefan M. Wild. 2014

11 citations recorded by the source corpus.

Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This situation is unfortunate because statistical methods have many attractive properties: global scope, handling noisy objectives, sensitivity analysis, and so forth. To narrow that gap, we propose a combination of response surface modeling, expected improvement, and the augmented Lagrangian numerical optimization framework. This hybrid approach allows the statistical model to think globally and the augmented Lagrangian to act locally. We focus on problems where the constraints are the primary bottleneck, requiring expensive simulation to evaluate and substantial modeling effort to map out. In that context, our hybridization presents a simple yet effective solution that allows existing objective-oriented statistical approaches, like those based on Gaussian process surrogates and expected improvement heuristics, to be applied to the constrained setting with minor modification. This work is motivated by a challenging, real-data benchmark problem from hydrology where, even with a simple linear objective function, learning a nontrivial valid region complicates the search for a global minimum.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Ocean Engineering

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Citations in the corpus

Predictive Entropy Search for Bayesian Optimization with Unknown Constraints (2015, methodology): “Finally, Gramacy et al. (2014) propose to combine EI with the augmented Lagrangian approach for constrained numerical optimization.”