Towards Non-linear Constraint Estimation for Expensive Optimization

Abstract

Constraints can render a numerical optimization problem much more difficult to address. In many real-world optimization applications, however, such constraints are not explicitly given. Instead, one has access to some kind of a “black-box” that represents the (unknown) constraint function. Recently, we proposed a fast linear constraint estimator that was based on binary search. This paper extends these results by (a) providing an alternative scheme that resorts to the effective use of support vector machines and by (b) addressing the more general task of non-linear decision boundaries. In particular, we make use of active learning strategies from the field of machine learning to select reasonable training points for the recurrent application of the classifier. We compare both constraint estimation schemes on linear and non-linear constraint functions, and depict opportunities and pitfalls concerning the effective integration of such models into a global optimization process.