Estimating Feasibility Using Multiple Surrogates and ROC Curves
Anirban Chaudhuri, Rodolphe Le Riche, M. Meunier · 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference · 2013
Constraint optimization aims at finding optimum points that satisfy equality or inequality constraints. An important part of constraint optimization is to estimate the feasibility of a point to be added in the next optimization cycle. This is especially evident in real-world problems which have multiple constraints with a very small, disconnected feasible space. The key issue, before seeking optimality, is to find a point in the feasible region. In this work we propose a family of methods for estimating feasibility at any new point in the design space using only the information from an initial design of experiment (DOE) when constraint calculations are computationally expensive, making the use of surrogates imperative. The method does not require additional resources and it is not limited to any particular choice of surrogate. Three different ways of predicting feasibility are described, where the choice of the DOE and surrogate uncertainties are taken into account through cross-validation and ROC curves. A way for combining feasibility predictions of multiple surrogates from their correlation and their confidence is also presented. These methods are compared using 2 analytic functions which have very small disconnected feasible regions. Nomenclature g(x) = True constraint value at point x PF(x) = Probability of Feasibility at point x