Surrogate-based optimization based on the probability of feasibility

Abstract

Surrogate models can be used to evaluate computationally expensive functions in optimization of nonlinear problems. The models are able to identify areas of interest in a multidimensional design space driven by methods of searching and evaluating new locations in a sparse design space. The use of constraints based on surrogates complicates the optimization problem as the uncertainty within the design space influences both the objective and constraint functions. While some optimization methods consider the mean prediction for the constraints, several methods have been reported on ways to include the uncertainty into the constraints. One way is to use a probability of feasibility to account for the mean prediction and its uncertainty. In this work, this approach is explored to evaluate its feasibility and compared to other alternate methods documented in the literature. Computationally efficient and reliable results were obtained for the mathematical test functions evaluated. The same advantageous trend could not be observed for more complex engineering applications since convergence was not reached within the prescribed computational cost by either this new approach or the established one. Nevertheless, more feasible designs were generated when the probability of feasibility was included in the objective function. For an airfoil drag minimization problem with aerodynamic and geometric constraints, improvements of ∼ 70% and ∼ 25% were achieved with the proposed methods considering inviscid and viscous flow conditions, respectively. These values are comparable to the ones obtained with an established upper trust bound approach.