When Life Hands You Lemons – Optimize Away!

Stefan Wild, Cornell University

Fundamental to mathematical optimization is the ability to exploit knowledge of an objective in order to more rapidly find a solution. But what happens when the objective depends on evaluating a simulator for which little to no insight is available? This scenario increasingly arises as high performance computing yields more realistic and detailed simulation models of complex physical systems. Besides leaving a sour taste in an optimizer‘s mouth, these problems often necessitate unrealistic computational budgets.

We develop algorithms for so-called “blackbox” problems where both the derivatives of the objective are unavailable and the computational expense of evaluating the simulator is a binding constraint for the optimization. Our approach is to build mathematically attractive surrogates, which both overcome many of the difficulties of the original objective and result in better solutions in fewer evaluations. The methods developed are general and can be applied to computational science problems as varied as calibration, design, and prediction.

Abstract Author(s): Stefan Wild, Christine Shoemaker, and Jorge Moré