Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints

Abstract

In many real-world applications of optimization, the underlying descriptive system model is defined by computationally expensive functions: simulation modules, numerical models and other “black box” model components are typical examples. In such cases, the model development and optimization team often has to rely on optimization carried out under severe resource constraints. To address this important issue, recently a Regularly Spaced Sampling (RSS) module has been added to the Lipschitz Global Optimizer (LGO) solver suite. RSS generates non-collapsing space filling designs, and produces corresponding solution estimates: this information is passed along to LGO for refinement within the given resource (function evaluation and/or runtime) limitations. Obviously, the quality of the solution obtained will essentially depend both on model instance difficulty and on the admissible computational effort. In spite of this general caveat, our results based on solving a selection of non-trivial global optimization test problems suggest that even a moderate amount of well-placed sampling effort enhanced by limited optimization can lead at least to reasonable or even to high quality results. Our numerical tests also indicate that LGO’s overall efficiency is often increased by using RSS as a presolver, both in resource-constrained and in completed LGO runs.