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TITLE: Recent Developments in the Use of Kriging Response Surfaces for Black-Box Global Optimization
SPEAKER: Dr. Donald Jones
ABSTRACT:
In "black-box" global optimization, we assume we do not have derivatives nor any special knowledge of the forms of the objective and constraint functions. Instead, we merely can evaluate or "sample" the functions at points of our choosing. From the very use of the word "sample," one can begin to see that statistics might have a role to play. Instead of assuming a deterministic form for the problem functions, statistics allows us to make weaker, statistical assumptions about how the function "tends to behave," assumptions that can be made rigorous through the use of Guassian stochastic process models and kriging response surfaces. The computational machinery of statistics can then be used to get answers to such questions as
"What point, if sampled, is most likely to give me an improvement over my current best point?"
"What point, if sampled, would most reduce my uncertainty about where the optimum is located?"
In this talk I will present a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response-surface approach. Some of the more recent developments in the literature will be highlighted.
