Value-based global optimization
Moore, Roxanne Adele
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Computational models and simulations are essential system design tools that allow for improved decision making and cost reductions during all phases of the design process. However, the most accurate models are often computationally expensive and can therefore only be used sporadically. Consequently, designers are often forced to choose between exploring many design alternatives with less accurate, inexpensive models and evaluating fewer alternatives with the most accurate models. To achieve both broad exploration of the alternatives and accurate determination of the best alternative with reasonable costs incurred, surrogate modeling and variable accuracy modeling are used widely. A surrogate model is a mathematically tractable approximation of a more expensive model based on a limited sampling of that model, while variable accuracy modeling involves a collection of different models of the same system with different accuracies and computational costs. As compared to using only very accurate and expensive models, designers can determine the best solutions more efficiently using surrogate and variable accuracy models because obviously poor solutions can be eliminated inexpensively using only the less expensive, less accurate models. The most accurate models are then reserved for discerning the best solution from the set of good solutions. In this thesis, a Value-Based Global Optimization (VGO) algorithm is introduced. The algorithm uses kriging-like surrogate models and a sequential sampling strategy based on Value of Information (VoI) to optimize an objective characterized by multiple analysis models with different accuracies. It builds on two primary research contributions. The first is a novel surrogate modeling method that accommodates data from any number of analysis models with different accuracies and costs. The second contribution is the use of Value of Information (VoI) as a new metric for guiding the sequential sampling process for global optimization. In this manner, the cost of further analysis is explicitly taken into account during the optimization process. Results characterizing the algorithm show that VGO outperforms Efficient Global Optimization (EGO), a similar global optimization algorithm that is considered to be the current state of the art. It is shown that when cost is taken into account in the final utility, VGO achieves a higher utility than EGO with statistical significance. In further experiments, it is shown that VGO can be successfully applied to higher dimensional problems as well as practical engineering design examples.