Budget-constrained experimental optimization
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Many problems of design and operation in science and engineering can be formulated as optimization of a properly defined performance/objective function over a design space. This thesis considers optimization problems where information about the performance function can be obtained only through experimentation/function evaluation, in other words, optimization of black box functions. Furthermore, it is assumed that the optimization is performed with limited budget, namely, where only a limited number of function evaluations are feasible. Two classes of optimization approaches are considered. The first, consisting of Design of Experiment (DOE) and Response Surface Methodology (RSM), explores the design space locally by identifying directions of improvement and incrementally moving towards the optimum. The second, referred to as Bayesian Optimization (BO), corresponds to a global search of the design space based on a stochastic model of the function over the design space that is updated after each experimentation/function evaluation. Two independent projects related to the above optimization approaches are reported in the thesis. The first, the result of a collaborative effort with experimental and computational material scientists, involves adaptations of the above approaches in order to solve two specific new materials development projects. The goal of the first project was to develop an integrated computational-statistical-experimental methodology for calibration of an activated carbon adsorption bed. The second project consisted of the application and modification of existing DOE approaches to a highly data limited environment. The second part consists of a new contribution to the methodology of Bayesian Optimization (BO) by significantly generalizing a non-myopic approach to BO. Different BO algorithms vary based on their choice of stochastic model of the unknown objective function, referred to as the surrogate model, and that of the so-called acquisition function, which often represents an expected utility of sampling at various points of the design space. Various myopic BO approaches which evaluate the benefit of taking only a single sample from the objective function have been considered in the literature. More recently, a number of non-myopic approaches have been proposed that go beyond evaluating the benefit of a single sample. In this thesis, a non-myopic approach/algorithm, referred to as z* policy, is considered that takes a different approach to evaluating the benefits of sampling. The resulting search approach is motivated by a non-myopic index policy in a sequential sampling problem that is shown to be optimal in a non-adaptive setting. An analysis of the z* policy is presented and it is placed within the broader context of non-myopic policies. Finally, using empirical evaluations, it is shown that in some instances the z* policy outperforms a number of other commonly used myopic and non-myopic policies.