Analysis-of-marginal-Tail-Means - a new method for robust parameter optimization
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This paper presents a novel method, called Analysis-of-marginal-Tail-Means (ATM), for parameter optimization over a large, discrete design space. The key advantage of ATM is that it offers effective and robust optimization performance for both smooth and rugged response surfaces, using only a small number of function evaluations. This method can therefore tackle a wide range of engineering problems, particularly in applications where the performance metric to optimize is "black-box" and expensive to evaluate. The ATM framework unifies two parameter optimization methods in the literature: the Analysis-of-marginal-Means (AM) approach (Taguchi, 1986), and the Pick-the-Winner (PW) approach (Wu et al., 1990). In this paper, we show that by providing a continuum between AM and PW via the novel idea of marginal tail means, the proposed method offers a balance between three fundamental trade-offs. By adaptively tuning these trade-offs, ATM can then provide excellent optimization performance over a broad class of response surfaces using limited data. We illustrate the effectiveness of ATM using several numerical examples, and demonstrate how such a method can be used to solve two real-world engineering design problems.
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