Analysis-of-Marginal-Tail-Means (ATM): A Robust Method for Discrete Black-Box Optimization

Abstract

We present a new method, called analysis-of-marginal-tail-means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications in many real-world engineering problems (e.g., manufacturing optimization, product design, and molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this by combining both rank- and model-based optimization, via the use of marginal tail means. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions from data, then finding a good compromise which best exploits additive structure. ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network.

KEYWORDS:

• Black-box optimization
• Conditional tail means
• Discrete optimization
• Parameter design
• Product family design
• Robust optimization

Notes

1 Here and in later simulations, we discretized continuous test functions to provide a test bank for the discrete problem; the goal is not to solve the underlying continuous optimization problem via discretization.

2 SELC (Mandal, Wu, and Johnson 2006) and $\mathcal{G}$-SELC (Mandal, Ranjan, and Wu 2009) are not included here, since these methods (as implemented in Johnson, Mandal, and Ding 2008) require a larger run size n in most simulation cases.