Efficient Global Optimization with Experimental Data: Revisiting the Paper Helicopter Design

Experimental optimization has been used since the early 20th century to help farmers maximize yields (defining inputs such as water and fertilizer). The traditional approach iterates in cycles consisting of fitting a polynomial to samples (that differed in the set of input variables) and optimizing the fitted surrogate. In each cycle, a set of designs is defined and tested. Although engineering design relies mostly on computer experiments, there are cases where simulations are expensive enough and the system is cheap enough to manufacture and test to favor experimental over analytical optimization. In this paper, we use the design of a paper helicopter to illustrate how we can adapt the modern efficient global optimization (EGO) algorithm to handle experimental data. The objective is to maximize the time a simple paper helicopter takes to fall from a specific height. We propose running EGO with multiple surrogates (MSEGO) for generating not only one, but multiple candidate designs per optimization cycle. Here, we use kriging, radial basis neural network, linear Shepard, and support vector regression. We also heavily penalize regions of the design space where designs are predicted to fail, using support vector classification to define the failure region. We found MSEGO reduced the impact of failed designs, allowed for exploration of the design space, and improved the fall time by 10% .