An Adaptive Sequential Experimentation Methodology for Expensive Response Surface Optimization - Case Study in Traumatic Brain Injury Modeling

The preset response surface designs often lack the ability to adapt the design based on the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this paper, we present an adaptive sequential methodology for n-dimensional response surface optimization (n-dimensional adaptive sequential response surface methodology (N-ASRSM)) for industrial experiments with high experimentation cost, which requires high design optimization performance. We also develop a novel risk adjustment strategy for effectively considering the effect of noise into the design. The N-ASRSM is a sequential adaptive experimentation approach, which uses the information from previous experiments to design the subsequent experiment by simultaneously reducing the region of interest and identifying factor combinations for new experiments. Its major advantage is the experimentation efficiency such that, for a given response target, it identifies the input factor combination in less number of experiments than the classical response surface methodology designs. We applied N-ASRSM to the problem of traumatic brain injury modeling and compared the result with the conventional central composite design. Also, through extensive simulated experiments with different quadratic and nonlinear cases, we show that the proposed N-ASRSM method outperforms the classical response surface methodology designs and compares favorably with other sequential response surface methodologies in the literature in terms of both design optimality and experimentation efficiency. Copyright © 2013 John Wiley & Sons, Ltd.