Response Surface Methodology
CentER Discussion Paper Series No. 2014-013
26 Pages Posted: 15 Feb 2014
Date Written: February 14, 2014
Abstract
This chapter fi rst summarizes Response Surface Methodology (RSM), which started with Box and Wilsons article in 1951 on RSM for real, non-simulated systems. RSM is a stepwise heuristic that uses first-order polynomials to approximate the response surface locally. An estimated polynomial metamodel gives an estimated local gradient, which RSM uses in steepest ascent (or descent) to decide on the next local experiment. When RSM approaches the optimum, the latest rst-order polynomial is replaced by a second-order polynomial. The fitted second-order polynomial enables the estimation of the optimum. Furthermore, this chapter focuses on simulated systems, which may violate the assumptions of constant variance and independence. The chapter also summarizes a variant of RSM that is proven to converge to the true optimum, under speci c conditions. The chapter presents an adapted steepest ascent that is scale-independent. Moreover, the chapter generalizes RSM to multiple random responses, selecting one response as the goal variable and the other responses as the constrained variables. This generalized RSM is combined with mathematical programming to estimate a better search direction than the steepest ascent direction. To test whether the estimated solution is indeed optimal, bootstrapping may be used. Finally, the chapter discusses robust optimization of the decision variables, while accounting for uncertainties in the environmental variables.
Keywords: simulation; optimization; regression, robustness; risk
JEL Classification: C0, C1, C9
Suggested Citation: Suggested Citation