Nonparametric and semiparametric response surface methodology: a review of designs, models and optimization techniques

Since the introduction of Response Surface Methodology in the 1950s, there have been many developments with the aim of expanding the range of applications of the methodology. Various new design, modeling and optimization techniques have been introduced for coping with unknown input-output relationships, costly or time-consuming experimental studies and irregular experimental regions (e.g., non-cubic or non-spherical regions induced by constraints in the input variables). Such developments may involve many different research areas simultaneously (e.g., the statistical design of the experiments, multivariate modeling, and multi-objective optimization). Experts in various research fields have been embracing and combining methodologies from other areas in order to achieve an improved efficacy and efficiency. This article aims to throw light on these methodological developments and provide a self-contained literature review with a statistical perspective.