Adaptive Response Surface Method

Wong S.M., Hobbs R.E., Onof C. 2005. An adaptive response surface method for reliability analysis of structures with multiple loading sequermes. Structural Safety n°4, 287-308. 

There exist several simplex methods. In this chapter, we will discuss three of them, in increasing order of complexity the basic simplex, the modified simplex and the super-modified simplex. The more sophisticated methods are able to adapt themselves better to the response surface studied. However, their construction requires a larger number of experiments. In spite of this, the modified and super-modified simplexes normally are able to come closer to the maximum (or minimum if this were of interest) with a total number of experiments that is smaller than would be necessary for the basic simplex. In this chapter, we will see examples with only two or three variables, so that we can graphically visualize the simplex evolution for instructive purposes. However, the efficiency of the simplex, in comparison with univariate optimization methods, increases with the number of factors. 

In the modified algorithm (Nelder and Mead, 1965), the simplex can change its size and form, and consequently adapt itself more efficiently to the response surface. This flexibility permits a more precise determination of the optimum point, because the simplex can shrink in its proximity. Besides this desirable characteristic, the modified method, compared to the basic simplex, can reduce the number of runs necessary to find the optimum, because it can stretch itself when it is far from the desired point, usually on a planar portion of the response surface. For this reason it approaches the experimental region of interest more rapidly. 

Bukman, L., A. C. Martins, E. O. Barizao, J. V. Visentainer, and V. C. Almeida. 2013. DPPH assay adapted to the FIA system for the determination of the antioxidant capacity of wines Optimization of the conditions using the response surface methodology. Food Analytical Methods 6(5) 1424-1432. 

Martins, A. C., L. Bukman, A. M. M. Vargas et al. 2013. The antioxidant activity of teas measured by the FRAP method adapted to the FIA system Optimizing the conditions using the response surface methodology. Food Chem. 138 574-580. 

Doob JL (1953) Stochastic processes. Wiley, New York Engelund S, Rackwitz R (1993) A benchmark study on importance sampling techniques in structural reliability. Street Saf 12(4) 255-276 Faravelli L(1989) Response-surface approach for reliability analysis. J Eng Mech 115 2763-2781 Grooteman F (2(X)8) Adaptive radial-based impoitanee sampling method for structural reliability. Street Saf 30(6) 533-542... 

To study the response of a large population of cells at the individual cell level, many efforts have been dedicated to the development of parallel and simple methods to localize precisely individual cells on a surface or create assemblies. It has been recently demonstrate that capillary assembly can be adapted to biological objects to create cells arrays. 

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