Optimization and experiments

Experimental Geometry Optimization Techniques for Multi-Element Airfoils

“…These definitions are consistent with the literature but some variation in strict meaning is found among authors [Fox, 1971;Box and Draper, 1987;Haftka, 1995, Haftka andGurdal, 1992]. The numerical quantities for which values are to be varied are called design variables or factors.…”

“…In a recent publication, which reviewed optimization methods as they apply to experiments, one of the strongest deciding factors listed in the selection of methods was the cost of each experiment [Scott and Haftka, 1995]. Another major factor was whether a method required derivatives of the objective function.…”

“…The sequential simplex method is one of the oldest search methods for optimization [Spendley, 1962]. This method has been used successfully with many problems, particularly those optimizing chemical processes [Khummongkol, 1992;Walters, 1991] [Scott and Haftka, 1995;Jacoby et al, 1972;Walters, 1991]. A major disadvantage is that no information is retained beyond two step cycles, often resulting in a less efficient path towards the optimum [Jacoby et al, 1972].…”

“…Design space is a term given to the n-dimensional space defined by the range of continuous design variables [Fox, 1971, Haftka andGurdal, 1992]. A design point is a point in design space defined by a unique set of design variables [Scott and Haftka, 1995]. A response surface is a simple function such as a linear or quadratic polynomial, used to describe response in a small neighborhood of the design space [Box and Draper, 1987].…”

“…If the noise is also found to be low, then this type of problem lends itself to more simplistic optimization methods originally developed for use with an analytic objective function. Adaptive control problems, such as adjusting chemical process variables on line, are possibly the most common examples of inexpensive, low noise, experimental optimization problems[Scott and Haftka, 1995]. Gradient methods are often used in these problems[Sameness and Lim 1990;Jacoby et al,1972;Fox, 1971].…”