By Robert C. Stern

London released sleek Conflicts - Air

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**Example text**

G. a Morris–Mitchell optimal Latin hypercube or some other space-filling plan) the cost still rises exponentially with the number of design variables. Once again, entia non sunt multiplicanda sine necessitate . . 2 we introduced some typical, simple objectives one may wish to optimize as part of the aerodynamic design process. These slot in at the lower levels of a hierarchy of objectives usually associated with most aerospace programmes. At the top of this hierarchy one may find objectives such as life cycle cost or profit; but since these are usually very hard to connect to the design variables via objective functions, lower level related objectives may be used.

Let us make it clear from the outset that this is a word laden with many different meanings, and misunderstandings can be rather confusing. For instance, consider the following plane curve: ???? = (x, y) = (cos u, sin u), u ∈ [0, 2????]. 11) From a mathematician’s perspective, this is the parametric curve (in terms of the parameter u) of a circle of radius one. From an engineer’s perspective – and this is the usage we adopt here – it is not a parametric geometry, because there are no knobs to twiddle, no obvious handles for changing the shape or size of the circle.

Some hill-climbers require objective function gradient information, others do not. Conjugate gradient techniques fall into the former category, and they are available in a range of iteration step length and direction calculation methods. One of the most efficient and robust such heuristics is the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm (Broyden, 1970). These techniques really come into their own when the objective function sensitivities with respect to the geometry parameters can be computed efficiently and accurately – we dedicate Chapter 10 to objective function derivatives and their computation in an aerodynamic optimization context.