A response surface is a map of the expected performance of a variety of components or systems all of which are expected to achieve the same objective. It is another form of an objective function.
It is usual to express a system or component performance (economic, or other measure of worth) as a single variable. If multidimensional and non- commensurate ratings or rankings are used, the general approach is to reduce the several measures to a single weighted measure of merit. Correlation or Eigen Values can be used to compute the final measure.
The weighted measure of merit of each alternative is the value of one (z) dimension of a response surface. You can visualize the response surface as being similar to the earth's surface. You search for the highest mountain or deepest valley.
The other (x, y, ...) dimensions are the values of the variables that uniquely define the each alternative, i.e. its position beneath the surface.
The response surface then is:
z = F(x1, x2, x3,... xk)
Since it is possible to have a large number of variables and a large number of alternatives the mathematical description of the surface can become very complicated. Systematic search using a SIMPLEX, STEEPEST ASCENT or other technique is used to find the highest or lowest point on the response surface.
When the surface is not defined by continuous variables, or there are discontinuities, a suitable search technique may be difficult to implement.
Random sampling of the response surface will discover a point that has a probability of 1 / n of being improved, where n is the number of samples.
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