Proposed method
The aim of this work is to find a region where the response of function
that is not well characterized in terms of optimality resembles another
one that is well-characterized in such terms, to find at least a local
optimum. This well-characterized function,\(\mathbf{Z\ =\ f}\left(\mathbf{R}\right)\), could be fixed or be,
ideally, an adjustable metamodel like, for example, a second order
polynomial regression with unknown parameters. Once the forms are
picked, an experimental region for both functions has to be defined. The
region where the maximum similarity occurs is identified by formulating
an optimization problem (2) which minimizes the functions’ SSE. The
solution will be the location and size of a window in the experimental
region where the maximum similarity between the responses occurs, except
when Z is a metamodel in which case the solution includes the metamodel
parameter estimates. The optimization problem formulation and an example
are illustrated below: