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: