Towards optimization by matching of response surfaces: Finding windows
of maximal similarity
Abstract
The ultimate goal of this work is to find a region where the response
surface of a function that is not well characterized in terms of
optimality resembles one that is well-characterized in such terms to
find, at least, a local optimum. The region in the functions’ input
space where this resemblance occurs, we call a Window of Maximal
Similarity (WMS) and is identified by formulating and solving an
optimization problem. The method is one of minimization of squared
errors and can be used to explore experimental, or simulated data. A
series of examples, that include several typical global optimization
test functions in literature, are presented in order to demonstrate the
method’s feasibility and capability for generating a two-dimensional
WMS. This tool is a viable element that will serve for the future
development of Optimization by Similarity.