  Black-box and preference-based optimization algorithms are global
optimization procedures that aim to find the global solutions of an
optimization problem using, respectively, the least amount of function
evaluations or sample comparisons as possible. In the black-box case, the
analytical expression of the objective function is unknown and it can only be
evaluated through a (costly) computer simulation or an experiment. In the
preference-based case, the objective function is still unknown but it
corresponds to the subjective criterion of an individual. So, it is not
possible to quantify such criterion in a reliable and consistent way.
Therefore, preference-based optimization algorithms seek global solutions using
only comparisons between couples of different samples, for which a human
decision-maker indicates which of the two is preferred. Quite often, the
black-box and preference-based frameworks are covered separately and are
handled using different techniques. In this paper, we show that black-box and
preference-based optimization problems are closely related and can be solved
using the same family of approaches, namely surrogate-based methods. Moreover,
we propose the generalized Metric Response Surface (gMRS) algorithm, an
optimization scheme that is a generalization of the popular MSRS framework.
Finally, we provide a convergence proof for the proposed optimization method.
