  Preference-based optimization algorithms are iterative procedures that seek
the optimal calibration of a decision vector based only on comparisons between
couples of different tunings. At each iteration, a human decision-maker
expresses a preference between two calibrations (samples), highlighting which
one, if any, is better than the other. The optimization procedure must use the
observed preferences to find the tuning of the decision vector that is most
preferred by the decision-maker, while also minimizing the number of
comparisons. In this work, we formulate the preference-based optimization
problem from a utility theory perspective. Then, we propose GLISp-r, an
extension of a recent preference-based optimization procedure called GLISp. The
latter uses a Radial Basis Function surrogate to describe the tastes of the
decision-maker. Iteratively, GLISp proposes new samples to compare with the
best calibration available by trading off exploitation of the surrogate model
and exploration of the decision space. In GLISp-r, we propose a different
criterion to use when looking for new candidate samples that is inspired by
MSRS, a popular procedure in the black-box optimization framework. Compared to
GLISp, GLISp-r is less likely to get stuck on local optima of the
preference-based optimization problem. We motivate this claim theoretically,
with a proof of global convergence, and empirically, by comparing the
performances of GLISp and GLISp-r on several benchmark optimization problems.
