  We perform a statistical analysis of deterministic energy-decreasing
algorithms on mean-field spin models with complex energy landscape like the
Sine model and the Sherrington Kirkpatrick model. We specifically address the
following question: in the search of low energy configurations is it convenient
(and in which sense) a quick decrease along the gradient (greedy dynamics) or a
slow decrease close to the level curves (reluctant dynamics)? Average time and
wideness of the attraction basins are introduced for each algorithm together
with an interpolation among the two and experimental results are presented for
different system sizes. We found that while the reluctant algorithm performs
better for a fixed number of trials, the two algorithms become basically
equivalent for a given elapsed time due to the fact that the greedy has a
shorter relaxation time which scales linearly with the system size compared to
a quadratic dependence for the reluctant.
