Should better moves always be accepted?
By avoiding the sigmoid calculation in the case of better and lateral moves, the Metropolis criterion saves some CPU cycles. On the other hand, the symmetric sigmoid algorithm provides a consistent logic independent of the quality of the move.
Using the reheating and the table-driven schemes, as described in Section 4.3.5, we compared the Metropolis criterion to our sigmoid-based approach, both accepting half the lateral moves, searching for significant differences in the final results.
Among the three datasets, based on 32 runs each, we found no significant difference among the reheating schemes, either before or after minimization. The table-driven schemes after minimization were significantly different than before minimization, but there were no reported differences within each group.
We have no statistically sound evidence that varying the probability for better moves differs significantly from the Metropolis criterion. Both approaches result in the same asymptotic distribution, since most considered moves are uphill.