  We propose a new strategy for Monte Carlo (MC) optimization on rugged
multidimensional landscapes. The strategy is based on querying the statistical
properties of the landscape in order to find the temperature at which the mean
first passage time across the current region of the landscape is minimized.
Thus, in contrast to other algorithms such as simulated annealing (SA), we
explicitly match the temperature schedule to the statistics of landscape
irregularities. In cases where this statistics is approximately the same over
the entire landscape, or where non-local moves couple distant parts of the
landscape, single-temperature MC will outperform any other MC algorithm with
the same move set. We also find that in strongly anisotropic Coulomb spin glass
and traveling salesman problems, the only relevant statistics (which we use to
assign a single MC temperature) is that of irregularities in low-energy
funnels. Our results may explain why protein folding in nature is efficient at
room temperatures.
