  We propose a new global optimization method ({\em Simulated Tempering}) for
simulating effectively a system with a rough free energy landscape (i.e. many
coexisting states) at finite non-zero temperature. This method is related to
simulated annealing, but here the temperature becomes a dynamic variable, and
the system is always kept at equilibrium. We analyze the method on the Random
Field Ising Model, and we find a dramatic improvement over conventional
Metropolis and cluster methods. We analyze and discuss the conditions under
which the method has optimal performances.
