Cohn, H.  ``On the Simulated Annealing Chain.'' Statistics
Department Research Report #1, 1995

                            Abstract

Cooling schedules of the form $\{c/{\log(k+1)}\}$, where $c$ is a
sufficiently large constant, have proven necessary for convergence
of the simulated annealing algorithm to the set of global minima.
Independence of the initial state and ability of the system to
escape from any set are often considered desirable attributes.
It is known that such properties hold for $c$ large enough.
However, there are convergent algorithms characterised by traps
which are not asymptotically independent.  It is shown that a
finely tuned cooling schedule renders a maximal set of states
transient and has one or more friendly "traps" leading to global
minima.  The performance of the algorithm relies heavily on the
value of $c$ for which the process exhibits phase transitions.