Abstract
A sizable part of the theoretical literature on simulated annealing deals
with a property called convergence which asserts that the simulated
annealing chain is in the set of global minima states of the objective
function with probability tending to one. However, in practice the
convergent algorithms are considered too slow whereas a number of
nonconvergent ones are usually preferred. We attempt a detailed analysis
of various temperature schedules. Examples will be given when it is both
practically and theoretically justified to use boiling, fixed temperature
or even fast cooling schedules which have a small probability of reaching
global minima. Applications to traveling salesman problems of various
sizes are also given.