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.