Elaborate Cooling Schedule - Simulated Annealing



Hello,

I have been trying to understand the applications of a few elaborate
cooling schedules in simulated annealing. I came across a condition
for terminating temperature in the cooling schedule proposed by Lundy
and Mees (1986) stated:

final_temperature <= epsilon/(Log(|R|-1)-Log(nu)), epsilon and nu
being constants and |R| being the cardinal value of the set of all
configurations that can possibly be reached from the currently
accepted configuration, in one single transition.

If my rule for obtaining new configurations from the older ones at any
instant is:
Configuration_New = Configuration_Old + A*(0.5 - U), where A is a
constant and U is random number picked from the uniform distribution
[0, 1), isn't the cardinal value of R, infinite in such case ? If it
is infinite, the final_temperature rule seems difficult to
understand.

Thanking you for your time,
Nick.

.



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