# How can I find the bounds that gets Simulated Annealing to converge?

According to Wikipedia on Simulated Annealing,

For any given finite problem, the probability that the simulated annealing algorithm terminates with a global optimal solution approaches 1 as the annealing schedule is extended.

I looked up the paper, Simulated Annealing: A Proof of Convergence, but unfortunately I didn't really understand how it related too well--it seemed to discuss a specific type of problem. I tried the experiment myself on the Four peaks problem, always starting from T=1E11 and as I upped the number of iterations, increased the cooling rate accordingly (cooling rate would be given by a number $0<c<1$, and finding the next T would just be c*T at each iteration). However, even with this, SA always converged to an inferior local optimum. I used the standard Boltzmann distribution probability.

So my question is, is the Wikipedia quote correct? If so, how can I decide on what the cooling schedule should be?

• The quotation is correct (it's a theorem about Markov chains)--but it cannot be checked empirically, because the annealing schedule might have to be extended to an astronomically large one. My experience with SA has been that different problems--at least those that are sufficiently complicated--seem to require different kinds of annealing schedules and different amounts of annealing to be successful, and even then you can be unlucky, so you need to run several trials anyway. – whuber Mar 9 '15 at 22:08