What is simulated annealing?

Beginning in 1983, simulated annealing was marketed as a global optimization methodology that mimics the physical annealing process by which molten substances cool to crystalline lattices of minimal energy. This marketing strategy had a polarizing effect, attracting those who delighted in metaphor and alienating others who found metaphor insufficient at best and facile at worst. In fact, the emotional outbursts that accompany many discussions of simulated annealing are an unfortunate distraction. Whatever its pros and cons, simulated annealing can be grounded in rigorous mathematics. Here we provide an elementary, self-contained introduction to simulated annealing in terms of Markov chains.