algorithms

Figure 9.11 Simulated annealing.
The trick is to start with T large and then gradually reduce it to zero. Thus initially,
the local search can wander around quite freely, with only a mild preference for low-cost
solutions. As time goes on, this preference becomes stronger, and the system mostly sticks to
the lower-cost region of the search space, with occasional excursions out of it to escape local
optima. Eventually, when the temperature drops further, the system converges on a solution.
Figure 9.11 shows this process schematically.
Simulated annealing is inspired by the physics of crystallization. When a substance is to
be crystallized, it starts in liquid state, with its particles in relatively unconstrained motion.
Then it is slowly cooled, and as this happens, the particles gradually move into more regular
configurations. This regularity becomes more and more pronounced until finally a crystal
lattice is formed.
The benefits of simulated annealing come at a significant cost: because of the changing
temperature and the initial freedom of movement, many more local moves are needed until
convergence. Moreover, it is quite an art to choose a good timetable by which to decrease the
temperature, called an annealing schedule. But in many cases where the quality of solutions
improves significantly, the tradeoff is worthwhile.
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