Equilibrium Definitions in Simulated Annealing: A Computational Experiment

Recently simulated annealing, a probabilistic heuristic motivated by an analogy between statistical mechanics and combinatorial optimization, has been used to obtain good solutions to various combinatorial problems. The method minimizes a function f(s) whose arguments are the elements of a finite set S of feasible configurations (or solutions when applied to a combinatorial optimization problem) by a sequence of actions called local exchanges. All exchanges which improve f are accepted where as exchanges which increase f are accepted with a probability depending on a parameter called the temperature. At a given temperature level, a sequence of local exchanges, the so called inner loop iterations, are executed until the system reaches an equilibrium. The number of temperature levels and the way the temperature is lowered is called the annealing schedule.