On simulated annealing with temperature-dependent energy and temperature-dependent communication

Simulated annealing (SA) is a generic optimization method that is quite popular because of its ease of implementation and its optimal convergence properties. Still, SA is widely reported to converge very slowly and it is common practice to allow extra freedom in its design at the expense of losing global convergence guarantees. In this paper, we derive simple sufficient conditions for the global convergence of SA when the cost function and the candidate solution generation mechanism are temperature-dependent. These conditions are surprisingly weak-they do not involve the variations of the cost function with temperature-and exponential cooling makes it possible to be arbitrarily close to the best possible convergence exponent of standard SA.