726 Relaxation Processes in Optimization by Simulated Annealing
Manabu Hasegawa, Takafumi Yamaguchi · The Proceedings of Conference of Kanto Branch · 2001
Approach to the equilibrium state associated with simulated annealing is examined with a focus on the time scale that the difference among the statistics of the values of the cost function obtained from different search processes disappear. A measure is introduced to quantify the degree of this convergence and is applied to a random Euclidean traveling salesman problem. Computer experiments show that the convergence seems to follow the power law in the long search processes in the wide range of temperatures. The time steps needed to reach a quasi equilibrium state rapidly increase when the system is cooled below the temperature at which the specific heat is maximized. The validity of dynamic (or adaptive) cooling schedules, which are based oh statistics gathered only from a single search process on a finite time scale, is discussed.