Cycle Decompositions and Simulated Annealing

The behavior of simulated annealing algorithms is tightly related to the hierarchical decomposition of their configuration spaces in cycles. In the generalized annealing framework, this decomposition is defined recursively. In this paper, its structure is extensively studied, and it is shown that the decomposition can be achieved through an implementable algorithm which allows exact computation of the fundamental constants underlying the behavior of these algorithms.