Classification of acceptance criteria for the simulated annealing algorithm

We present a complete and explicit description of the class of all acceptance criteria for the simulated annealing algorithm that are uniformly and locally cost dependent and that lead to reversibility when combined with a symmetric generation matrix. In particular we identify the subclass consisting of those acceptance criteria that depend uniformly on the difference in cost. Furthermore, we present a simple characterization of the Metropolis and the Barker criterion.