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 uniformly depend on the cost of the current and the candidate confirmation and that lead to detailed balance when combined with a symmetric generation matrix. Here the cost dependence is called uniform if it is expressed by one and the same function for all cost functions. As an important special case 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.