We present a complete and explicit description of the class of all acc
eptance criteria for the simulated annealing algorithm that uniformly
depend on the cost of the current and the candidate confirmation and t
hat 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 c
riteria that depend uniformly on the difference in cost. Furthermore.
we present a simple characterization of the Metropolis and the Barker
criterion.