We present a simulated annealing algorithm formulated with six parameters that have physical significance. Therefore; appropriate choices of these parameters can be made by the user of the algorithm. Using both Haverly＇s Pooling Problems and a Benzene Alkylation Problem, we have studied the effect that varying the values of these parameters has on the performance of the annealing algorithm. These problems have been transformed such that all variables have the same range (0-1), and there are no constraints except those that define this range. We call such problems "practically unconstrained", and they allow a generalizable study of parameter effects. We have compared the results obtained by using both single-variable system state changes and multiple-variable system state changes. We have also shown that the best values for most of these parameters are largely problem independent.