The folding of several model proteins is studied using three optimization algorithms which are based on the simulated annealing of an approximation to the classical density distribution. These methods are derived from the approximate solution of equations of motion for the time or temperature evolution of the density distribution. Therefore, it is of interest to analyze not only the resulting lowest energy molecular conformations but also the folding mechanism followed during the annealing runs. The results are compared with classical simulated annealing based on molecular dynamics and the diffusion equation method of Scheraga and coworkers. The model proteins studied are 22-mers and a 46-mer based on a three-letter code used by Honeycutt and Thirumalai. The potential models the basic properties of attractive interactions between hydrophobic residues, to encourage the formation of a hydrophobic core, and the propensity of hydrophilic residues to be found at the protein surface. Analysis of the thermodynamically dominant structures during annealing reveals a collapse transition at high temperature followed by a strong folding transition to the native state at lower temperatures. This general mechanism has been seen previously in simulations of similar model proteins and predicted on the basis of mean field theories of heteropolymers. We find that the probability of success in finding the set of lowest energy native states is strongly correlated with the energy separation between the native (and native-like) and non-native states. Our optimization algorithms are effective in finding those low-energy structures which correspond to the global energy minimum fold. The results indicate that dynamical phase space simulated annealing methods may have an advantage over configuration space based search for complex fold topologies.