In this paper, we perform a comparative study of four stochastic optimization methods for calculating the phase stability of reactive and nonreactive mixtures. We have compared the algorithms: simulated annealing, very fast simulated annealing, a modified version of direct search simulated annealing, and stochastic differential equations. We test the numerical performance and reliability of these methods using several stability problems. From our results, the simulated annealing algorithm appears to be the most reliable method for minimization of the tangent plane distance function for both reactive and nonreactive mixtures.