Direct search optimization is applied to Gibbs free energy minimization to determine phase compositions at equilibrium. The method selected is the random search optimization procedure of Luus and Jaakola, which has been shown to be successful for solving difficult global optimization problems. II is implemented in a multipass fashion where the region size for a variable at the beginning of each pass is put equal to the change in that variable in the previous pass. Results obtained with typical examples for vapor-liquid equilibrium and vapor-liquid equilibrium with reaction, where the liquid and vapor phases may be non-ideal, show that the LJ optimization procedure can be used to find very accurately the global minimum in only a few seconds of computation time on a personal computer. The method is easy to use and has high reliability of locating the global optimum, thus providing a useful means of checking the results obtained by other methods.