A simple method for the numerical evaluation of binodal curves, in ternary systems polymer-liquid (1)-liquid (2) and polymer (1)-polymer (2)-solvent, is presented. The technique exploits the SIMPLEX-MS-3 method. The objective function (fitness) is represented by the weighted sum of the square differences of chemical potentials of the two phases of each component, obtained evaluating first derivatives of Gibbs free energy of the mixture with respect to the number of moles of the components. The proposed method: (1) is numerically stable since it does not require the evaluation of first derivatives of the objective function and (2) can be applied in a wide range of cases changing the equation of state. Several comparisons with simplified iterative procedures presented in the past in the technical literature for mixtures of two polymers with identical characteristics in a solvent and for mixtures of solvent-nonsolvent-polymer with solvent-polymer interaction parameter equal to zero are reported. Finally, a comparison between present results and the alternating tangent approach is reported for two technically meaningful binary systems, when a simplified PC-SAFT equation of state is adopted. The comparisons show that reliable results could be obtained by means of the proposed algorithm and suggest that the presented procedure could be used for practical purposes. The obtained phase diagrams compare well with those calculated with the alternating tangent approach. Provisional conclusions follow. An optimization algorithm for the numerical evaluation of binodal curves in ternary systems, liquid (1)-liquid (2)-polymer and polymer (1)-polymer (2)-solvent, was presented. The technique exploits the SIMPLEX-MS-3 optimization method. Objective function was represented by the weighted sum of square differences of chemical potentials of two phases of each component, obtained evaluating first derivatives of Gibbs free energy of mixture with respect to number of moles of components.