Global minimization of the Gibbs energy of multicomponent systems Involving the presence of order/disorder phase transitions

We present in this paper a robust strategy to determine the equilibrium state, in the isobaric-isothermal (NPT) ensemble, of complex multicomponent systems in which solid solutions presenting order/disorder transitions are stable. The algorithm specifically designed to construct the first estimate of the phase assemblage describing the equilibrium state of the system is presented in detail in this work and tested on different binary and ternary systems in which solid solutions are modeled using i) the cluster site approximation or ii) the cluster variation method in the tetrahedron approximation for both the face-centered and body-centered cubic solutions. The performance of the sequential quadratic strategy using an exact Newton method and a linesearch method, implemented in this work for the specific resolution of Gibbs free energy minimization problems, is compared to the one of other large-scale optimization software packages: SNOPT, IPOPT, and KNITRO. Key subroutines implemented in the strategy to locate local minima, and specifically implemented to improve the convergence toward targeted local minima, are also presented in this work and highlight the robustness of our approach.