Evaluation of the genetic algorithm performance for the optimization of the grand potential in the cluster variation method

Due to the importance of phase diagrams in a wide range of material based industries, additional efforts should be dedicated to their elaboration techniques. The cluster variation method is a promising technique to model the entropy within different plane lattices and is recognized by the materials physics community as a powerful modeling framework. Motivated by the efficiency of genetic algorithms in solving numerous types of optimization problems, our aim in this work is to investigate their performance in minimizing the grand potential in the context of the cluster variation method. A comparison is conducted with respect to numerical iterative techniques namely the Newton-Raphson and natural iteration methods, where many performance criteria are computed and compared. The obtained results allow the ranking of the considered approaches according to their performance measures and suggest a more profound investigation of metaheuristics particularly for complicated cluster structures in the future.