MGS Evolutionary Algorithms and Its Convergence Analysis by Leong Weng In Thesis Supervisor: Prof. Tam, Sik Chung Faculty of Science and Technology There is an important major branch in optimization called Evolutionary Algorithms. Some of them are Simple Genetic Algorithm (SGA) and I-Ching Divination Evolutionary Algorithm (IDEA). Although they are different, they still have some common mechanisms so that they can be utilized as optimizers. We abstract those mechanisms and establish a framework called MGS Evolutionary Algorithm in this thesis so that if an evolutionary algorithm fits such framework, its convergence can be analyzed. We employ homogenous Markov Chain as a model for MGS evolutionary algorithms. We have shown that the corresponding Markov Chain is ergodic. Hence, MGS evolutionary algorithms will never converge. However, if we keep the super string from generation to generation, then the convergence of MGS evolutionary algorithm can be guaranteed.