The Markov Model of Bean Optimization Algorithm and Its Convergence Analysis

By simulating the self-adaptive phenomena of plants in nature, a novel evolutionary algorithm named Bean Optimization Algorithm (BOA) was proposed in 2008. BOA can be used for resolving complex optimization problems. As BOA is a new optimization algorithm, theoretical analysis of the algorithm is still very preliminary. Research on the state transfer process and the convergence behavior of BOA is of great significance for understanding it. In this paper, we build the Markov chain model of this algorithm and analyze the characters of this Markov chain. Then we analyze the transferring process of the bean memeplex status series and point out that the memeplex status series will enter the best status set. We also prove that this algorithm meets the requirement of global convergence criterion of random search algorithms. Finally we get the conclusion that BOA will make sure to get the global optimum.