Theoretical Framework of Binary Ant Colony Optimization Algorithm

The convergence speed of ant colony optimization (ACO) is one of the open problems in ACO research. We begin this theoretical analysis with the study of a simple version of ACO named binary ant colony optimization (BACO) algorithm. This paper draws a conclusion on the theoretical framework of BACO including modeling, convergence and convergence speed. First, BACO is modeled as an absorbing Markov process (AMP) and the premise of modeling is given. Second, the convergence and convergence speed of BACO are discussed based on the AMP model. Finally, the convergence speeds of a BACO algorithm are analyzed for case study by estimating the expected first hitting time.