The Global Convergence Analysis of the Bat Algorithm Using a Markovian Framework and Dynamical System Theory

With the development of computational intelligence [1, 2, 19, 26], nature-inspired algorithms have been shown to be effective and thus become widely used for various optimization problems [15, 17, 2]. However, there is still a significant gap between theory and practice. Though the applications of algorithms are very successful, the relevant fundamental theory lacks behind or no theory at all. For example, the bat algorithm (BA), developed by Xin-She Yang in 2010 [3, 4], has been shown to very efficient in practice, but there is no mathematical theory for analyzing this algorithm. In fact, most of the swarm intelligence based algorithms for computational intelligence have no or little theoretical analyses, except for a few algorithms, such as the well known particle swarm optimization [10, 12, 25, 27] and genetic algorithms [16, 34]. Though we know these algorithms can work well in practice, we rarely understand why they work so well and under what conditions or parameter ranges. These key challenges require further in-depth theoretical studies.