Convergence Analysis of Whale Optimization Algorithm

The whale optimization algorithm (WOA) has been widely used in different applications. It has simple control parameters and novel population updating mechanism. However, there is few theoretical analysis of WOA and the convergence property of WOA is ambiguity. This paper analyzes the convergence property of WOA by using the Markov chain of the stochastic process theory. The Markov chain model of the WOA algorithm is established. The one step transition probabilities and convergence properties of different population updating mechanisms in WOA are given. It's proved that the convergence property of WOA is determined by its shrinking encircling mechanism. Finally, three algorithms with different population updating mechanisms are tested with thirteen benchmark functions on accuracy and convergence speed. The simulation results on benchmark functions verify the validity of the theoretical analysis of WOA. (paper)