Abstract: Taking inspiration from the phenomena of water waves for global optimization,water wave optimization (WWO) is a novel evolutionary algorithm which mimics wave motions including propagation,refraction and breaking for effectively searching in a high-dimensional solution space,which has shown promising performance advantage over a variety of state-of-the-art metaheuristic optimization methods on well-known benchmark problems and real-world engineering problems.The paper theoretically analyzed the convergence conditions of the WWO algorithm.By simplifying the target problem and the parameter setting of the algorithm,we demonstrated that in WWO any individual can guaran-tee the convergence in two special cases:1) when only performing the propagation operation and 2) when only perfor-ming the refraction operation,which respectively happen under two special states of fitness changing.The paper also conducted numerical simulations for the two special cases respectively to validate the above convergence conditions.

Key words: Evolutionary algorithm,Water wave optimization algorithm ,Convergence,Propagation,Refraction