On the Convergence of Prey Predator Algorithm

Unlike their success in solving complex and difficult problems, there is a lack of proper mathematical analysis and discussion of metaheuristic algorithms. Even though some researches are done on these aspects, the gap is still wide and different researchers outlined that more needs to be done to understand and analyse the search behaviour mathematically in order to move towards explainable AI. Convergence analysis is one of the issues researchers are trying to address. In this paper, a discussion on the convergence of prey predator algorithm will be presented. It is a swarm based algorithm which shows promising results. Furthermore, some initial researches show that it is a generalized algorithm where some well known algorithms fall as its special case. Hence, its analysis can be customized and used for other algorithms as well. Based on mathematical arguments, this paper discusses the convergence analysis of the algorithm to a near optimal solution with appropriate implementation, i.e. appropriate parameter setting. Prey predator algorithm is shown to be an \(\epsilon \) $ϵ$ -convergent algorithm that means there is a non infinity iteration number to get at least epsilon less quality from an optimal solution.