On Convergence of Pigeon Inspired Optimization Algorithm

Abstract

The pigeon inspired optimization (PIO) is a metaheuristic algorithm which finds an optimal solution in the complex search spaces using homing behavior of pigeons. PIO algorithm has been applied to solve various optimization problems in different domains and is empirically shown to perform well. However, the convergence of this algorithm has not been established analytically in the literature. In this paper, the update equations of PIO algorithm are regarded as a discrete time-varying system and its convergence is analysed. This paper attempts to establish the convergence of PIO algorithm using two methods. The first method uses the state transition matrix approach and the second method is based on showing the convergence using the solution of linear discrete time-varying systems. Further, the appropriate choice of the parameter in PIO algorithm and its influence on the convergence of the algorithm is also discussed.