An Unbiased Butterfly Optimization Algorithm

Abstract

Several bio-inspired optimization techniques have been used to solve multidimensional multimodal optimization problems. Butterfly optimization algorithm (BOA) is a recent bio-inspired technique that emulates butterflies’ foraging which is based on their sense of smell to determine the location of nectar. BOA shows fast convergence compared to other optimization techniques such as particle swarm optimization (PSO), genetic algorithm (GA) and biogeography based optimization (BBO) when compared over several standard optimization problems. In this paper, the basic algorithm of BOA is demonstrated to be biased to search for optimal points near origin. This feature is the main cause of the fast convergence of BOA in standard test problems where the optimal points is at (or near) the origin. Without this biasing effect, BOA suffers from slow convergence and may not converge to the global minimum even for unimodal low dimensionality problem. The evidence of biasing is demonstrated, and an unbiased version of the BOA (UBOA) is proposed to alleviate this problem. UBOA is proved to outperform BOA in case of shifted functions. Test results using several benchmark problems demonstrate that UBOA provides a competitive optimization method with respect to other bio-inspired methods.