An archived firefly algorithm; a mathematical software to solve univariate nonlinear equations

Abstract

In this article, we are presenting a software solution that proposes some modifications to the existing firefly algorithm. The modification; archived firefly algorithm [AFFA] exhibits the ability of finding almost all complex roots of a given nonlinear equation within a reasonable range. The software implementation includes two main properties; an archive to collect the better fireflies and a flag to determine poor performance in firefly generations. The new modification is tested over genetic algorithms (GA), a phenomenal success in the field of nature inspired algorithms and also with a modified GA embedded with same properties that the AFFA has. A simple graphical user interface (GUI) is developed using MATLAB GUIDE to present the findings. Computer simulations show that the AFFA performs well in solving nonlinear equations with real as well as complex roots within a specified region.