An Archived Firefly Algorithm; A Mathematical Software to Solve Univariate Nonlinear Equations

Abstract

The future of optimization is now being conquered by modern meta-heuristic algorithms. Genetic algorithms, differential evolution, harmony search, firefly algorithm and cuckoo search are such meta-heuristic algorithms which have marked their success over many optimization tasks. Simplicity of the algorithm, less memory consumption and the accuracy of the approximations can be stated as the major reasons for their popularity. 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 the real and 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 in the field of nature inspired algorithms and also with a modified GA embedded with same properties the AFF A has. A simple GUI is developed using Matlab GUIDE to present the findings. Computer simulations show that the AFFA performs well in solving nonlinear equations with real and complex roots within a specified region. The suggested method can be further extended to solve a given system of nonlinear equations.