A Modified Firefly Algorithm to solve Univariate Nonlinear Equations with Complex Roots

Abstract

Recently developed meta-heuristic algorithms such as firefly algorithm, bat algorithm, particle swarm optimization and harmony search arc now becoming popular for providing nearly accurate solutions for tough optimization problems. This paper addresses the problem of finding all roots of a given univariate nonlinear equation with real and complex roots using a modified firefly algorithm (MOD FA). The appropriate modifications are applied to the existing firefly algorithm (FA) by introducing an archive. Better fireflies are noted and stored in the archive during the iteration process and then their positions are replaced by new random ones. A comparison was carried out with the original firel1y algorithm and also with the genetic algorithm (GA) which has a similar behaviour to the firefly algorithm. Computer simulations show that the proposed firefly algorithm 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.