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

Abstract

AttachedR e c e n tly d e v e lo p e d m e ta -h e u ris tic a lg o r ith m s s u c h as f ir e fly a lg o rith m , b a t a lg o rith m , p a r t ic le s w a r m o p t im iz a tio n a n d h a rm o n y s e a rc h a re n o w b e c o m in g p o p u la r f o r p r o v id in g n e a rly a c c u ra te s o lu tio n s f o r to u g h o p t im iz a tio n p r o b le m s . T h is p a p e r a d d re sse s th e p r o b le m o f fin d in g a ll ro o ts o f a g iv e n u n iv a ria te n o n lin e a r e q u a tio n w it h r e a l a n d c o m p le x ro o ts u s in g a m o d ifie d fir e f ly a lg o rith m ( M O D F A ) . T h e a p p ro p r ia te m o d ific a tio n s a re a p p lie d to th e e x is tin g f ir e fly a lg o r ith m ( F A ) b y in tr o d u c in g a n a rc h iv e . B e tte r fir e flie s a re n o te d a n d s to re d in th e a rc h iv e d u r in g th e it e r a tio n p ro c e s s a n d th e n th e ir p o s itio n s a re re p la c e d b y n e w ra n d o m o n es. A c o m p a ris o n w a s c a r r ie d o u t w it h th e o r ig in a l f ir e fly a lg o r ith m a n d a ls o w it h th e g e n e tic a lg o r ith m ( G A ) w h ic h h a s a s im ila r b e h a v io u r to th e f ir e fly a lg o rith m . C o m p u te r s im u la tio n s s h o w th a t th e p ro p o s e d f ir e fly a lg o rith m p e r fo rm s w e ll in s o lv in g n o n lin e a r e q u a tio n s w it h r e a l a n d c o m p le x ro o ts w it h in a s p e c ifie d re g io n . T h e su g g e ste d m e th o d c a n be fu r t h e r e x te n d e d to s o lv e a g iv e n s y ste m o f n o n lin e a r e q u a tio n s .