Attached
The use of numerical methods to solve univariate
nonlinear equations has many drawbacks. We propose a modified
firefly algorithm [MOD FA] with a self-tuning ability to solve a
given univariate nonlinear equation. Our modification is capable
of finding almost all real as well as complex roots of a nonlinear
equation within a reasonable interval/range. The modification
includes an archive to collect best fireflies and a flag to determine
poorly performed iterations. It is also capable of tuning the
algorithm-specific parameters while finding the optimum solutions. The self-tuning concept allows the users of our application
to use it without any prior knowledge of the algorithm. We
validate our approach on examples of some special univariate
nonlinear equations with real as well as complex roots. We have
also conducted a statistical test: the Wilcockson sign rank test.
By conducting a comparison with the genetic algorithm and
differential evolution with same modifications [MOD GA] [MOD
DE] and with the original firefly algorithm [FA], we confirm the
efficiency and the accuracy of our approach.
