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Existing numerical methods to solve univariate nonlinear equations sometimes fail to return the required results. 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.
