Empirical likelihood is a nonparametric method based on a data-driven likelihood. The flexibility of empirical likelihood facilitates its use in complex settings, which can in turn create computational challenges. Additionally, the Empty Set Problem (ESP) which arises with the Empirical Estimating Equations approach can pose problems with estimation, as data are unable to meet constraints when the true parameter is outside the convex hull. As an alternative to the Newton and quasi-Newton methods conventionally used in empirical likelihood, this dissertation develops and examines various Evolutionary Algorithms for global optimization of empirical likelihood estimates, as well as a comparison of the ESP versus non-ESP data sets on an overdetermined problem. Finally, we carry out a preliminary application of composite empirical likelihood methods, noting the impact of the ESP on the subsets of data, and compare the results obtained on all possible combinations against those from convergent subsets only.