This study focuses on solving the green economic load dispatch problem by considering the presence of green energy sources, including wind energy and solar power plants. The main objective function of the whole study is to minimize the total fuel cost (TFC) of all the thermal generating sources (TGSs) in the system. Moreover, the multiple selection of all TGSs is also evaluated. Fire hawk optimization (FHO) and the Zebra optimization algorithm (ZOA) are applied to solve the problem of achieving the best TFC value and satisfying all the constraints involved. The results indicated that ZOA can achieve a better optimal solution compared to FHO. Particularly, the results obtained by ZOA are completely superior to FHO in all comparison criteria at two load demand levels, such as Best TFC value (Best.Cost), Average TFC value (Aver.Cost), and Maximum TFC value (Max.Cost). On top of that, ZOA is the only algorithm of two applied ones providing the fast convergence capability to the optimal value of the main objective functions in two cases of load demand levels. Therefore, ZOA is an efficient search method to deal with such GELD problems.