This research applied a novel meta-heuristic algorithm called the zebra optimization algorithm (ZOA) to solve the RES-ELD problem, which evaluates the presence of both wind and solar power plants in the power system. The main objective function of the whole research is to minimize the total fuel cost (TFC). The results achieved by ZOA are compared to another modern meta-heuristic algorithm, average and subtract-based optimization (ASBO), using different criteria. The comparison results indicate that ZOA is completely superior to ASBO in all comparison criteria. Particularly, ZOA is better than ASBO at 0.139% in Min. TFC, 0.145% in Aver. TFC, 0.151% in Max. TFC, and 91.97% in standard deviation. Besides, ZOA not only provides a high speed of convergence to the optimal value but also finds a solution that meets all the involved constraints characterized by the RES-ELD problem. Because of the striking results while dealing with such large-scale problems, RES-ELD, therefore ZOA, deserves the powerful search method and is highly suggested for use to deal with other large-scale optimization problems.