This work presents the assessment of the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and one of its variants to optimize a proposed electric power production system. Such variant implements a chaotic model to generate the initial population, aiming to get a better distributed Pareto front. The considered power system is composed of solar, wind and natural gas power sources, being the first two renewable energies. Three conflicting objectives are considered in the problem: (1) power production, (2) production costs and (3) CO2 emissions. The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is also adopted in the comparison so as to enrich the empirical evidence by contrasting the NSGA-II versions against a non-Pareto-based approach. Spacing and Hypervolume are the chosen metrics to compare the performance of the algorithms under study. The obtained results suggest that there is no significant improvement by using the variant of the NSGA-II over the original version. Nonetheless, meaningful performance differences have been found between MOEA/D and the other two algorithms.