Most optimization-based community detection approaches formulate the problem in a single- or bi-objective framework. In this paper, we propose two variants of a three-objective function optimization formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. The first variant, named NSGA-III-KRM, considered Kernel k-means, ratio cut, and modularity, as three objective functions; whereas the second variant, named NSGA-III-CCM, considers community score, community fitness and modularity, as three objective functions. Experiments are conducted on four benchmark network datasets. Comparison with state-of-the-art and baseline methods along with decomposition-based multi-objective evolutionary algorithm variants (MOEA/D-KRM and MOEA/D-CCM) indicates that the proposed variants yield comparable or better results. This is particularly significant because the addition of the third objective does not worsen the results of the other two objectives. We also propose a simple method to rank the Pareto solutions obtained by proposing a new measure—the ratio of the hyper-volume and inverted generational distance. The higher the ratio, the better is the Pareto set. This strategy is particularly useful in the absence of empirical attainment function in the multi-objective framework, where the number of objectives is more than two.