Studying the evolutionary community structure in complex networks is crucial for uncovering the links between structures and functions of a given community. Most contemporary community detection algorithms employs single optimization criteria (i.e., modularity), which may not be adequate to represent the structures in complex networks. We suggest community detection process as a Multi-objective Optimization Problem (MOP) for investigating the community structures in complex networks. To overcome the limitations of the community detection problem, we propose a new multi-objective optimization algorithm based on enhanced firefly algorithm so that a set of non-dominated (Pareto-optimal) solutions can be achieved. In our proposed algorithm, a new tuning parameter based on a chaotic mechanism and novel self-adaptive probabilistic mutation strategies are used to improve the overall performance of the algorithm. The experimental results on synthetic and real world complex networks suggest that the multi-objective community detection algorithm provides useful paradigm for discovering overlapping community structures robustly.