Unlike traditional analytical optimization techniques, bio-inspired multi-objective optimization has recently enjoyed an intense interest regarding wireless sensor network (WSN) issues. Network lifetime and target coverage are among the major concerns in many well-established scenarios of WSNs, such as routing and node deployment. For set covers scenario in WSNs, however, little attention has been paid to the role of multi-objective requirements. In this paper, we take a step toward exploring the feasibility of such bio-inspired algorithms for solving multi-objective set covers problem in WSNs. The main contributions of this study are twofold. First, we extend the set covers problem and address it with three issues: network lifetime, target coverage, and network connectivity as a multi-objective set covers (MOSC) formulation. To the best of our knowledge, this is the first effort to define such a general multi-objective set covers problem. Second, we design and elaborate four well-known multi-objective optimization algorithms from evolutionary and swarm intelligence community to tackle the formulated MOSC problem. All characteristic components of the adopted algorithms are tailored specifically to handle the formulated problem. Further, a self-adaptive heuristic mutation operator is proposed to attain and emphasize the strength of the algorithms in terms of network lifetime and coverage probability. Extensive simulations are performed to test and demonstrate the performance of the designed algorithms to tackle the problem appropriately.