Coupling sensors in a sensor network with mobility mechanism can boost the performance of wireless sensor networks (WSNs). In this paper, we address the problem of self-deploying mobile sensors to reach high coverage. The problem is modeled as a multi-objective optimization that simultaneously minimizes two contradictory parameters; the total sensor moving distance and the total uncovered area. In order to resolve the aforementioned deployment problem, this study investigates the use of biologically inspired mechanisms, including evolutionary algorithms and swarm intelligence, with their state-of-the-art algorithms. Unlike most of the existing works, the coverage parameter is expressed as a probabilistic inference model due to uncertainty in sensor readings. To the best of our knowledge, probabilistic coverage of mobile sensor networks has not been addressed in the context of multi-objective bio-inspired algorithms. Performance evaluations on deployment quality and deployment cost are measured and analyzed through extensive simulations, showing the effectiveness of each algorithm under the developed objective functions. Simulations reveal that only one multi-objective evolutionary algorithm; the so-called multi-objective evolutionary algorithm with decomposition survives to effectively tackle the probabilistic coverage deployment problem. It gathers more than 78 % signals from all of the targets (and in some cases reaches 100 % certainty). On the other hand, non-dominated sorting genetic algorithm II, multi-objective particle swarm optimization, and non-dominated sorting particle swarm optimization show inferior performance down to 16-32 %, necessitating further modifications in their internal mechanisms.