Mobile wireless sensor networks (MWSNs), a sub-class of wireless sensor networks (WSNs), have recently been a growing concern among the academic community. MWSNs can improve network coverage quality which reflects how well a region of interest is monitored or tracked by sensors. To evaluate the coverage quality of WSNs, we frequently use the minimal exposure path (MEP) in the sensing field as an effective measurement. MEP refers to the worst covered path along which an intruder can go through the sensor network with the lowest possibility of being detected. It is greatly valuable for network designers to recognize the vulnerabilities of WSNs and to make necessary improvements. Most prior studies focused on this problem under a static sensor network, which may suffer from several drawbacks; i.e., failure in sensor position causes coverage holes in the network. This paper investigates the problem of finding the minimal exposure paths in MWSNs (hereinafter MMEP). First, we formulate the MMEP problem. Then the MMEP problem is converted into a numerical functional extreme problem with high dimensionality, non-differentiation and non-linearity. To efficiently cope with these characteristics, we propose HPSO-MMEP algorithm, which is an integration of genetic algorithm into particle swarm optimization. Besides, we also create a variety of custom-made topologies of MWSNs for experimental simulations. The experimental results indicate that HPSO-MMEP is suitable for the converted MMEP problem and performs much better than existing algorithms.