With the rapid development of mobile technology, mobile applications have increasing requirements for computational resources, and mobile devices can no longer meet these requirements. Mobile edge computing (MEC) has emerged in this context and has brought innovation into the working mode of traditional cloud computing. By provisioning edge server placement, the computing power of the cloud center is distributed to the edge of the network. The abundant computational resources of edge servers compensate for the lack of mobile devices and shorten the communication delay between servers and users. Constituting a specific form of edge servers, cloudlets have been widely studied within academia and industry in recent years. However, existing studies have mainly focused on computation offloading for general computing tasks under fixed cloudlet placement positions. They ignored the impact on computation offloading results from cloudlet placement positions and data dependencies among mobile application components. In this paper, we study the cloudlet placement problem based on workflow applications (WAs) in wireless metropolitan area networks (WMANs). We devise a cloudlet placement strategy based on a particle swarm optimization algorithm using genetic algorithm operators with the encoding library updating mode (PGEL), which enables the cloudlet to be placed in appropriate positions. The simulation results show that the proposed strategy can obtain a near-optimal cloudlet placement scheme. Compared with other classic algorithms, this algorithm can reduce the execution time of WAs by 15.04–44.99%.