The advent of fifth-generation(5G) telecommunication technology and the rapid growth of smart mobile equipment have led to many processing demands in this area. Many mobile applications developed with this technological growth. In most cases, the services required by mobile cloud users are offered online. The high volume of processes, such as the Internet of Things, online games, electronic education, and e-commerce, which are processing-oriented, consumes a large amount of energy. The limited power of mobile equipment and their battery capacity causes some users' data and applications to be offloaded on network edge servers. Proper placement of mobile cloud resources has an important impact on their efficiency and energy consumption. The appropriate resource placement model can reduce latency and improve energy consumption. Because of the large number of mobile servers, finding the best geographical placement of all resources is an NP-Hard problem, so researchers have introduced some optimization methods for the problem solution. Parallelization methods can improve the scalability of the resource placement problem and reduce the time complexity of finding the optimal solution. In the proposed method, a novel multi-objective edge server placement algorithm, using the trees social relations optimization algorithm(TSR) and the DVFS(dynamic voltage and frequency scaling) technique (MSP-TD), has been introduced for optimal placement of edge servers to extend the network coverage. The simulation results show that our proposed model leads to less latency and energy consumption reduction than some state-of-the-art and similar algorithms.