Edge computing systems have become increasingly important in recent years due to the exponential growth of data generated by the Internet of Things (IoT). The placement of servers in edge computing systems plays a crucial role in optimizing performance and enhancing user experience. This paper addresses the optimal edge server placement (ESP) in Mobile Edge Computing (MEC) to enhance performance and minimize access delay. The paper introduces the multistart power of d choices algorithm, named MPdC, which combines multistart procedure and greedy-randomized technique to solve the ESP problem. The algorithm comprises two phases: The first phase employs an adaptive greedy-randomized approach to minimize a predefined objective, while the second phase embeds this algorithm within a multistart framework, reporting the best solution as the final one. Performance evaluation is conducted using a real dataset from Shanghai Telecom. The proposed algorithm is evaluated by comparing its performance to that of baseline methods, in terms of load balancing and average distance. The experimental results indicate that the proposed algorithm achieves better performance in the case of d=16. Also, it can be observed that selecting the average distance as the objective function in the proposed algorithm is a better criterion.