Edge Servers (ESs) enhance the efficiency and reliability of modern Beyond Fifth-Generation (B5G) network systems by reducing latency, boosting responsiveness, and optimizing network usage. From an industry standpoint, the optimal positioning of ESs is critical to enhancing coverage reach while reducing potential conflicts with neighboring servers, guaranteeing consistent and reliable user access. Traditional circular coverage for ESs is suboptimal due to inherent constraints. The hexagonal model, known for symmetrical and consistent distribution, emerges as a superior choice. Implementing Fault Tolerance Edge Server Placement (FT-ESP) demands workload distribution across servers to prevent overloading and mitigate service failures. The complexity of assigning multiple Base Stations (BSs) to ESs categorizes FT-ESP as a Nondeterministic Polynomial Time (NP-hard) problem. To address this, the Subset Sum Encoding Scheme (S2ES) has been introduced, linking BSs to ESs. This research Fault Tolerance Subset Sum Encoding Scheme (FT-S2ES) examines various Edge Server Placement Problem (ESPP) strategies, highlighting the proposed method's efficacy compared to traditional techniques. The empirical findings indicate that, when tested on real-world datasets, the suggested strategy successfully achieves a balanced workload and utilization rate of 8.82% and 7.67%, respectively. Compared to the Grey Wolf Optimizer (GWO) algorithm, energy usage is significantly reduced by 32.23%. In addition, the proposed approach ensures a reduction in latency by 22.80% with an increasing number of BSs and 9.47% with an increasing number of ESs.