<p>In an edge computing environment, service providers place services on edge servers to deliver low-latency responses to users. The user coverage range and service takeover capability of a placement strategy-referred to as coverage and robustness, respectively-are two key performance metrics for assessing its effectiveness. the trade-off between coverage and robustness becomes a critical issue. Existing studies typically employ joint benefit models and optimize placement strategies using greedy algorithms, yielding noticeable improvements in overall performance. However, due to the scale disparity between the two benefit metrics, these approaches struggle to achieve a satisfactory trade-off and exhibit limited adaptability across diverse scenarios. To address these issues, this paper formulates a Trade-off between Coverage and Robustness Edge Service Placement problem based on a same-scale benefit model and proves it to be NP-hard. On this basis, a hybrid optimization method, PSO-TK, is proposed by integrating Particle Swarm Optimization (PSO) with a TOP-K heuristic strategy to enhance global search performance. Experimental results on public datasets demonstrate that PSO-TK outperforms three baseline algorithms in overall benefit across different scenarios, effectively balancing coverage and robustness while also achieving superior performance in individual metrics. Furthermore, a comprehensive weight-sensitivity analysis reveals the variation trends of coverage and robustness benefits under different weight settings, demonstrating the stability and adaptability of PSO-TK across diverse scenarios. This study presents an effective modeling and optimization framework to address the trade-off between coverage and robustness in edge service placement, providing valuable insights for future research and practical applications across diverse scenarios.</p>