Mobile Edge Computing (MEC) enhances service quality by decentralizing computational resources to network edges, thereby reducing latency and improving Quality of Service (QoS). However, the spatial distribution of edge servers critically impacts network transmission efficiency, while heterogeneous user perceptions of QoS metrics frequently lead to suboptimal Quality of Experience (QoE). Current research on Edge Server Placement (ESP) predominantly focuses on localized optimization of QoS metrics, yet fails to adequately incorporate systematic QoE modeling and coordinated optimization frameworks, leading to significant discrepancies between actual user experience and satisfaction with resource allocation. To address this gap, this study establishes a formalized QoE-aware Edge Server Placement (EESP) framework by rigorously characterizing the interdependence between QoE and QoS. We first prove the NP-completeness of the EESP problem through computational complexity analysis. Subsequently, we develop an Integer Linear Programming-based exact solver (EESP-O) for small-scale scenarios and propose an Enhanced Genetic Algorithm (EESP-EGA) for large-scale deployments. The EESP-EGA integrates adaptive crossover probability mechanisms and elite retention strategies to achieve near-optimal solutions for complex real-world configurations. Experimental evaluations conducted on a broad range of real-world datasets demonstrate that the proposed method outperforms several existing representative approaches in terms of QoE