Floating offshore wind turbines (FOWTs) have become a promising solution for harnessing wind energy in deeper seas. However, the complex interplay between FOWT layout, mooring line patterns, and wake effects significantly influences the overall performance of a floating offshore wind farm (FOWF). This paper proposes a novel optimization methodology that integrates mooring line constraints into the FOWF layout optimization process. The wake-induced power deficit is considered, whereas the vortices are neglected. The new method considers the constraint areas for each FOWT, which are defined based on both mooring line buffer zones and wind turbine buffer zones. By defining constraint areas, the optimization process ensures that FOWTs are optimally positioned while avoiding interference and collisions. By carefully considering the buffer zones, the power potential of FOWFs with three-line, four-line, and six-line mooring configurations can be improved by 122%, 100%, and 78%, respectively. Then, a genetic algorithm is employed to optimize the FOWT positions and mooring line angles simultaneously. The effectiveness of the proposed method is demonstrated through a case study in Guangdong, resulting in a significant 5% increase in power output potential compared to conventional approaches. This research contributes to the advancement of FOWT layout optimization and provides valuable insights for the design and deployment of future FOWFs.