Designing mooring lines for floating buoys is essential to keep them stable and secure, especially in open water with unpredictable waves, wind, and currents. This paper introduces a practical way to improve mooring line design by using catenary theory to model how the line behaves and applying the Multi-objective Mantis Search Algorithm (MOMSA) for optimization. The aim is to find mooring line solutions that use less material and reduce how far the buoy drifts from its intended position. The approach also considers real-world requirements, such as choosing line weights from standard product lists and following national technical standards. The results show that MOMSA can successfully provide engineers with various good design options, helping them choose between safety and material costs.