A Real-World Application of Multi-Optimization for a Berthing Structure Using the MOMVO Algorithm

The Multi-Objective Multi-Verse Optimizer (MOMVO) is applied to the structural optimization of a real-world berthing dolphin (BD). The BD structure is represented in SAP2000 using a detailed finite element model of piles and cap, with berthing and mooring loads defined in accordance with international guidelines. Two conflicting objectives are considered simultaneously: minimizing construction cost and minimizing the maximum structural displacement. Structural and geotechnical requirements are incorporated through a penalty-based constraint handling scheme to ensure compliance with Vietnamese design standards. The optimization results indicate that MOMVO generates well-distributed Pareto-optimal solutions that outperform the existing design. Relative to the baseline configuration, the optimal solutions achieve cost reductions of up to 70% while significantly decreasing structural displacement, with several compromise solutions available to balance both objectives. The results demonstrate that the proposed MOMVO–FEM framework provides practical and feasible design alternatives for improving the efficiency and safety of pile-supported marine structures.