Two-Stage NSGA II–PSO Optimization for Ballast-Water Allocation of Semi-Submersible Barge During Coastal Load-Out Operations

During roll-on load-out of a semi-submersible barge, ballast-water regulation directly affects floating-state accuracy, operational safety, and longitudinal structural response. Conventional ballasting relies heavily on predefined plans and operator experience, making it difficult to simultaneously ensure stern-draft matching, engineering operability, and structural safety under continuously changing heavy-load conditions. This study proposes an engineering-oriented two-stage ballast-water optimization framework incorporating field-derived expert knowledge and coordinated floating state–deflection control for a 45,000-ton semi-submersible barge. Ballast adjustments in individual tanks are used as decision variables subject to physical, floating-state, operational, and structural constraints. In Stage I, an NSGA-II-based population search explores the feasible ballast space using stern-draft deviation as the primary ranking criterion while enforcing trim, heel, tank-capacity, and operational constraints. In Stage II, PSO performs local refinement of the selected feasible solutions; trim and heel are included in the fitness evaluation and remain subject to hard operational limits. Hull longitudinal deflection is subsequently incorporated to form coordinated floating state–deflection optimization. Field measurements from the Module-001 load-out process are used for validation. Compared with standalone PSO, the proposed two-stage method reduces the maximum stern-draft error from 0.103 m to 0.019 m and decreases the average optimization time from approximately 18 min to 4 min. Additional validation using the more complex Module-002 load-out case yields stern-draft errors of approximately 0.001 m for most conditions and a maximum error of 0.007 m. Under coordinated optimization, stern-draft deviations remain within ±0.02 m, trim and heel satisfy the prescribed operational limits, and the maximum relative hull deflection is controlled within approximately 0.06 m. The optimized strategy evolves from fore-and-aft-dominated regulation to coordinated whole-tank regulation, with midship tanks contributing to longitudinal deformation control. The proposed method therefore provides a practical framework for intelligent ballast regulation during heavy-load roll-on operations.