A Review of Mathematical Optimization Methods in Offshore Wind Energy Systems: Design, Layout, and Control

Offshore wind energy plays an increasingly important role in the global energy transition, while its design, layout, and operation involve complex optimization problems with strong nonlinearity, high computational cost, and uncertainty. This paper reviews recent advances (2021–2025) in mathematical optimization methods applied to offshore wind energy systems, focusing on turbine system design, wind farm layout, and control strategy optimization. A systematic and semi-quantitative comparison of optimization methods is conducted, including gradient-based methods, metaheuristic algorithms, surrogate-assisted approaches, and multi-objective optimization techniques. These methods are analyzed in terms of computational efficiency, applicability, global search capability, and engineering relevance, supported by representative results reported in the literature. The review further identifies key methodological patterns, discusses trade-offs among different approaches, and proposes practical guidelines for method selection. Finally, research gaps are highlighted, particularly regarding uncertainty modeling, computational scalability, and integrated optimization frameworks. The findings provide useful insights for both researchers and engineers in offshore wind optimization.