Significance: The global offshore wind power industry is experiencing rapid growth, with floating offshore wind energy technology emerging as a pivotal solution for exploiting wind resources in deep sea areas. The floating foundation, a critical component of floating offshore wind power systems, plays an essential role in ensuring the stability and safe operation of wind turbines. However, the design and analysis of these foundations are fraught with challenges due to their intricate system composition, distinctive dynamic characteristics, and the harsh marine environment they must endure. Traditional design methods, which rely heavily on experience and trial-and-error, are not only inefficient but also fail to integrate multidisciplinary theories, highlighting the need for the more scientific design and optimization tools. Progress: As research delves deeper, technological advancements, and accumulated development experience have led to the application of multidisciplinary optimization design and analysis techniques in the floating wind power sector. The field of floating offshore wind power foundation optimization has seen significant advancements in recent years, with a shift towards more sophisticated multidisciplinary, multi-objective optimization techniques. These techniques have been crucial in addressing the complex interplay between various factors such as structural mechanics, hydrodynamics, aerodynamics, and economic considerations. MDAO techniques, initially from aerospace, enable system-wide optimization by considering interdisciplinary interactions, crucial for managing the complex dynamics between wind turbines and environmental loads. In the realm of optimization algorithms, genetic algorithms, particularly the Non-Dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ), have become prominent due to their ability to handle multiple conflicting objectives simultaneously. These algorithms have been effectively utilized to identify a set of Pareto-optimal solutions, providing a range of options that balance different performance criteria such as cost, structural fatigue, motion response, and tower acceleration. The use of frequency domain analysis has been widespread for early-stage optimization research due to its efficiency in capturing key dynamic characteristics of the floating structures. However, the industry has also recognized the need for time-domain simulations to capture the nonlinear dynamics of the system, especially when precision is paramount. Hybrid methods that combine the benefits of both frequency and time-domain analyses, as well as the application of surrogate model, are being developed to achieve a balance between computational efficiency and accuracy. These innovative techniques offer scientific guidance for the scale planning and optimization design of floating foundations, striving to achieve an optimal balance in cost, performance, and environmental adaptability. This paper provides a comprehensive review of the evolution and application of multi-objective, multidisciplinary optimization methods in the scale optimization of floating offshore wind power foundations. Conclusions: The integration of multi-objective, multi-disciplinary optimization technology is of paramount importance for the optimized design of floating offshore wind power foundations. By merging structural optimization concepts with efficient optimization algorithms and precise simulation tools, it is possible to enhance design efficiency, abbreviate the design cycle, and more scientifically and swiftly obtain floating foundation design that exhibit superior comprehensive performance. This approach not only streamlines the design process but also ensures that the final scheme is more robust and cost-effective, meeting the stringent requirements of the offshore wind power industry. Looking ahead, the field is expected to see further integration of advanced computational methods, machine learning techniques, and high-fidelity simulations to push the boundaries of floating offshore wind power foundation design, leading to more efficient, cost-effective, and durable solutions that can withstand the test of time and the rigors of the marine environment.