The wake in a large-scale Floating Offshore Wind Farm (FOWF) can reduce the wind speed in downstream areas, thereby affecting and reducing the power production of FOWF. To maximize the power production of the FOWF, it is necessary to solve the power optimization problem and obtain the optimal control actions for the coordinated operation of wind turbines. Due to the complexity of the optimization problem, there remains difficulty in applying swarm intelligence algorithms, and thus we propose a dimensionality reduction-based surrogate-assisted framework. Firstly, a low-dimensional surrogate model is constructed using data generated by swarm intelligence algorithms and dimensionality reduction algorithms during the optimization process. Secondly, based on the low-dimensional surrogate model, multi-subswarms pre-screening is carried out to filter out poor solutions in the population and reduce the time consumption of calculating the objective function. Thirdly, the trust region range is determined and a local surrogate model is constructed for multiple local searches using the results of the multi-subswarms pre-screening, and the elite individuals obtained further guide the population individuals to search for optimization, improving the optimization efficiency of the algorithm. Finally, the proposed method is simulated and verified in a FOWF with 64 wind turbines. Under the wind direction where the wake effect is severe, the steady-state power production can be increased by more than 6%. Compared with conventional swarm intelligence algorithms and numerical solution methods, the proposed method produces more power while having smaller time cost under different wind conditions.