Among all the existing possibilities within the renewable energies field, wind energy stands out due to the significant expansion of offshore turbines installed in coastal and deep-sea areas. Although the latter represent considerable energy generation potential due to their larger size and location in areas of strong winds, they are exposed to harsh environmental disturbances, particularly waves, causing these structures to experience vibrations, increasing in this way fatigue, reducing efficiency, and leading to higher maintenance and operational costs. In this work, vibration reduction is achieved using two structural control systems for a 5 MW barge-type floating offshore wind turbine (FOWT), tuned via a metaheuristic method, with genetic algorithms (GAs). Firstly, the standard deviation of the Top Tower Displacement (TTD) is used as a cost function in the GA to optimize a passive Tuned Mass Damper (TMD), resulting in a vibration suppression rate of 34.9% compared to a reference standard TMD. Additionally, two semi-active structural control systems based on a gain scheduling approach are proposed. In one of the approaches, the TMD parameters are optimized based on the amplitude of oscillations, achieving a suppression rate of 45.4%. In the second approach, the TMD parameters are optimized in real time for the identified wave frequencies, demonstrating superior performance for medium-high frequencies compared to the other TMDs.