In recent years, the criticality of fore-aft vibrations induced by winds on wind turbine towers has increased; these vibrations are generally evaluated using equivalent fatigue load (EFL). This is the first study to adopt wind speed histories from large eddy simulations as input for dynamic analysis of wind turbines, and to evaluate EFL against real wind distribution. Tuned mass damper (TMD) and rotational inertial double tuned mass damper (RIDTMD) were employed to control these vibrations. Parametric analysis of the damper parameters was conducted. An innovative global optimization tool was developed based on a radial basis function neural network and genetic algorithm. Moreover, for the first time, GPU acceleration technologies were adopted to enable the optimizations of dampers through massive cases. Numerical results show that damper optimizations under real wind distributions are essential, and that optimized dampers reduce 44% EFL. The performance of RIDTMD is better than TMD but has a narrower system control bandwidth. The optimized dampers are significantly affected by wind speed; however, they are least affected by wind direction. The developed GPU-based codes can run 2001 times faster than the CPU-based ones, and the optimization tool can further reduce 85% computational time, which is open to other researchers. (c) 2020 Elsevier Ltd. All rights reserved.