  In a free-electron laser equipped with variable-gap undulator modules, the
technique of undulator tapering opens up the possibility to increase the
radiation power beyond the initial saturation point, thus enhancing the
efficiency of the laser. The effectiveness of the enhancement relies on the
proper optimization of the taper profile. In this work, a multidimensional
optimization approach is implemented empirically in the x-ray free-electron
laser FLASH2. The empirical results are compared with numerical simulations.
