We propose and demonstrate the use of an adaptive membrane mirror to increase the efficiency of coupling light into optical single-mode fibers. The membrane mirror has an active area of 12 mm in diameter and is electrostatically activated by 37 electrodes. Two optimization algorithms are compared. The first one is a maximization algorithm, while the second one is an evolutionary algorithm. These algorithms are used either to optimize the electrode voltages or to optimize a set of low-order Zernike polynomials describing the membrane deformation.