Optimization of the storage modulus and the hysteretic damping capacity of multilayer carbon nanotube (CNT) nanocomposites is carried out via a differential evolution algorithm coupled with a nonlinear finite element implementation of a 3D mesoscale theory of nanocomposites exhibiting CNT/polymer stick-slip behavior. Such constitutive theory describes the hysteresis due to the shear stick-slip between the carbon nanotubes and the long molecular chains of the hosting matrix wrapped around them. The storage modulus and the amount of energy dissipated through the CNT-matrix stick-slip depend on the nanocomposite microstructural parameters, such as the elastic mismatch, the nanofiller content, its distribution, and the CNT-matrix interfacial shear strength. The optimization problem seeks to determine the set of material parameters of a multilayer stacking sequence that can give rise to the largest storage modulus and damping capacity of the ensuing nanocomposite. The results confirm that the genetic-type multilayer nanocomposite damping optimization resorting on a sound mechanical model of the nonlinear hysteretic material response can be an effective and affordable design method.