It has been demonstrated that adding a few percent of nanoscale reinforcements, leads to remarkable improvement in mechanical properties of the polymers such as stiffness, damping, and energy absorption. These lightweight materials are attractive substitutes for the heavy metallic structural parts in the automotive, military, aerospace and many other industries. However, due to complexity of these multiphase materials, accurate modeling of their behavior in real loading cases is still ambiguous. The impact simulation is a vital step in design procedure of a vehicle, where a strain rate-dependent model of its components is required. In this paper, an elasto-viscoplastic modeling procedure of the polymer-based nanocomposites, assuming the elastic behavior of the nano-phase is presented; whereas the polymeric matrix deformation is dependent to the loading rate and is characterized by the method of Genetic algorithm optimization-based fitting to the experimental observations. By introducing a modified Halpin-Tsai method, the nanocomposite is then modeled as a homogenized material where the modification algorithm is the main challenge. A combination of approaches including parametric analysis, central composite design of experiments and response surface method is proposed to modify the tangent modulus of the polymeric matrix to be passed as the input to the Halpin-Tsai equations. Finally, the procedure is implemented to a set of epoxy-GNP nanocomposites under unidirectional compressive loads with different rates and the stress-strain curves are predicted with a decent precision.