Recently, it has been demonstrated that a Vibro-Impact type Nonlinear Energy Sink (VI-NES) can be used efficiently to mitigate vibration of a Linear Oscillator (LO) under transient loading and harmonic force. In this paper, a design optimization procedure of an optimal VI-NES coupled to LO for energy pumping is presented theoretically and numerically. Due to the small mass ratio between the flying mass of the VI-NES and LO, the obtained equation of motion is possible to use the method of multiple scales in the case of 1:1 resonance. It is showed that there exist different response regimes like Strongly Modulated Response (SMR) proved to be the most efficient reponse regime for vibration reduction. An optimization procedure is presented and the results are verified numerically
