Enhanced efficiency of heavy-duty truck powertrains with constraints imposed on noise, vibration, and harshness requires novel solutions for torsion vibrations attenuation. In the paper, the weight-vibration Pareto optimization problem for a novel vibration absorber, a triple mass flywheel, for application in heavy-duty truck powertrains is considered. Global sensitivity analysis and Pareto optimization method are used to design a novel vibration absorber. The optimization method attempts to minimize oscillations of the torque at the transmission input shaft as well as to minimize total mass inertia of the absorber. It is shown that there exists a Pareto front between the measure of the attenuation of oscillations of the torque and the total mass inertia of a triple mass flywheel. The optimized design parameters for the absorber are obtained that provide the best attenuation of oscillations of the torque at the transmission input shaft for different mean values of the engine driving torque. The analysis shows real evidence of the feasibility of the application of this concept of vibration absorbers in heavy-duty truck powertrains. It is also shown that optimized design parameters of a triple mass flywheel put this concept in a superior position in comparison with a dual mass flywheel.