In this work an improved method for designing a linear vibrational absorber, excited by random vibrations is presented and analyzed. First, analytical expressions, for non-stationary white noise accelerations, are derived. The criterion is different from the conventional criteria, used for structural design under random vibration, and it is based on minimum displacement or acceleration response of the main structure, without considering required performance against failure. In this study, in order to control the structural vibrations induced on a mechanical structure excited by non-stationary based acceleration random process, the Multi-objective optimum (MOO) design of a vibration absorber has been developed. This has been performed using the bees optimization algorithm. The analysis is developed by considering a case study of a multi degree of freedom system with uncertain parameters, subject to random vibrations and equipped with a vibration absorber. Results demonstrate the importance of performing a pre-design procedure and show that the multi-objective pre-design methodology is economical and leads to time reduction and raw data accumulation. This method is particularly well performed for structures with higher degrees of freedom (DOF.