Vibrations' mitigation of linear structures, subjected to random excitations, using linear tuned mass dampers (TMDs), has been widely adopted in the field of structural dynamics. Although the TMDs are reliable and constitute a very efficient low-cost solution, their dynamic parameters should be carefully tuned in order to guarantee optimal performances. Several optimization methods can be used such as the reliability-based optimization (RBO) of the TMD parameters. Even though the efficiency of the RBO strategy is proven, its main drawback shows up when addressing a multi-degree of freedom structure. Indeed, only the targeted vibrating mode exhibiting the largest amplitude is controlled whereas the other modes, with relatively smaller vibrating magnitudes, remain uncontrolled. In the present work a new band-limited BL-RBO criterion is presented. The new criterion is based on