Optimized designs of tuned inerter dampers (TIDs) have been studied by presetting TID locations for the control of structures with multiple degrees of freedom (MDOF). In addition to the stiffness and damping coefficients, the importance of the inerter device constant, termed inertance, has been recognized. However, research on the effect of inertance on the design of multiple TIDs for controlling multimode responses is insufficient. This study investigates the generalized optimal design of the TIDs for controlling MDOF structures subject to stochastic excitation, where all parameters including TID stiffness, damping, inertance, and locations were considered as variables to be potentially optimized. The excitation was modeled as filtered white noise and combined with a model of an MDOF structure attached with multiple TIDs to create an augmented state space representation. Global optimization was performed to identify the modes of tuning the TIDs, with the TID location and inertance fixed, and the design was improved by adding the inertance as a parameter, and the mechanism of the performance enhancement by optimizing the inertance was demonstrated. Using the global optimization results as initial values, localized placement designs of multiple TIDs were realized using topology optimization and optimal TID tests were performed on three- and ten-story buildings. Results show that the control performance was improved by optimizing the inertance, along with the frequencies and damping ratios, and that the localized placement of multiple TIDs with equal total inertance is optimally designed and can achieve comparable performance of the TIDs distributed at the structure.