This study investigates the influence of installation methods on the optimization design and vibration reduction perfor mance of a novel tuned mass damper inerter （NTMDI）. Firstly， the mechanical model of NTMDI-R （reverse-installed NTMDI） is introduced in detail， and its optimization design of NTMDI-R is performed using classical fixed-point theory， resulting in analyti cal expressions for the optimal structural parameters of NTMDI-R. Subsequently， a comparative study is conducted to analyze the vibration reduction effects of NTMDI-R and four existing classical tuned mass dampers （TMD， TMDI， VTMD， and NTMDI） under harmonic and random excitations， while also investigating the influence of installation methods on the vibration reduction per formance of NTMDI-R. The results demonstrate that the optimized parameters of the two dampers （NTMDI and NTMDI-R） dif fer， and the installation method has a significant impact on their vibration reduction performance. When the apparent mass ratio β is less than 0.1， NTMDI-R exhibits a lower vibration reduction effect compared to NTMDI. However， when β exceeds 0.1， the vi bration reduction effect of NTMDI-R becomes similar to that of NTMDI. Therefore， when adopting NTMDI for structural vibra tion reduction， the installation direction should be specified. Under base acceleration and load force conditions， the vibration reduc tion effect of NTMDI-R is reduced by 3.9% and 4.7%， respectively， compared to NTMDI.