###### Abstract
The article by [PERSON] and [PERSON] [18] describes a study involving a single tuned mass damper (STMD) using a model of a building with multiple degrees of freedom (MDOF). It applied an optimization method based on the \(\mathrm{H}_{\infty}\) norm in the STMD control process. [PERSON], in the work [19], presents an exact \(\mathfrak{H}_{\infty}\) optimal solution for a serial TMD with a double mass connected to a damped primary system. In the optimization of \(\mathfrak{H}_{\infty}\) of the transfer function, a very precise numerical solution was successfully obtained by solving the sixth-order algebraic equation. MTMD parameters were studied by [PERSON] and [PERSON] [20], who utilized \(\mathfrak{H}_{2}\) optimization. They demonstrated that optimal structures did not have uniformly distributed tuning frequencies or identical damping factors for individual TMDs, and the applied optimization of individual parameters within an MTMD system provided significant improvement of the entire SDOF system with MTMD. In response to the aforementioned study, [PERSON] and [PERSON] [21] presented an optimization method for MTMDs with non-uniformly distributed mass, based on a gradient with linear search of the objective function. By solving the problem of multi-target optimization based on the objective function in the mode of maximum displacement or frequency response, the authors obtained optimized, unevenly distributed MTMDs. In work [22], [PERSON] and [PERSON] applied a method utilizing subgradients of a non-smooth objective function. Besides the gradient methods, also genetic algorithms are used in terms of MTMD optimization, for example, by [PERSON], [PERSON], and [PERSON] [23]. Heuristic methods, such as the particle swarm optimization (PSO), were also used. The PSO method for the determination of optimal MTMD parameters was used, among others, in the research by [PERSON] and [PERSON] [24] and [PERSON] et al. [25]. Other methods used for optimizing the objective function in MTMD issues include simulated annealing (SA) applied by [PERSON] et al. [26] for optimizing the parameters in a multi-story building. Recent works on MTMD include the one by [PERSON] and [PERSON] [27]. The article discusses the analysis of linear MTMDs with numerous practical configurations, attached to an SDOF structure, subjected to white noise input. Six practical configurations were developed and analyzed comparatively, each of which was linearly restricted with distributed tuning factors, mass ratios, damping factors, and their combinations. In [28], [PERSON] et al. analyzed TMDs and MTMDs distributed at various degrees of freedom of an MDOF system in a building with base isolation (BI). The analysis involved 40 earthquake ground motions for the adopted pattern of an MDOF structure with attached TMD and MTMDs and indicated the efficiency of the latter. In [29], [PERSON] et al. analyzed a new type of TMD system named bounding tuned mass damper (PTMD). The coupled equations were created by combining the equations of motion of both the bridge and moving vehicles. In order to compare the damping performance, a parametric study of the various numbers and locations, mass ratio, and stiffness of the MPTMDs were investigated. The article presents an alternative method for developing motion equations for a MTMD structure. The method enables adding single TMDs or MTMD groups to completely different degrees of freedom of the primary system. The system of equations allows for easy MTMD tuning for complex vibrations modes, with MTMDs located in local maxima of these vibrations modes, while still analyzing the SDOF system with attached MTMDs. MTMD parameter optimization based on \(\mathfrak{H}_{2}\) and \(\mathfrak{H}_{\infty}\) norms for the transfer function associated with the modal coordinate of an SDOF system was proposed. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs.