---

Tuned mass dampers (TMDs) systems are one of the vibration controlled devices used to reduce the response of buildings subject to lateral loadings such as wind and earthquake loadings. Although TMDs system has received much attention from researchers due to their simplicity, the optimization of properties and placement of TMDs is a challenging task. Most research studies consider optimization of TMDs properties. However, the placement of TMDs in a building is also important. This paper considers optimum placement as well as properties of TMDs. Genetic algorithms (GAs) is used to optimize the location and properties of TMDs. Because the location of TMDs at a particular floor of a building is a discrete number, it is represented by binary coded genetic algorithm (BCGA), whereas the properties of TMDS are best suited to be represented by using real coded genetic algorithm (RCGA). The combination of these optimization tools represents a hybrid coded genetic algorithm (HCGA) that optimizes discrete and real values of design variables in one arrangement. It is shown that the optimization tool presented in this paper is stable and has the ability to explore an unknown domain of interest of the design variables, especially in the case of real coding parts. The simulation of the optimized TMDs subject to earthquake ground accelerations shows that the present approaches are comparable and/or outperform the available methods.

---

In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based on minimization of maximum inter-story drift of nonlinear structure which genetic algorithm(GA) has been used to solve the optimization problem. For numerical analysis, a nonlinear eight-story shear building with bilinear hysteresis material behavior has been used. Fragility curves for the structure equipped with optimal variable damping and stiffness SATMDs have been developed for different performance levels and compared with that of uncontrolled structure as well as structure controlled using passive TMD. Numerical analysis has shown that for most range of intensity measure optimal SATMDs have been effective in enhancement of the seismic fragility of the nonlinear structures which the improvement has been more than passive TMDs. Also, it has been found that, although variable stiffness SATMD shows to be more reliable in lower mass ratios, however in higher mass ratios variable stiffness and damping SATMDs performs similarly to improve reliability of the structure.