## 1 Introduction  
Nowadays, it is generally accepted that passive vibration control can provide effective solutions for advanced seismic protection of buildings and civil structures [1, 2]. Broadly speaking, those solutions can be classified into three main categories: base isolation (BI), tuned dampers (TDs) and inter-substructure dampers (ISSDs) [3]. Typical implementations of that kind of passive vibration control strategies for seismic protection of multistory buildings are schematically displayed in Figure 1.  
BI systems use a layer of flexible isolation elements to reduce the ground-to-structure transmission of the seismic disturbance. The main drawback of BI systems is the large base displacements produced by strong earthquakes, which can require the inclusion of sophisticated control strategies to achieve a proper trade-off between the desired level of seismic isolation and the base-displacement constraints [4, 5, 6, 7]. TDs are auxiliary vibrational devices that are attached to the structural system to absorb and dissipate a significant fraction of the structural kinetic energy induced by the seismic excitation. TD systems include classical tuned mass dampers (TMDs) [8] and a variety of other configurations as pendulum TMDs [9], tuned liquid dampers [10] and particle tuned mass dampers [11]. In seismic protection of multistory buildings, the effectiveness of passive TD systems can be compromised by a number of relevant factors, as large size and mass requirements, poor performance against broad-band seismic excitations, and detrimental effects of soil-structure interactions. Frequently, those limitations are addressed by considering enhanced hybrid TD control systems with active or semiactive elements [12; 13]. Other solutions include hybrid combinations of TD and BI systems [14]. ISSD systems take advantage of the out-of-phase vibrational response of different parts in compound structures (for example, adjacent stories in multistory buildings) and use energy-dissipation devices as inter-substructure links to increase stability and mitigate the overall seismic response of the structure. Energy-dissipation ISSD links can be implemented using a wide variety of damping elements [2], including metallic dampers [15], friction dampers [16], viscoelastic dampers [17] and fluid viscous dampers (FVDs) [18]. It is also possible to design distributed ISSD systems with TD characteristics by considering inerter elements, which are a promising new class of light and compact two-terminal TD devices [19]. Passive ISSD systems are simple, reliable, robust, technologically feasible, easy to install and maintain, and can operate without external power sources [17; 18]. Moreover, properly designed passive ISSD systems can provide a high level of seismic protection, being able to match the performance of active or semiactive feedback control systems [20]. In this case, a major difficulty is to design optimal configurations for the distributed ISSD elements. That issue has motivated a notable theoretical and computational research activity and comprises two challenging problems: (i) optimal tuning, which aims at determining a suitable set of parameter values for a given distribution of the ISSD elements; and (ii) optimal allocation, which seeks for optimal distributions of the damping links in sparse ISSD systems. Recent works in that line include ISSD designs based on a wide variety of optimization objectives, such as structural performance [21], energy dissipation [22], total-building performance [23], retrofitting cost [24] and structural reliability [25]. Advanced ISSD designs consider soil-structure interactions [26], irregular 3D structures [21] and multi-building  
Figure 1: Passive vibration control strategies for seismic protection of multistory buildings. problems [27; 28]. Enhanced design strategies include simplifying procedures to deal with the high computational cost in nonlinear studies [29], design methodologies based on active control approaches [30; 31] and special seismic excitation schemes [32].