# Adaptive Harmony Search for Tuned Liquid Damper Optimization under Seismic Excitation
## 1 Introduction  
Passive dampers are the preferred systems for vibration control of structures because of their low cost, ability to be added to existing buildings, and ease of maintenance and repair. A tuned liquid damper (TLD) is a passive control device that absorbs the movement of the building without any external energy. It has sloshing energy provided by the viscosity and density of the liquid it contains. In terms of basic operating principles, it is similar to tuned mass dampers (TMD), which consist of a spring and mass model. A TLD aims to minimize damage to the structure caused by dynamic effects by connecting the structure with spring and liquid mass. The type of fluid chosen for damping affects the damping performance significantly. The density of the liquid, or its kinematic viscosity, affects the damping performance, and, thus, the sloshing. When evaluated in terms of the characteristic features of the design of TLDs, there are studies in which the use of water, and mixtures including water, as the liquid, has shown good results in terms of performance in various vibration control, easy accessibility, and cost [1, 2]. Another feature that affects damping is the geometrical characteristics of the damper tank. TLD tanks can be designed in rectangular prism, cylindrical, or conical shapes. The effects of tank shapes on vibration control have been investigated in various studies. It has been determined that they have remarkable effects on damping. [PERSON] and [PERSON] found that rectangular-based TLDs have remarkable effects in preventing eddy vibrations in their study [3]. [PERSON] et al. showed that the truncated conical TLD tank model can be an alternative to the cylindrical TLD tank [4]. [PERSON] and [PERSON] worked on the constraints of the rectangular shape in tank designs and developed a TLD tank design method [5]. [PERSON] took tank geometry in another direction with his research, and observed that curved-bottom TLDs could be better than flat-bottom TLDs, with less liquid [6]. [PERSON] et al. conducted an experimental studywith round, rectangular, and inclined TLD tanks, and concluded that the inclined tank can provide more efficient results, but is less durable [7]. Effective liquid length and tank height are the main parameters in the damping effect of the tank geometry. The effective liquid length is the base size, which denotes the long side, where agitation is easily directed. [PERSON] et al. (1992) suggested a ratio between this length and the tank height in a study [8]. Another parameter that affects TLD performance is mass. The recommended 5% mass ratio for TMDs can be applied to TLDs as well, and it is recommended in the literature that TLD mass should be between 1% and 4% [9; 10; 11; 12]. The importance of the design parameters of TLDs in vibration control has necessitated the optimization process. For this purpose, optimization is carried out using various algorithms. Metaheuristic algorithms take their inspiration from spontaneous events in nature, and the instinctive behavior of living things. These algorithms transform a mathematical model of the instinctive behavior of living things, such as the magnificent order in the flight of the birds, the path of the bees to their colony in search of food, bats' detection of objects by echolocation, or the bubble road map created by humpback whales while hunting, into a metaheuristic algorithm, and ensure that the best solutions are obtained. The minimum energy that living things expend to survive, processed by order based on maximum gain, in the algorithms, makes optimum efficiency possible. The systematic order in mathematical models distinguishes metaheuristic algorithms from other optimization algorithms. The harmony search algorithm (HS) is a type of metaheuristic algorithm developed by [PERSON] et al. [13].