# Optimization Design of RC Elevated Water Tanks under Seismic Loads
## 1 Introduction  
Elevated tanks are critical structures in water supply networks. These tank facilities are usually located on tall structures that provide sufficient pressure for water distribution systems. Tanks also serve for storage that covers possible interruptions in the pumping system. Thus, this structure is essential for public services and there is a vital need for it to remain operational after severe earthquakes. The poor seismic performance of these inverted pendulum-type constructions are frequently reported during major earthquakes [1; 2; 3; 4]. The seismic response of concrete and steel tanks was extensively investigated through experimental and numerical methods [5; 6; 7; 8]. Factors that affect the seismic response of tanks include the tank size [9], the soil-structure interaction [10], and the fluid-structure interaction [11]. Regarding the optimized design of elevated RC water tanks, to the best of the authors' knowledge, there was no research conducted to date. Structural engineering aims to achieve maximum safety with minimum investment. This target is not easy as long as various design variables with multiple combinations characterize structural problems. Researchers have explored new ways to achieve structural efficiency. In conjunction with evolutionary-based optimization procedures, finite element modeling techniques were used to design conical steel water tanks on elevated towers [12] and rectangular RC reservoirs [13]. However, most of the approaches found in the literature were not suitable to be implemented in real-life structures [14]. Much research was conducted recently concerning metaheuristics applied to structural optimization, such as metasimulated annealing and metathreshold accepting [15], harmony search [16; 17; 18], swarm intelligence methods [19; 20], and biogeography-based optimization [21], among others. Models without physical meaning or without being based on nature can also be used in structural optimization, as in the case of machine learning algorithms [22]. Since machine learning models do not have a physical meaning, further study and deepening of the model output are necessary. Once a model is calibrated, the next step is to find the main patterns and variables that explain this model. Analyzing the variables makes it possible to understand the correlation between them and associate this correlation with an expert meaning that comes from a physical model or an expert in the area. These machine learning models allow for understanding or eliminating specific patterns or relationships that the model has found. On the other hand, when these conditions are found, they can be introduced as a physical constraint to calibrate the model [23; 24]. The results obtained in the structural design case can be used to analyze the variables that have the most significant impact on the design, the values they take, and their relationship. Subsequently, it is possible to identify which physical condition sustains these relationships. This paper employs the hybridization strategy to combine the strengths of individual algorithms and exploit the complementary character of different optimization strategies. [PERSON] et al. [25] provided a survey on the hybridization of metaheuristics with other techniques for optimization problems. In this context, these techniques proved the efficiency of threshold accepting-based techniques to optimize bridge piers [26], post-tensioned concrete box girder bridges [27], and wind turbine foundations [28]. Following this line of work, this paper focuses on the economic seismic optimization of columns for elevated concrete water storage conical tanks. To this end, a Fortran program encompasses modules for structural analysis, limit states verification, and cost evaluation. A hybrid threshold acceptance adaptive algorithm with a mutation operator (abbreviated herein as OBAMO) was then used to search the solution space in order to identify a set of solutions with optimized values for the designer.