## 1 Introduction  
The wind turbine tower, as the structure supporting the wind turbine, represents a highly significant component of wind turbine systems and accounts for approximately 30% of the overall investment in onshore installations [1]. With the increase in unit power capacity of wind turbines, the heights of wind turbine towers have increased for the purpose of capturing wind energy efficiently, as wind profiles are strong and steady at higher elevations [2; 3; 4]. In recent years, wind turbine towers with a height of over 100 m have been widely employed in practice alongside increasing investment [5]. Many wind farms have been developed or are under construction in mountainous areas in the mainland of China after decades of wind farm development in plain areas. The transportation of segmental steel tubes and long blades to the top of mountains is a challenging task with risks. Moreover, the construction of temporary transportation roads with large turning radii in mountains leads to additional investment and environmental destruction [6]. The traditional steel-tubular wind turbine tower systems are typical soft supporting systems, and it is hard to meet the stiffness requirements of large capacity wind turbines due to the limitation of steel-tube diameter transportation. In recent years, the prestressed concrete-steel hybrid (PCSH) wind turbine tower has been proposed to overcome the difficulty of transportation and the limitation of the structural mechanical behavior of traditional steel tubular towers. Compared with the full-height steel tubular tower, the PCSH wind turbine tower results in a lower center of gravity and higher flexural stiffness. The use of concrete leads to a lower sensitivity to fluctuations in steel prices [2]. Moreover, by replacing parts of the steel tubular segments with prestressed concrete (PC), the total cost of the PCSH tower system can be decreased while the design-servicing life of PC is much longer than steel. This leads to reasonable life-cycle cost savings and decreases in the levelized cost of energy (LCOE) in a life-cycle perspective. The development of the PCSH wind turbine tower has received great attention in recent years. [PERSON] [7] investigated concrete construction for wind energy towers and highlighted the advantages of concrete as the major construction material for wind turbine towers. [PERSON] [8] compared a steel and concrete hybrid tower with a steel tower and concluded that hybrid towers are an effective alternative to traditional steel towers, can be built at nearly every site, and help overcome transportation issues caused by mountains or other terrains. The optimization algorithm plays key roles in realizing the economical results that withstand the most demanding functional requirements arising during their service life [9], [PERSON] et al. [10] proposed and tested five different optimization strategies for a 100 kW wind turbine system considering the natural frequencies as the most representative objective function. [PERSON] et al. [11] used optimization to calculate the least cost of a steel wind turbine tower that meets the structural demands and emphasized the influence of ring stiffeners. [PERSON] et al. [12; 13] redesigned wind turbine towers with a generalized reduced gradient (GRG) method and analyzed how individual design variables affected the objective function of a hybrid wind turbine tower. Employing the genetic algorithm (GA), [PERSON] et al. [14] optimized a 100 m PC tower system for a 5 MW wind turbine and discussed the advantages of a PC wind turbine tower. [PERSON] et al. [15] explored three different state-of-the-art analytical gradient-based optimization approaches to minimize the mass of a jacket structure for wind turbines considering fatigue and frequency constraints and provided insight into critical structural and modeling parameters. Adopting GA, [PERSON] et al. [16] suggested that the optimal height of the concrete segment should be 80.5 m for one 120 m PCSH wind turbine tower.