# Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading
## 1 Introduction  
Guyed masts are extensively used in the telecommunications industry, and the size, shape, and topology optimization can significantly benefit their transportation and installation. The main loads acting on guyed mast structures arise from wind [1; 2], earthquakes [3; 4; 5; 6], sudden rupture of guys [7], galloping of guys [8], and sudden ice shedding from ice-laden guy wires [9]. Their optimization must fulfil several requirements under ultimate and service limit states [10]. Specifically, service limit states are crucial for guyed mast structures due to high-amplitude oscillations caused by their high deformability. In some cases, these vibrations have led to a signal loss caused by excessive displacement and rotation of the antennas and, in other cases, have resulted in permanent deformation or failure. Therefore, size optimization of the guyed mast structure represents a challenging task since the increment of the performance ratio of the materials should be counterbalanced by an adequate lateral stiffness to reduce high-vibration drawbacks [11]. [PERSON] [12] reported several happenings where heavy icing combined with moderate wind resulted in severe misalignment of towers and complete failure. [PERSON] et al. [13] showed that ice accumulation on some parts of the guy wires and moderate winds could lead to the guy galloping, resulting in unacceptable stress levels throughout the structure. The main topics investigated in the field of guyed structures can be summarized as follows:  
* Structural design. Several researchers investigated the dynamic response of guyed mast structures through experimental tests and numerical modeling to derive designapproaches and recommendations [14; 15; 16]. In particular, there are studies dealing with the dynamic identification and accurate estimate of the wind loads [17; 18; 19; 20; 21]. * Nonlinear dynamics. The proneness to global and local instabilities challenged several scholars to estimate and predict the nonlinear behaviour of guyed masts [22; 23; 24; 25; 26]. * Structural optimization. The need for guyed structures that are easy to install and transport challenged several scholars to optimize their shape in order to reduce the structural mass without reducing the lateral stiffness and prevent instability phenomena [27]. * Structural control. There are some attempts of control methods to reduce vibrations in mast-like structures [28; 29; 30]. Among others, [PERSON] [31] proposed the use of a hydraulic actuator to control cable forces in guyed masts using Kalman filtering. This paper tackles the size and shape optimization of guyed mast structures. A video of the considered structure is available in Supplementary Material. Since the first attempts by [PERSON] and [PERSON] [32], many engineers attempted to optimize guyed masts under wind loads using deterministic global optimization algorithms. However, as pointed out by [27], this approach leads to local optimum points, since each design variable was considered separately. [PERSON] et al. [33] and [PERSON] et al. [34] proposed general procedures for optimizing steel towers under dynamic loads. To the author's knowledge, [PERSON] and [PERSON] [35] were the first to implement a multi-objective optimization method for guyed mast structures under wind loads using the stochastic simulated annealing algorithm for size optimization. The objective function implemented by [35] included the sum of the squares of the nodal displacements and the in-plan width of the structure. [PERSON] and [PERSON] [36] attempted to achieve both shape and size optimization in a two-step procedure using the ant colony algorithm (ACA). [PERSON] et al. [37] proposed an alternative approach in which the multi-objective optimization problem has been reduced to a single-objective problem through suitable parameters.