# Genetic Algorithm as a Tool for the Determination of the Self-Stress States of Tensegrity Domes
## 1 Introduction
The stiffness of the structure is determined not only by the geometry and material characteristics but also by the level of self-stress. This means that the stiffness of these structures can be controlled. In contrast to traditional steel domes [17, 18], tensegrity domes are lightweight structures. This feature is very important, especially in long span space structures [19, 20]. In the process of designing such structures, the key issue is how to reduce the weight of the structure and thus the cost of construction. The first tensegrity-inspired dome was proposed and patented in 1988 by [PERSON] [21]. In the opening paragraph of his tensegrity patent, he claims that \"the cable truss dome is adapted for spanning large areas where the cables form a low shallow arch which supports a flexible membrane as a covering\". The Geiger dome was used as the roofs of the Olympic Gymnastics Hall and the Fencing Hall in Seoul [20]. The Seoul gymnastics stadium dome is 118 m in diameter and 15 m high. This type of roof has low-profile configurations that reduce wind lift, uneven snow settling and use less material to cover the roof. One of the main advantages of this structure is that its weight per square meter does not change as the span increases. Additionally, the diameter of Geiger domes can be expanded indefinitely with little additional weight or expense per square meter of roof. The second cable dome was developed in 1994 by [PERSON] [19, 22]. [PERSON]'s idea was used to build the largest existing cable dome, the Georgia Dome, designed for the Atlanta Olympics in 1996. The Georgia Dome with its elliptical configuration is covered by a roof extending 193 m along the minor axis and 240 m along the major axis and is referred to in the literature as a hyper-tensegrity dome [12, 16]. The main difference between the Geiger dome and the Levy dome is the arrangement of the ridge cables. In a Geiger dome, the ridge cables are arranged radially so that the roof is divided into multiple flat load-bearing girders. In the Levy dome, the ridge cables form a triangular pattern. The roof surface consists mainly of quadrilateral anticlastic membrane panels connected by ridge cables. In addition, it facilitates the application of cable domes on an elliptical plan shape. The Geiger and Levy domes are the most known types of tensegrity domes. They have been and still are an inspiration to create new and hybrid forms of cable domes [14, 23, 24, 25, 26, 27]. These structures have been repeatedly studied by the researchers throughout the years. There are more than 10,000 articles from the years 1990-2022 that mention the Geiger dome and more than 18,000 that mention the Levy dome (according to the information from Google Scholar). Another cable dome, less popular than Geiger and Levy (appeared only in 500 articles), is the Kiewitt dome form [14]. This structure is inspired by the lamella lattice shell developed in 1960 by [PERSON] [28]. The Kiewitt cable domes, as with the tensegrity structures, have structural rigidity only when the self-equilibrium forces are applied to cables and struts [12; 13; 14; 15; 16; 29]. Therefore, calculating the self-stress state is the key step for any cable structure. The search for self-stress states, independent of the load, is called form-finding methods in the literature. In fact, these methods consist of determining such a configuration of elements at which self-balancing forces occur. The review of the literature has shown a great variety of form-finding methods, and these methods are constantly being modified and improved. The overviews of the methods can be found, e.g., in [30; 31; 32; 33]. The commonly used form-finding methods are the force density method [34], dynamic relaxation [35], energy optimization [36], reduced coordinates method [37], iteration method [38], singular value decomposition [7; 39] or spectral analysis of the truss matrices [7].