## 1 Introduction  
Nowadays, cable-stayed bridge structure accounts for a large proportion of modern bridge construction because of their beautiful shape and powerful crossing capacity. Compared with continuous girder bridge structures and rigid frame bridge structures, the advantage of cable-stayed bridge structures is that the distribution of its internal forces can be more uniform and reasonable by adjusting cable forces. Since the variation of cable force directly determines the internal force distribution of a whole bridge, the determination of reasonable cable forces and construction cable forces is the focus of cable-stayed bridge construction and its difficulty [1]. Specifically speaking, in the construction process of a cable-stayed bridge structure, it is necessary to stretch the cable several times in stages. The deformation and stress state of the bridge tower and main beam can be improved through the optimization of tension cable forces. Then, the reasonable state can be achieved by the reasonable bridge construction process within the allowable range of error. The common methods to determine the reasonable bridge cable force include the zero-displacement method, the force balance method, the rigid supported continuous beam method, the minimum bending energy method, and the influence matrix method. [PERSON] et al. [2], first proposed the zero-displacement method in 1993, which was used in order to determine the post-cable tension of cable-stayed bridges under dead load. [PERSON] et al. [3]. proposed a new method to determine the cable force of cable-stayed bridges using the idea of force balance. Compared with the zero-displacement method, this method is easier to understand and more efficient. All other traditional methods have their own scope of application. For instance, the rigid supported continuous beam method takes the bending moment of the main beam as the control objective, which is simpler and more intuitive, and can overcome the defect that the zero-displacement method cannot deal with the local unreasonable bending moment of the main beam. However, the method does not consider the stress state of the bridge tower. It is worth noting that a non-negligible problem is that the traditional cable force adjustment method also cannot realize automatic optimization of the cable force in the adjustment process [4]. The traditional method of determining the cable force of a single formed bridge only reflects the variation between the corresponding structural responses of the structure due to its action of constant load and so on. This is not only subjective, but also lacks rigorous mathematical calculations. For example, the influence matrix method describes the functional relationship between the adjustable variables and the target conditions, which only expresses a law of the structural mechanics system, and it does not obtain the optimal solution by itself [5]. To overcome this deficiency, an increasing number of scholars have introduced swarm intelligence algorithms into the cable force optimization process of cable-stayed bridges in the past decade [6]. The phenomenon continues to grow, which means that the cable force optimization problem of the swarm intelligence algorithms has attracted more and more scholars' interest in recent years, and has gradually become a research hotspot. Nowadays, particle swarm optimization (PSO) and genetic algorithms are mainly used in cable force optimization of cable-stayed bridges [7]. Since the particle swarm optimization algorithm was proposed, it has been widely used in various fields because of its many advantages, such as easy-to-understand principle, fast convergence speed, easy implementation of algorithm code, and small number of parameters. [PERSON] et al. [8] applied a genetic algorithm to cable force optimization of cable-stayed bridges.