## 1 Introduction  
Pedestrian bridges are more and more common in urban regions. However, with the development of architectural creativeness and structural technologies, they are becoming lighter and more slender, which might lead to serviceability problems under human-induced vibrations [1]. These pedestrian bridges usually have low inherent damping, and large vibrations may be caused by resonance because their natural frequency is usually located within the range of pedestrians' stride frequency. A notable vibration will not only cause serviceability problems but also threaten structural safety. Tuned mass dampers (TMD) are one of the most traditional vibration control devices [2; 3; 4; 5; 6], and it usually consists of a mass, some springs and damping elements [7]. Because TMDs have the advantages of small size and little interference to pedestrian bridges, they are widely used to control human-induced vibrations and solve the serviceability problem [8; 9; 10]. The vibration response of a pedestrian bridge is controlled by the inertia force given by the TMD, and the vibration energy of the TMD will be dissipated through its damping element [11; 12; 13]. TMD is a single degree of freedom vibration absorber, the three dynamic parameters of TMD, which are mass, stiffness and damping coefficient, have a great influence on its control effect. TMDs have been researched and used to solve the serviceability problem of pedestrian bridges by many researchers. [PERSON] et al. [14] proposed a contribution to the modelling of pedestrian-induced excitation of footbridges. [PERSON] et al. [15] used human-induced dynamic excitation to estimate modal mass in pedestrian bridges. [PERSON] et al. [16] proposed the application of non-linear multiple TMDs to suppress human-induced vibrations of a footbridge. [PERSON] et al. [17] introduced the performance enhancement of a long-span bridge using tune mass dampers. [PERSON] et al. [18] proposed the application of multiple TMDs to control human-induced vibrations in suspension footbridges. [PERSON] et al. [19] studied the application of TMD to control pedestrian-induced vibration of the Expo Culture Centre. [PERSON] et al. [20] studied the pedestrian-induced random vibration of pedestrian bridges and vibration control methods using multiple TMDs. [PERSON] et al. [21] introduced the robust design and application of a TMD in a footbridge. [PERSON] et al. [22] studied controlling pedestrian-induced vibrations of a footbridge using tuned mass dampers. [PERSON] et al. [23] introduced the vibration control effect of multiple TMDs in the towers of bridges. The mass ratio and damping ratio of a TMD will affect its vibration control effect, and TMD is especially sensitive to the frequency ratio [24; 25; 26; 27; 28]. Therefore, the three dynamic parameters of TMD should be well designed. The classic [PERSON] method [29] has a wide application in TMD design. Besides, many new design methods are proposed. In order to search the optimum parameters of TMD for different optimization goals, a naturel-inspired computational algorithm has been used for parameters optimization of TMDs by many researchers. [PERSON] et al. [30; 31] proposed the particle swarm optimization of TMDs by non-stationary base excitation during earthquake. [PERSON] et al. [32] introduced the estimating optimum parameters of tuned mass dampers using harmony search. [PERSON] et al. [33] designed optimal multiple tuned mass dampers using genetic algorithms (GAs) to mitigate the seismic response of structures. [PERSON] et al. [34] introduced the robust optimum design of TMDs to mitigate pedestrian-induced vibrations using multi-objective genetic algorithms. Therefore, the naturel-inspired algorithms play an important role in TMD parameter optimization. Considering the advantages of flexibility, great convergence speed, great accuracy, fault tolerance, etc. [35; 36], the artificial fish swarm algorithm (AFSA) is applied to optimize TMD parameters in controlling the human-induced vibrations of footbridges.