Metaheuristic algorithms have been applied to tackle challenging optimization problems in various domains, such as health, education, manufacturing, and biology. In particular, the field of Structural Health Monitoring (SHM) has received significant interest, particularly in the area of damage identification in structures. Popular optimization algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Cuckoo Search (CS), Teaching Learning Based Optimization (TLBO), Artificial Hummingbird Algorithm (AHA), Moth Flame Optimizer (MFO), among others, have been employed to address this problem. However, notwithstanding the wide recognition of the current algorithms, their constraints are commonly acknowledged. Hence, this article advocates for the adoption of innovative hunting-inspired algorithms, namely the Ant Lion Optimizer (ALO), African Vulture Optimization Algorithm (AVOA), Grey Wolf Optimizer (GWO), Marine Predator Algorithm (MPA), and Whale Optimization Algorithm (WOA), which emulate the behaviors of wildlife species, to discern the areas and magnitudes of deterioration in a suspension footbridge. Moreover, in order to reduce computational time, only natural frequencies are applied as objective functions. The obtained results indicate that all the utilized algorithms can accurately detect the damages in the considered structure.