## 1 Introduction  
Optimization methods are essential in structural engineering, particularly for rapidly evaluating and analyzing complex systems during preliminary design. In damage identification tasks, for example, accurately estimating the degraded stiffness or cross-sectional areas of elements within large truss structures can be formulated as a minimization problem: measured displacements and strains serve as inputs to an objective function, and an optimizer seeks the parameter values that best reconcile model predictions with observations. In [1], a partial-model-based strategy for long-span steel truss bridges leverages this paradigm by constructing localized stiffness matrices around suspected damage zones, thereby reducing the dimensionality of the global problem. Displacement and strain measurements drive the objective function, which is minimized through two local-search optimizers: the derivative-free Nelder-Mead simplex method [2] and a derivative-basedquasi-Newton algorithm. Applied to several regions of a truss bridge, this approach successfully identifies and quantifies damage, with the quasi-Newton solver demonstrating rapid convergence compared to the Nelder-Mead routine. While local optimizers like Nelder-Mead and quasi-Newton excel at fine-tuning solutions in relatively smooth, convex landscapes, structural applications often involve highly nonlinear, multimodal response surfaces, particularly when topology, material heterogeneity, or discrete design variables come into play. In such cases, metaheuristic algorithms inspired by natural phenomena have emerged as powerful tools for addressing complex optimization tasks, particularly when traditional deterministic or gradient-based methods prove insufficient [3]. These approaches, inspired by biological evolution and collective behaviors observed in nature, have yielded notable successes across a variety of engineering and scientific disciplines. Prominent among these are the Genetic Algorithm (GA) [4; 5; 6; 7; 8; 9], the Firefly Algorithm (FA) [10; 11; 12; 13; 14], and the Group Search Optimizer (GSO) [15; 16; 17; 18; 19], each distinguished by a unique strategy for exploring the search space. The Genetic Algorithm, whose foundational concepts and schema theory were introduced by [PERSON] in 1975 [4], represents one of the earliest and most thoroughly studied evolutionary metaheuristics. GA maintains a population of candidate solutions that evolve through iterative application of selection, crossover, and mutation operators. Individuals are evaluated by a fitness function, with higher fitness solutions having a greater reproducing probability, thereby transmitting their advantageous traits to the next generation. Crossover promotes the recombination of promising genetic material, while mutation injects controlled randomness to preserve diversity and mitigate premature convergence. Since its inception, GA has been applied extensively within structural optimization contexts: continuum and plate topology design [5], composite-material configuration [6; 7], shape optimization of solid components [8], and sizing optimization in truss and frame systems [9], among others. For example, in [5], the authors proposed a graphical encoding scheme for continuum topology, together with customized crossover and mutation operators that preserve key geometric features. In [6], an adaptive-operator GA incorporating an \"elite comparison\" mechanism optimizes fiber orientations in composite laminates, achieving accelerated convergence. A multi-objective GA for stacking-sequence design in lightweight composites is presented in [7], where mechanical constraints and objectives are embedded into the initialization and selection processes. In reference [8], the efficacy of the GA methodology is illustrated through two case studies in which material is selectively removed or added to achieve the final optimal shape of the component. Finally, Ref.