Large-scale mathematical optimization problems pervade engineering, logistics, economics, and computational science. Classical gradient-based methods struggle with high-dimensional, multimodal, non-convex search spaces, making metaheuristic approaches indispensable. This article surveys three principal metaheuristic paradigms—Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO)—analyzing their mechanisms, comparative strengths, and applications to large-scale problems. Performance indicators including convergence speed, solution quality, and scalability are examined, and a generalized optimization workflow is presented. Results indicate that hybrid and adaptive metaheuristic strategies consistently outperform single-paradigm approaches on benchmark functions and real-world large-scale instances.