Metaheuristic Algorithms for Engineering and Combinatorial‎Optimization: A Comparative Study Across Problems Categories and Benchmarks

Optimization remains a cornerstone of modern engineering and computational intelligence, playing a vital role in the design, control, and ‎allocation of limited resources across industries ranging from logistics to structural engineering. Traditional optimization methods, such as ‎gradient-based and exact algorithms, often struggle with the nonlinear, multimodal, and constrained nature of real-world problems, necessitating the adoption of metaheuristic approaches. These biologically and physically inspired algorithms offer flexibility, scalability, and robustness in navigating complex search spaces.‎ This study presents a systematic categorization of optimization problems—including combinatorial, continuous, constrained, and multi-‎objective classes—followed by a rigorous comparative analysis of nine prominent metaheuristics: Ant Colony Optimization (ACO), Lion ‎Algorithm (LA), Cuckoo Search (CS), Grey Wolf Optimizer (GWO), Vibrating Particles System (VPS), Social Spider Optimization (SSO), ‎Cat Swarm Optimization (CSO), Bat Algorithm (BA), and Artificial Bee Colony (ABC). The algorithms are evaluated across five representative benchmark problems: the Traveling Salesman Problem (TSP), Welded Beam Design (WBD), Pressure Vessel Design (PVD), ‎Tension/Compression Spring Design (TSD), and the Knapsack Problem (KP).‎ Key contributions include: 1)Domain-specific suitability analysis, revealing how algorithmic mechanisms align with problem structures.‎ ‎ 2) Performance benchmarking under standardized conditions, highlighting convergence speed, solution quality, and constraint-handling ‎efficacy. 3) Practical insights for practitioners on algorithm selection, hybridization potential, and adaptation challenges.‎ Results demonstrate that no single algorithm dominates universally; instead, problem characteristics dictate optimal choices. For instance, ‎ACO excels in discrete problems (TSP, KP), while GWO and BA outperform in continuous engineering designs (WBD, PVD). The study ‎concludes with recommendations for future research, including dynamic parameter tuning, hybrid models, and real-world scalability ‎assessments‎.