Metaheuristic Algorithms for Engineering and CombinatorialOptimization: A Comparative Study Across Problems Categories and Benchmarks
Awaz Ahmed Shaban, Saman M. Almufti, Renas Rajab Asaad
Abstract
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.