Optimization Algorithms: Comprehensive Classification, Principles, and Scientometric Trends

In recent years, optimization algorithms have emerged as powerful computational tools for addressing complex and dynamic challenges across diverse domains. These domains include engineering, technology, management, and decision-making. Their growing importance is motivated by (a) the increasing complexity of modern systems, (b) the need for efficient resource utilization, and (c) the demand for scalable algorithmic solutions. These algorithms enable the systematic and computational exploration of large solution spaces, supporting decision-making and design under uncertainty, large-scale data, and evolving requirements. This study provides a structured review and comparative scientometric analysis of optimization algorithms, covering: (a) exact methods, (b) approximation techniques, (c) metaheuristics, and (d) emerging physics-informed frameworks. The analysis highlights algorithmic trends, performance-oriented research directions, and the increasing integration of mathematical programming, machine learning, and numerical methods. The results show a renewed focus on classical algorithmic paradigms. Moreover, rapid growth in hybrid and physics-informed optimization approaches is observed. These findings confirm the central role of optimization algorithms in modern algorithm engineering and interdisciplinary computational research.