Exploring Common Patterns in Well-Known Metaheuristic Optimization Algorithms

Considering the wide range of problems in various fields of science and engineering researchers always think of finding possible real-world solutions to improve the quality of people’s lives. Metaheuristic algorithms are optimization techniques that can discover desirable solutions to complex problems in a reasonable time. According to previous studies, approximately 540 Metaheuristic Algorithms have been introduced, more than 350 of which appeared in the last decade. The emergence of various metaheuristic algorithms has grown significantly in recent years and must be fully investigated. Due to the introduction of their variant models in recent years, the issue of basic similarities among algorithms with different names has expanded. This raises a fundamental question: Can a mathematical equation be proposed as a general template covering several similar main algorithms by applying minor changes in its variables or parameters? In this study, we aim to provide a general mathematical formulation that can help us to understand the algorithms better and improve them more easily, which will reduce redundancy, and improve the parameter settings, in some cases, algorithms may need unique formulations to address distinct challenges effectively.