Heavy Ball Optimizer: A Momentum-Driven Metaheuristic with Superior Scalability and Real-World Applications

The rapid development of the intelligent information era has led to increasingly complex optimization problems across various scientific and engineering domains. Although many metaheuristic algorithms have shown success in solving such problems, they still suffer from challenges such as premature convergence, insufficient exploration, and limited robustness in high-dimensional and nonconvex search spaces. These limitations highlight the need for more effective optimization methods that balance exploration and exploitation while maintaining computational efficiency. To address these challenges, this paper proposes the Heavy Ball Optimizer (HBO), a physics-inspired population-based algorithm derived from the classical heavy ball method. The algorithm integrates three main components: the Heavy Ball Search Rule (HBSR) for enhanced exploration, the Effective Heavy Ball Strategy (EHBS) for balancing exploration and exploitation, and the Accelerated Convergence Mechanism (ACM) for improving convergence speed and stability. The performance of HBO is evaluated on 23 classical benchmark functions (with dimensions 30, 100, 500, and 1000), 30 CEC2014 functions, 10 CEC2019 functions, and 12 CEC2020 real-world constrained engineering problems, and compared with twelve state-of-the-art algorithms. The results show that HBO demonstrates highly competitive performance compared with competing methods, achieving the lowest Friedman average rankings of 2.96, 2.62, 2.38, and 2.23 on the classical benchmarks, 2.17 on CEC2014, 2.50 on CEC2019, and 2.21 on CEC2020 problems, indicating strong and stable statistical performance across all test suites. Furthermore, in EEG-based Alzheimer’s disease feature selection, HBO achieves classification accuracies of 98.50% and 99.40% on two datasets, validating its robustness and practical applicability in medical feature selection tasks. The results indicate that HBO provides competitive solution quality, strong stability, and effective scalability, making it a promising optimization framework for engineering and medical applications. The source codes of the HBO can be found at: https://github.com/IBRAlShourbaji/HBO_Optimizer and https://www.mathworks.com/matlabcentral/fileexchange/184141-heavy-ball-optimizer .