Three-body deterministic optimizer (TBD): a novel non-random, nature-inspired metaheuristic for engineering design and hyperparameter optimization

The widespread use of metaheuristic optimization algorithms across engineering, machine learning, and scientific modeling has led to significant advancements in solving complex, high-dimensional, and nonlinear problems. However, a persistent limitation in most existing metaheuristics is their inherent reliance on stochastic operators, random sampling, mutation, and probabilistic decisions. Although these stochastic elements enhance exploration capabilities, they compromise reproducibility and introduce variability in results across repeated runs. This inconsistency presents challenges in safety-critical and industrial applications where deterministic behavior and result traceability are essential. In this paper, we propose the Three-Body Deterministic Optimizer (TBD) to address these gaps. This novel metaheuristic eliminates all stochastic elements and introduces a fully deterministic search process inspired by orbital mechanics and chaos theory. Drawing on the classical three-body problem, TBD formulates two maneuver mechanisms, the Newtonian and Lagrangian maneuvers, to simulate gravitational attraction and multi-body interactions. These maneuvers are driven by a chaotic logistic map, which introduces complex yet fully reproducible dynamics. TBD is evaluated on the CEC2017 and CEC2022 benchmark suites, as well as on real-world engineering design problems such as cantilever beam, spring, and pressure vessel optimization, together with its application to Convolutional Neural Network (CNN) hyperparameter tuning. Experimental results show that TBD consistently achieves high-quality solutions, matching or outperforming state-of-the-art stochastic optimizers in accuracy and convergence speed, while maintaining strict determinism. The findings demonstrate that deterministic metaheuristics can retain the exploration-exploitation balance necessary for global optimization, offering a promising alternative for applications demanding transparency, repeatability, and computational rigor. The source code of TBD is publicly available for both MATLAB at: (https://www.mathworks.com/matlabcentral/fileexchange/182063-three-body-deterministic-optimizer-tbd) and PYTHON at: (https://github.com/AliRodan/Three-Body-Deterministic-Optimizer-TBD).