A Novel Hybrid Swarm Optimizer Integrating Quasi-Reflective Learning and RRT for Gear Train Design

Optimization problems are becoming increasingly complex and require metaheuristics capable of adaptively balancing exploration and exploitation across various landscapes. To evaluate algorithm performance, this study uses the Gear Train Design benchmark, a discrete error minimization problem that seeks to minimize the difference between the achieved and target transmission ratios, with four gear tooth counts as integer decision variables. Various algorithms such as GWO, PSO, GA, and DE have produced competitive solutions; however, there remains room for improvement in terms of convergence stability, explorationexploitation balance, and robustness across different problem characteristics. This study proposes Q-REO, a hybrid framework that integrates Quasi-Reflective Initialization, RRTO, ESOA, and EAO into a unified adaptive mechanism. Experimental results show that Q-REO achieves the best fitness value approaching zero (approximately 2.7E-12) on the Gear Train Design problem with near-perfect solution consistency across all 30 runs. In the Friedman rank test, Q-REO achieved the lowest mean rank of 1.98 among all comparison algorithms, and the performance difference was statistically significant (p= 0.0000), indicating consistent solution quality, robustness, and convergence efficiency.