A Hybrid Nonlinear Greater Cane Rat Algorithm with Teaching–Learning-Based Optimization for Global Optimization and Constrained Engineering Applications

The greater cane rat algorithm (GCRA) represents an emerging swarm intelligence paradigm derived from the instinctual survival patterns exhibited by greater cane rats (GCRs), which simulates the typical male-dominated survival patterns of the GCR species, including rainy-season mating and reproduction behaviors, dry-season behavioral differentiation of solitary males and clustered females, and their nonlinear adaptive foraging characteristics. Nevertheless, the original GCRA suffers from inherent defects in complex and high-dimensional optimization scenarios, encompassing premature convergence phenomena, inadequate local exploitation proficiency, constrained convergence precision, and a proneness to stagnation at local optima, which severely restrict its practical engineering application. To address the aforementioned limitations, this work introduces an enhanced hybrid variant of the greater cane rat algorithm, amalgamated with Teaching-and-Learning-Based Optimization (TLBO) and designated as the TLGCRA, incorporating three pivotal targeted innovations. Specifically, the TLGCRA innovatively introduces the two-stage teacher–student interactive learning mechanism of TLBO on the basis of retaining the core evolutionary and behavioral characteristics of the original GCRA, which effectively compensates for the insufficient local disturbance capability of the original algorithm and enriches population diversity to avoid local optimum stagnation. Furthermore, an adaptive parameter tuning strategy is innovatively designed and embedded in the iterative optimization process, which dynamically balances the global exploration and local exploitation capabilities of the algorithm, fundamentally improving the low learning efficiency and weak mining performance of the GCRA. A suite of computational simulations is conducted across 23 canonical benchmark functions and six representative constrained engineering design optimization scenarios. The introduced TLGCRA is benchmarked against the canonical GCRA, LPSO, and ten cutting-edge metaheuristic approaches. Empirical outcomes substantiate that the TLGCRA attains marked performance advantages in terms of convergence velocity, solution precision, and algorithmic resilience. In particular, the optimized design effectively improves the optimal solution precision of the algorithm in complex multimodal function optimization, and the standard deviation of multiple independent runs in six engineering application cases is close to zero, verifying its excellent stability. Statistical verification employing the Friedman test and Wilcoxon signed-rank test additionally corroborates that the TLGCRA exhibits statistically robust and dependable optimization efficacy. In summary, the proposed innovative fusion strategies endow the TLGCRA with stronger environmental adaptability and comprehensive optimization performance, enabling it to realize faster convergence speed and higher computational accuracy, as well as outstanding stability and robustness, thus furnishing a viable resolution framework for intricate constrained engineering optimization challenges.