Red-Legged Tortoise Optimization Algorithm

To address the problems of oscillating search, repeated direction switching, and over-reliance on instantaneous optimal solutions in traditional swarm intelligence optimization algorithms for high-dimensional, non-convex, and noisy objective functions, this paper proposes a novel metaheuristic optimization method—the Red-legged Tortoise Optimization Algorithm. Inspired by the slow but highly stable movement behavior of the red-legged tortoise, this algorithm introduces a temporal geometric perspective to model the search process. Instead of relying on spatial distance or instantaneous descent of the objective function as the primary driving force, it uses the geometric stability of the search trajectory in the temporal dimension as the core criterion. By constructing a temporal curvature metric, irreversible direction gating, adaptive submanifold search, and exploring energy self-inhibition mechanisms, the algorithm can automatically enter a stable search state without explicit convergence determination. Theoretically, this method constitutes a class of irreversible optimization frameworks driven by time structure, providing a new modeling approach for complex optimization problems.