Hermann's Tortoise Optimization Algorithm

To address the common problems of path oscillation, optimal region destruction, and high sensitivity to noise in existing swarm intelligence optimization algorithms for complex continuous optimization problems, this paper proposes a novel swarm optimization method—the Hermann Tortoise Optimization Algorithm. This algorithm, based on the behavioral patterns of Hermann's tortoises in their natural environment, constructs an optimization framework with path irreversibility, safe zone fixation, and rational stagnation as its core mechanisms. Unlike traditional swarm intelligence methods that rely primarily on random perturbations and bidirectional search, the proposed algorithm emphasizes long-term memory of stable directions, irreversible constraints on verified paths, and proactive stagnation decisions under conditions of insufficient information. Through systematic modeling of the algorithm's state variables, path consistency metrics, regional stability criteria, and energy-driven update rules, this paper presents a complete mathematical description and algorithm flow. Theoretically, this method effectively suppresses ineffective exploration behavior and is practically applicable to high-dimensional, noisy optimization tasks with high requirements for solution stability.