Long-Tailed Shark Optimization Algorithm

To address the problems of isotropic search, premature convergence, and lack of unified theoretical explanation in traditional swarm intelligence optimization algorithms for high-dimensional complex problems, a thresher shark optimization algorithm based on the coupling mechanism of deformable manifold structure and impact dynamics is proposed. The algorithm embeds the search space into an adaptive Riemannian structure by constructing a manifold metric tensor induced by swarm covariance; simultaneously, it introduces an anisotropic impact tensor to achieve direction-aware perturbation; establishes a total energy functional coupling impact and compression to characterize the swarm evolution process; avoids over-convergence through a phase transition mechanism; and finally constructs a non-equilibrium dissipative dynamic model, giving the algorithm momentum memory and energy decay characteristics. Theoretical analysis shows that the algorithm can be interpreted as a nonlinear dynamic system with dissipative and stochastic impact terms, possessing asymptotic stability and global exploration capability under certain conditions. This method provides a geometric and physical interpretation framework for swarm optimization algorithms.