A Second-Order Hydrodynamic Swarm Optimization Framework Inspired by Mackerel Schooling Dynamics

To address the shortcomings of traditional swarm intelligence algorithms, which generally employ first-order position update models and lack physical dynamic structure and continuous field modeling, a second-order mackerel optimization algorithm based on ocean hydrodynamic system modeling is proposed. This method models the swarm search process as a second-order dynamic system with anisotropic damping, introducing a hydrodynamic damping tensor, vortex information field, information density gradient driving mechanism, and irreversible energy dissipation constraints. The algorithm no longer relies on a simple velocity superposition model but achieves dynamic evolution through acceleration-driven processes. By constructing a continuous density field and a rotating topological field, a unity of global exploration and local convergence is achieved. Theoretical analysis shows that the algorithm possesses asymptotic stability under certain conditions. The time complexity is O(NT), which becomes O(N^2) when the density field is incorporated, and can be optimized to O(N log N) through neighborhood truncation. This method provides a new dynamic modeling framework for swarm intelligence algorithms.