Hawksbill Shark Optimization Algorithm

To address the problems of premature convergence, orientation distortion, information propagation imbalance, and insufficient convergence stability in swarm intelligence algorithms for complex high-dimensional nonlinear optimization problems, an adaptive curvature-information flow coupled swarm optimization algorithm is proposed. This algorithm, within the traditional swarm random search framework, introduces a local second-order difference curvature sensing mechanism to achieve geometrically adaptive adjustment of the search step size; it constructs an information flow topology adaptive switching model, enabling the swarm to maintain dispersed propagation during the exploration phase and achieve centralized fusion during the convergence phase; it proposes a fractional-order memory dynamics model based on a power-law decay kernel, ensuring that individual historical trajectories exhibit non-exponential decay over time; it constructs a non-equilibrium dissipative free energy function, coupling and unifying fitness, velocity energy, and swarm entropy; and it establishes an asymptotic stability control framework through spectral radius constraints. Theoretical analysis shows that the algorithm satisfies mean-square boundedness and asymptotic contraction under certain parameter conditions. The proposed method constructs a unified model from the perspectives of geometry, graph theory, fractional-order dynamics, and non-equilibrium statistical physics, providing a new theoretical structure for swarm intelligence algorithms.