Longhorn Beetle Optimization Algorithm

To address the multimodal structure, ill-conditioned condition number, and premature convergence issues in high-dimensional nonlinear complex optimization problems, this paper proposes a tensor-curvature coupled longhorn beetle optimization algorithm. This algorithm simulates the behavior of the longhorn beetle using its two tentacles for environmental perception and directional flight. Based on this, an anisotropic tentacle tensor structure and a local diagonal curvature estimation mechanism are introduced, extending the direction search from a single scalar difference to a tensor-based preconditioning transformation. Simultaneously, an information energy dissipation model is constructed to give the population evolution process nonlinear damping characteristics, thereby improving global stability. To enhance the efficiency of swarm information propagation, the algorithm designs an adaptive topology structure, dynamically switching between fully connected and ring structures. Furthermore, a continuous-time dynamical system model is established, and asymptotic stability analysis is given based on Lyapunov functions. Theoretical analysis and structural derivation show that this method possesses strong direction perception and local curvature adaptation capabilities on complex multimodal functions, providing a new research approach for tensor quantization and dynamical system modeling in swarm intelligence algorithms.