Curvature-Adaptive Territorial Stag Beetle Optimization: A Nonlinear Energy-Driven Swarm Framework

To address the problems of local extremum traps and decreased search efficiency in complex nonlinear, multimodal, and high-dimensional optimization problems, this paper proposes a swarm intelligence optimization algorithm based on curvature perception, potential energy regulation, and dynamic adversarial topology—the Curvature Adaptive Territorial Stag Beetle Optimization Algorithm. The algorithm draws biological inspiration from the competitive and adversarial behavior of stag beetles, constructing an anisotropic jaw tensor mechanism to achieve second-order information approximation, introducing a force potential energy field model to characterize individual nonlinear transition behavior, and realizing a self-organizing competitive structure through a dynamic topological network. Simultaneously, a density compression function is designed to suppress excessive swarm aggregation and improve global exploration capabilities. This paper systematically elaborates on the algorithm construction, dynamic interpretation, stability analysis, and complexity analysis, and presents a continuous-time limit model and a discussion of Lyapunov stability. This method theoretically achieves a unified framework for gradient approximation, curvature regulation, and stochastic search, providing a new research path for the mathematical development of swarm intelligence optimization algorithms.