American Cockroach Optimization Algorithm: A Continuous-Time Motion–Field–Quantum Coupled Framework

Swarm intelligence optimization algorithms demonstrate strong global search capabilities in complex nonlinear optimization problems. However, traditional algorithms are largely based on the superposition of empirical behavioral rules, lacking systematic dynamic interpretation and field coupling modeling. To enhance the theoretical depth and structural expressive power of these algorithms, this paper proposes a quantum field-driven American cockroach optimization algorithm. The algorithm is based on a continuous-time second-order nonlinear dissipative dynamical system, introducing a swarm information potential coupling model, constructing an anisotropic curvature-aware tensor correction mechanism, and designing a quantum probabilistic jump structure incorporating the concept of nonequilibrium Boltzmann transitions. Simultaneously, an adaptive topological network is constructed to achieve swarm communication control. This paper systematically analyzes the algorithm's dynamical system structure, stability conditions, Lyapunov convergence, and computational complexity. Theoretical results show that under reasonable parameter conditions, the system monotonically converges in the expected sense and possesses a unified ability for global exploration and local fine-grained convergence. The proposed method provides a modeling paradigm for swarm intelligence optimization algorithms based on physical field coupling and dissipative structures.