German Cockroach Evolutionary Field Optimization Based on Resistance Matrix Adaptation and Tensor Pheromone Diffusion

To address the problems of premature convergence, insufficient characterization of dimensionality correlation, and difficulty in adaptively adjusting the exploration-exploitation balance in complex high-dimensional non-convex optimization problems, this paper proposes an optimization method based on the survival dynamics model of a German cockroach colony. The algorithm abstracts several mathematical mechanisms from drug resistance evolution behavior, pheromone diffusion behavior, and resource competition behavior, constructing a resistance evolution matrix, an adaptive tensor diffusion field, and a dual-potential survival model, all characterized within a unified non-equilibrium dissipative stochastic dynamic system framework. The main search direction is constructed using a covariance tensor, the step size is individually adjusted using the resistance evolution matrix, and a dynamic weight function is constructed using exploration and exploitation potentials, achieving a self-regulating mechanism that does not require manual setting of the exploration-exploitation ratio. Simultaneously, a population splitting and recombination strategy is introduced to alleviate convergence stagnation. Theoretical analysis shows that the algorithm can be represented as a stochastic gradient flow system with dissipative terms and satisfies Lyapunov stability under certain conditions. This method provides a new dynamic system perspective for swarm intelligence optimization.