Self-Organizing Silverfish Optimization Algorithm Based on Anisotropic Metric Learning and Fractional-Order Memory Dynamics

To address the problems of premature convergence, insufficient directionality, and lack of adaptive geometric adjustment capability in the search structure of traditional swarm intelligence algorithms for complex high-dimensional non-convex optimization problems, a self-organizing silverfish optimization algorithm is proposed. Starting from the silverfish's tendency to move towards darkness and its environmental perception mechanism, the algorithm constructs a non-Euclidean perception metric space and introduces an anisotropic metric matrix driven by the population covariance, giving the search direction natural gradient characteristics. Based on this, a coupled potential function of the darkness field and pheromone field is constructed to form a dynamic aggregation structure, achieving multi-peak tracking capability. Furthermore, fractional-order memory dynamics is introduced to characterize explosive crawling behavior, giving the individual evolution process long-range dependence. Finally, an entropy-driven topology reconstruction mechanism achieves adaptive adjustment of the population structure. This paper presents a unified dynamical system expression and analyzes the convergence behavior and complexity. Theoretical analysis shows that the algorithm has good stability and scalability at the geometric, adaptive, and dynamical system levels.