Nested-Refinement Metamorphosis: Reflective Evolution for Efficient Optimization of Networking Problems

Large Language Models (LLMs) excel in network algorithm design but suffer from inefficient iterative coding and high computational costs.Drawing inspiration from butterfly metamorphosis-where structured developmental phases (Phase I: larval nutrient accumulation Phase II: pupal transformation) enable adaptive evolution-we propose Nested-Refinement Metamorphosis (NeRM).Building on this principle, we introduce Metamorphosis on Prompts (MoP) to iteratively refine task descriptions (e.g.latency / bandwidth constraints) and Metamorphosis on Algorithms (MoA) to generate more effective solutions (e.g.appropriate network processing architecture).Their nested refinement ensures task-algorithm alignment, systematically improving both task descriptions and algorithmic solutions for more efficient algorithm design.To further enhance efficiency, we incorporate predictor-assisted code evaluation, mimicking natural selection by filtering out weak candidates early and reducing computational costs.Experimental results on TSP (routing), MKP (resource allocation), and CVRP (servicenetwork coordination) demonstrate that NeRM consistently outperforms state-of-the-art approaches in both performance and efficiency.