Autonomous Algorithm Synthesis via Large Language Models for Multi-Hop Routing in IoT Networks

Multi-hop routing optimization in IoT networks involves complex energy–latency trade-offs that challenge traditional algorithm design approaches. This letter presents a systematic framework for Large Language Model (LLM)assisted algorithm synthesis for multi-hop routing in digital twin (DT)-enabled IoT systems. The proposed three-phase methodology enables LLMs to support algorithmic design by analyzing problem structures, synthesizing hybrid optimization strategies, and iteratively refining routing heuristics under energy, reliability, and latency constraints. The framework generates multiple specialized algorithms, including Advanced Smart Constraint (ASC) for adaptive construction, Energy-Focused Iterative (EFI) refinement, and problem-specific large neighborhood search operators. Extensive experiments on synthetic IoT networks with K = 5–50 devices demonstrate consistent energy reductions of approximately 45% over the random baseline, with statistical significance (p < 0.05) and very large effect sizes (Cohen’s d ≈ 2.5–3.2). Algorithm specialization emerges naturally across network scales, with EFI performing best on small networks and ASC dominating medium to larger configurations. These results indicate that LLM-assisted algorithm synthesis provides a practical and scalable approach for constrained routing optimization in DT-enabled IoT systems.