Senthilnath Jayavelu
Publications
Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization
Recent research has demonstrated the effectiveness of large language models (LLMs) in solving combinatorial optimization problems (COPs) by representing tasks and instances in natural language. However, purely language-based approaches struggle to accurately capture complex relational structures inherent in many COPs, rendering them less effective at addressing medium-sized or larger instances. To address these limitations, we propose AlignOPT, a novel approach that aligns LLMs with graph neural solvers to learn a more generalizable neural COP heuristic. Specifically, AlignOPT leverages the semantic understanding capabilities of LLMs to encode textual descriptions of COPs and their instances, while concurrently exploiting graph neural solvers to explicitly model the underlying graph structures of COP instances. Our approach facilitates a robust integration and alignment between linguistic semantics and structural representations, enabling more accurate and scalable COP solutions. Experimental results demonstrate that AlignOPT achieves state-of-the-art results across diverse COPs, underscoring its effectiveness in aligning semantic and structural representations. In particular, AlignOPT demonstrates strong generalization, effectively extending to previously unseen COP instances.
DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization
Large Language Models (LLMs) have recently shown promise in addressing combinatorial optimization problems (COPs) through prompt-based strategies. However, their scalability and generalization remain limited, and their effectiveness diminishes as problem size increases, particularly in routing problems involving more than 30 nodes. We propose DRAGON, which stands for Decomposition and Reconstruction Agents Guided OptimizatioN, a novel framework that combines the strengths of metaheuristic design and LLM reasoning. Starting from an initial global solution, DRAGON autonomously identifies regions with high optimization potential and strategically decompose large-scale COPs into manageable subproblems. Each subproblem is then reformulated as a concise, localized optimization task and solved through targeted LLM prompting guided by accumulated experiences. Finally, the locally optimized solutions are systematically reintegrated into the original global context to yield a significantly improved overall outcome. By continuously interacting with the optimization environment and leveraging an adaptive experience memory, the agents iteratively learn from feedback, effectively coupling symbolic reasoning with heuristic search. Empirical results show that, unlike existing LLM-based solvers limited to small-scale instances, DRAGON consistently produces feasible solutions on TSPLIB, CVRPLIB, and Weibull-5k bin packing benchmarks, and achieves near-optimal results (0.16% gap) on knapsack problems with over 3M variables. This work shows the potential of feedback-driven language agents as a new paradigm for generalizable and interpretable large-scale optimization.
DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization
Large Language Models (LLMs) have recently shown promise in addressing combinatorial optimization problems (COPs) through prompt-based strategies. However, their scalability and generalization remain limited, and their effectiveness diminishes as problem size increases, particularly in routing problems involving more than 30 nodes. We propose DRAGON, which stands for Decomposition and Reconstruction Agents Guided OptimizatioN, a novel framework that combines the strengths of metaheuristic design and LLM reasoning. Starting from an initial global solution, DRAGON autonomously identifies regions with high optimization potential and strategically decompose large-scale COPs into manageable subproblems. Each subproblem is then reformulated as a concise, localized optimization task and solved through targeted LLM prompting guided by accumulated experiences. Finally, the locally optimized solutions are systematically reintegrated into the original global context to yield a significantly improved overall outcome. By continuously interacting with the optimization environment and leveraging an adaptive experience memory, the agents iteratively learn from feedback, effectively coupling symbolic reasoning with heuristic search. Empirical results show that, unlike existing LLM-based solvers limited to small-scale instances, DRAGON consistently produces feasible solutions on TSPLIB, CVRPLIB, and Weibull-5k bin packing benchmarks, and achieves near-optimal results (0.16% gap) on knapsack problems with over 3M variables. This work shows the potential of feedback-driven language agents as a new paradigm for generalizable and interpretable large-scale optimization.