DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization

Chen Shengkai, Zhiguang Cao, Jianan Zhou, Yaoxin Wu, Senthilnath Jayavelu, Zhuoyi Lin, Xiaoli Li, Shili Xiang

Keywords: Combinatorial Optimization, Large-scale optimization, Metaheuristics

Abstract:

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 **D**ecomposition and **R**econstruction **A**gents **G**uided **O**ptimizatio**N**, 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 evaluations 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 demonstrates the potential of feedback-driven language agents as a new paradigm for generalizable and interpretable large-scale optimization.

Area: Search, Optimization, Planning, and Scheduling (SOPS)

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Submission Number: 1634