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

TL;DR

DRAGON introduces an LLM-driven divide-and-conquer framework for large-scale combinatorial optimization by alternating between decomposition and reconstruction stages. A decomposition agent identifies high-potential subregions and compresses problem data, while a reconstruction agent solves constrained subproblems and enforces global feasibility through an experience memory. Empirical results across routing and packing benchmarks show DRAGON achieves feasible solutions on very large instances and near-optimal gaps on knapsack problems with millions of variables, outperforming several prompt-based baselines in scalability. The work demonstrates a generalizable, interpreter-friendly paradigm for large-scale COPs, with solver-agnostic design and avenues for integration with traditional solvers and hybrid architectures.

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 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.

Figures (8)

• Figure 1: Illustration of DRAGON on a TSP instance, where metadata represent the coordinates of locations to visit, serving as the main environment for the agents. The decomposer identifies a suboptimal active segment {4,6,7,8} (grayed) from a global solution. The segment is locally refined and reintegrated by the reconstructor to improve the global tour.
• Figure 2: Overview of the state passing among agents in DRAGON framework. With (a) given COP data input and current global solution, the DRAGON pipeline process alternates between two key stages: (b) A decomposition step uses an LLM to split a large-scale COP into manageable active and static segments. These are compressed into a smaller subproblem; (c) A reconstruction step solves the reduced problem with additional constraints to yield a refined local solution. This is then reintegrated into the global solution.
• Figure 3: Constraint satisfaction in reconstruction is ensured via experience accumulation.
• Figure 4: Average Optimality Gap (%) (log scale) across problem size groups for different methods on TSPLIB.
• Figure 5: Optimality Gap (%) for different methods on CVRPLIB.