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

• URL: http://arxiv.org/abs/2601.06502v1
• Date: Sat, 10 Jan 2026 09:31:40 GMT
• Title: DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization
• Authors: Shengkai Chen, Zhiguang Cao, Jianan Zhou, Yaoxin Wu, Senthilnath Jayavelu, Zhuoyi Lin, Xiaoli Li, Shili Xiang,
• Abstract summary: Large Language Models (LLMs) have recently shown promise in addressing optimization problems (COPs) through prompt-based strategies.<n>We propose DRAGON, which combines the strengths of metaheuristic design and LLM reasoning.<n>By continuously interacting with the optimization environment and leveraging an adaptive experience memory, the agents iteratively learn from feedback.
• Score: 40.88623618289683
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Reasoning in a Combinatorial and Constrained World: Benchmarking LLMs on Natural-Language Combinatorial Optimization [28.52469449694436]
  Large language models (LLMs) have shown strong performance in math and logic reasoning.<n>But their ability to handle systematic optimization (CO) remains underexplored.<n>We introduce NLCO, a benchmark that evaluates LLMs on end-to-end CO reasoning.
  arXiv  Detail & Related papers  (2026-02-02T14:55:48Z)
• Multi-Objective Hierarchical Optimization with Large Language Models [41.41567058185742]
  Large Language Models (LLMs) are not the off-the-shelf choice to drive multi-objective optimization yet.<n>In this paper, we close this gap by leveraging LLMs as surrogate models and candidate samplers inside a structured hierarchical search strategy.
  arXiv  Detail & Related papers  (2026-01-20T12:10:13Z)
• Optimizing Prompt Sequences using Monte Carlo Tree Search for LLM-Based Optimization [20.44067161623662]
  Large language models (LLMs) have demonstrated remarkable capabilities in code generation and structured reasoning.<n>We propose a novel neural-symbolic framework that formulates prompt selection as a sequential decision process guided by Monte Carlo Tree Search.<n>Our method explores and refines multi-step prompt sequences for the goal of improving code generation quality.
  arXiv  Detail & Related papers  (2025-08-08T04:01:24Z)
• OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems [19.586884180343038]
  OPT-BENCH is a benchmark designed to evaluate Large Language Models (LLMs) on large-scale search space optimization problems.<n> OPT-Agent emulates human reasoning when tackling complex problems by generating, validating, and iteratively improving solutions through historical feedback.
  arXiv  Detail & Related papers  (2025-06-12T14:46:41Z)
• Optima: Optimizing Effectiveness and Efficiency for LLM-Based Multi-Agent System [75.25394449773052]
  Large Language Model (LLM) based multi-agent systems (MAS) show remarkable potential in collaborative problem-solving.<n>Yet they still face critical challenges: low communication efficiency, poor scalability, and a lack of effective parameter-updating optimization methods.<n>We present Optima, a novel framework that addresses these issues by significantly enhancing both communication efficiency and task effectiveness.
  arXiv  Detail & Related papers  (2024-10-10T17:00:06Z)
• In-context Demonstration Matters: On Prompt Optimization for Pseudo-Supervision Refinement [71.60563181678323]
  Large language models (LLMs) have achieved great success across diverse tasks, and fine-tuning is sometimes needed to further enhance generation quality.<n>To handle these challenges, a direct solution is to generate high-confidence'' data from unsupervised downstream tasks.<n>We propose a novel approach, pseudo-supervised demonstrations aligned prompt optimization (PAPO) algorithm, which jointly refines both the prompt and the overall pseudo-supervision.
  arXiv  Detail & Related papers  (2024-10-04T03:39:28Z)
• LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning [56.273799410256075]
  The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability.
  arXiv  Detail & Related papers  (2024-10-03T18:12:29Z)
• A Problem-Oriented Perspective and Anchor Verification for Code Optimization [43.28045750932116]
  Large language models (LLMs) have shown remarkable capabilities in solving various programming tasks.<n>This paper investigates the capabilities of LLMs in optimizing code for minimal execution time.
  arXiv  Detail & Related papers  (2024-06-17T16:10:10Z)
• LLM as a Complementary Optimizer to Gradient Descent: A Case Study in Prompt Tuning [69.95292905263393]
  We show that gradient-based and high-level LLMs can effectively collaborate a combined optimization framework.<n>In this paper, we show that these complementary to each other and can effectively collaborate a combined optimization framework.
  arXiv  Detail & Related papers  (2024-05-30T06:24:14Z)
• Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization [15.476478159958416]
  We employ a large language model (LLM) to enhance evolutionary search for solving constrained multi-objective optimization problems. Our aim is to speed up the convergence of the evolutionary population.
  arXiv  Detail & Related papers  (2024-05-09T13:44:04Z)
• SparseLLM: Towards Global Pruning for Pre-trained Language Models [12.057369029549534]
  We propose SparseLLM, a novel framework that redefines the global pruning process into manageable, coordinated subproblems. SparseLLM's approach conceptualizes LLMs as a chain of modular functions and leverages auxiliary variables for problem decomposition. It demonstrates significant performance improvements, particularly in high-sparsity regimes.
  arXiv  Detail & Related papers  (2024-02-28T00:09:07Z)
• Robust Prompt Optimization for Large Language Models Against Distribution Shifts [80.6757997074956]
  Large Language Model (LLM) has demonstrated significant ability in various Natural Language Processing tasks. We propose a new problem of robust prompt optimization for LLMs against distribution shifts. This problem requires the prompt optimized over the labeled source group can simultaneously generalize to an unlabeled target group.
  arXiv  Detail & Related papers  (2023-05-23T11:30:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.