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Yi-Xiang Hu

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3 papers

1 author row

AAAI Conference 2025 Conference Paper

FFCG: Effective and Fast Family Column Generation for Solving Large-Scale Linear Program

Yi-Xiang Hu
Feng Wu
Shaoang Li
Yifang Zhao
Xiang-Yang Li

Column Generation (CG) is an effective and iterative algorithm to solve large-scale linear programs (LP). During each CG iteration, new columns are added to improve the solution of the LP. Typically, CG greedily selects one column with the most negative reduced cost, which can be improved by adding more columns at once. However, selecting all columns with negative reduced costs would lead to the addition of redundant columns that do not improve the objective value. Therefore, selecting the appropriate columns to add is still an open problem and previous machine-learning-based approaches for CG only add a constant quantity of columns per iteration due to the state-space explosion problem. To address this, we propose Fast Family Column Generation (FFCG) — a novel reinforcement-learning-based CG that selects a variable number of columns as needed in an iteration. Specifically, we formulate the column selection problem in CG as an MDP and design a reward metric that balances both the convergence speed and the number of redundant columns. In our experiments, FFCG converges faster on the common benchmarks and reduces the number of CG iterations by 77.1% for Cutting Stock Problem (CSP) and 84.8% for Vehicle Routing Problem with Time Windows (VRPTW), and a 71.4% reduction in computing time for CSP and 84.0% for VRPTW on average compared to several state-of-the-art baselines.

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IJCAI Conference 2025 Conference Paper

Guiding Large Language Models in Modeling Optimization Problems via Question Partitioning

Xiaotian Pan
Junhao Fang
Feng Wu
Sijia Zhang
Yi-Xiang Hu
Shaoang Li
Xiang-Yang Li

Optimization problems are ubiquitous across various domains, such as resource scheduling, production planning, and sales management. Traditionally, they are modeled manually, leading to inefficiencies due to difficulties in communication and collaboration between modeling and domain experts. The emergence of Large Language Models (LLMs) has made automated modeling possible. However, real-world applications are often large-scale and have numerous variables and constraints, limiting the applicability of existing methods. To address this, we propose PaMOP, a novel modeling framework based on LLMs, to model optimization problems automatically, given only natural language descriptions. Specifically, we extract and partition the problems using a tree structure, guiding the LLMs to model each set of constraints with self-augmented prompts, thus reducing the demands on the LLM's capabilities of large contents. The mathematical model is then iteratively corrected and validated through our correction procedures. The experiments demonstrate that our method improves performance on the common benchmark dataset NLP4LP, achieving an accuracy of 62. 3% and a code executability rate of 86. 8% when tested on GPT-4. Additionally, we demonstrate the effectiveness of our PaMOP in handling large real-world problems.

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NeurIPS Conference 2025 Conference Paper

MURKA: Multi-Reward Reinforcement Learning with Knowledge Alignment for Optimization Tasks

WANTONG XIE
Yi-Xiang Hu
Jieyang Xu
Feng Wu
Xiangyang Li

Optimization plays a central role in Operations Research (OR) and numerous industrial applications, yet automating the end-to-end process of translating natural language descriptions into executable optimization programs remains a formidable challenge. While recent efforts have applied Large Language Models (LLMs) to this task, existing approaches are hindered by high inference costs, limited robustness across domains, and weak verification mechanisms. In this work, we propose MURKA, a reinforcement learning and knowledge distillation-based framework that enhances LLM-driven optimization modeling via collaborative agent alignment. MURKA orchestrates three specialized agents---Extractor, Solver, and Checker---to achieve accurate problem understanding, robust formulation, and verifiable execution. The Extractor is trained using group relative policy optimization with a composite reward function that incorporates semantic correctness and execution fidelity. The Solver benefits from knowledge distillation from a powerful teacher model, yielding structurally valid and executable formulations in AMPL. The Checker iteratively verifies solution correctness via solver feedback. We validate MURKA's generalizability through extensive experiments across diverse OR benchmarks, demonstrating its robustness and scalability. Experimental results on eight diverse OR benchmarks, including NLP4LP, ComplexOR, and NL4Opt, demonstrate that MURKA, built on the LLaMa3-8B backbone, achieves a 5. 9\% absolute improvement in solution accuracy and a 5. 1\% increase in execution success rate compared to leading baselines. These results establish MURKA as an effective and scalable paradigm for LLM-driven optimization, with strong potential for deployment in real-world OR applications.

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