@inproceedings{liu-etal-2026-learn,
title = "Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution",
author = "Liu, Beidan and
Zhu, Zhengqiu and
Gao, Chen and
Pu, Tianle and
Zhao, Yong and
Qi, Wei and
Yin, Quanjun",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.48/",
pages = "1075--1094",
ISBN = "979-8-89176-390-6",
abstract = "Large Language Model (LLM)-based optimization has recently shown promise for autonomous problem solving, yet most approaches still cast LLMs as passive constraint checkers rather than proactive strategy designers, limiting their effectiveness on complex Constraint Optimization Problems (COPs). To address this, we present AutoCO, an end-to-end Automated Constraint Optimization method that tightly couples operations-research principles of constraint relaxation with LLM reasoning. A core innovation is a unified triple-representation that binds relaxation strategies, algorithmic principles, and executable codes. This design enables the LLM to synthesize, justify, and instantiate relaxation strategies that are both principled and executable. To navigate fragmented solution spaces, AutoCO employs a bidirectional global{--}local coevolution mechanism, synergistically coupling Monte Carlo Tree Search (MCTS) for global relaxation-trajectory exploration with Evolutionary Algorithms (EAs) for local solution intensification. This continuous exchange of priors and feedback explicitly balances diversification and intensification, thus preventing premature convergence. Extensive experiments on three challenging COP benchmarks validate AutoCO{'}s consistent effectiveness and superior performance, especially in hard regimes where current methods degrade. Results highlight AutoCO as a principled and effective path toward proactive, verifiable LLM-driven optimization."
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<abstract>Large Language Model (LLM)-based optimization has recently shown promise for autonomous problem solving, yet most approaches still cast LLMs as passive constraint checkers rather than proactive strategy designers, limiting their effectiveness on complex Constraint Optimization Problems (COPs). To address this, we present AutoCO, an end-to-end Automated Constraint Optimization method that tightly couples operations-research principles of constraint relaxation with LLM reasoning. A core innovation is a unified triple-representation that binds relaxation strategies, algorithmic principles, and executable codes. This design enables the LLM to synthesize, justify, and instantiate relaxation strategies that are both principled and executable. To navigate fragmented solution spaces, AutoCO employs a bidirectional global–local coevolution mechanism, synergistically coupling Monte Carlo Tree Search (MCTS) for global relaxation-trajectory exploration with Evolutionary Algorithms (EAs) for local solution intensification. This continuous exchange of priors and feedback explicitly balances diversification and intensification, thus preventing premature convergence. Extensive experiments on three challenging COP benchmarks validate AutoCO’s consistent effectiveness and superior performance, especially in hard regimes where current methods degrade. Results highlight AutoCO as a principled and effective path toward proactive, verifiable LLM-driven optimization.</abstract>
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%0 Conference Proceedings
%T Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution
%A Liu, Beidan
%A Zhu, Zhengqiu
%A Gao, Chen
%A Pu, Tianle
%A Zhao, Yong
%A Qi, Wei
%A Yin, Quanjun
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F liu-etal-2026-learn
%X Large Language Model (LLM)-based optimization has recently shown promise for autonomous problem solving, yet most approaches still cast LLMs as passive constraint checkers rather than proactive strategy designers, limiting their effectiveness on complex Constraint Optimization Problems (COPs). To address this, we present AutoCO, an end-to-end Automated Constraint Optimization method that tightly couples operations-research principles of constraint relaxation with LLM reasoning. A core innovation is a unified triple-representation that binds relaxation strategies, algorithmic principles, and executable codes. This design enables the LLM to synthesize, justify, and instantiate relaxation strategies that are both principled and executable. To navigate fragmented solution spaces, AutoCO employs a bidirectional global–local coevolution mechanism, synergistically coupling Monte Carlo Tree Search (MCTS) for global relaxation-trajectory exploration with Evolutionary Algorithms (EAs) for local solution intensification. This continuous exchange of priors and feedback explicitly balances diversification and intensification, thus preventing premature convergence. Extensive experiments on three challenging COP benchmarks validate AutoCO’s consistent effectiveness and superior performance, especially in hard regimes where current methods degrade. Results highlight AutoCO as a principled and effective path toward proactive, verifiable LLM-driven optimization.
%U https://aclanthology.org/2026.acl-long.48/
%P 1075-1094
Markdown (Informal)
[Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution](https://aclanthology.org/2026.acl-long.48/) (Liu et al., ACL 2026)
ACL
- Beidan Liu, Zhengqiu Zhu, Chen Gao, Tianle Pu, Yong Zhao, Wei Qi, and Quanjun Yin. 2026. Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1075–1094, San Diego, California, United States. Association for Computational Linguistics.