Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution

Researchers introduce AutoCO, a new method that combines large language models with constraint optimization to solve complex problems more effectively. The approach uses bidirectional coevolution with Monte Carlo Tree Search and Evolutionary Algorithms to prevent premature convergence and improve solution quality.

• →AutoCO transforms LLMs from passive constraint checkers into proactive strategy designers for optimization problems.
• →The method uses a unified triple-representation that combines relaxation strategies, algorithmic principles, and executable code.
• →Bidirectional coevolution mechanism balances exploration and intensification using MCTS and evolutionary algorithms.
• →Extensive experiments show superior performance on challenging constraint optimization benchmarks.
• →The approach represents a significant advancement toward verifiable LLM-driven optimization solutions.