BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization
Zijun Liao, Jinbiao Chen, Debing Wang, Zizhen Zhang, Jiahai Wang
Abstract
Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose *Best-anchored and Objective-guided Preference Optimization (BOPO)*, a training paradigm that leverages solution preferences via objective values. It introduces: (1) a best-anchored preference pair construction for better explore and exploit solutions, and (2) an objective-guided pairwise loss function that adaptively scales gradients via objective differences, removing reliance on reward models or reference policies. Experiments on Job-shop Scheduling Problem (JSP), Traveling Salesman Problem (TSP), and Flexible Job-shop Scheduling Problem (FJSP) show BOPO outperforms state-of-the-art neural methods, reducing optimality gaps impressively with efficient inference. BOPO is architecture-agnostic, enabling seamless integration with existing NCO models, and establishes preference optimization as a principled framework for combinatorial optimization.
BibTeX
@inproceedings{
liao2025bopo,
title={{BOPO}: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization},
author={Zijun Liao and Jinbiao Chen and Debing Wang and Zizhen Zhang and Jiahai Wang},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=FLy6yXdrlW}
}