BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization

Zijun Liao, Jinbiao Chen, Debing Wang, Zizhen Zhang, Jiahai Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:37456-37475, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liao25a, title = {{BOPO}: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization}, author = {Liao, Zijun and Chen, Jinbiao and Wang, Debing and Zhang, Zizhen and Wang, Jiahai}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {37456--37475}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/liao25a/liao25a.pdf}, url = {https://proceedings.mlr.press/v267/liao25a.html}, 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.} }
Endnote
%0 Conference Paper %T BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization %A Zijun Liao %A Jinbiao Chen %A Debing Wang %A Zizhen Zhang %A Jiahai Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-liao25a %I PMLR %P 37456--37475 %U https://proceedings.mlr.press/v267/liao25a.html %V 267 %X 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.
APA
Liao, Z., Chen, J., Wang, D., Zhang, Z. & Wang, J.. (2025). BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:37456-37475 Available from https://proceedings.mlr.press/v267/liao25a.html.

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