COExpander: Adaptive Solution Expansion for Combinatorial Optimization

Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:42130-42164, 2025.

Abstract

Despite rapid progress in neural combinatorial optimization (NCO) for solving CO problems (COPs), as the problem scale grows, several bottlenecks persist: 1) solvers in the Global Prediction (GP) paradigm struggle in long-range decisions where the overly smooth intermediate heatmaps impede effective decoding, and 2) solvers in the Local Construction (LC) paradigm are time-consuming and incapable of tackling large instances due to the onerous auto-regressive process. Observing these challenges, we propose a new paradigm named Adaptive Expansion AE with its instantiation COExpander, positioned to leverage both advantages of GP and LC. COExpander utilizes informative heatmaps generated by a global predictor, which is learned under the guidance of locally determined partial solutions, to in turn direct the expansion of determined decision variables with adaptive step-sizes. To ensure transparent evaluation, we further take the lead to canonicalize 29 benchmarks spanning 6 popular COPs (MIS, MCl, MVC, MCut, TSP, ATSP) and various scales (50-10K nodes), upon which experiments demonstrate concrete SOTA performance of COExpander over these tasks. Source code and our standardized datasets will be made public.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-ma25r, title = {{COE}xpander: Adaptive Solution Expansion for Combinatorial Optimization}, author = {Ma, Jiale and Pan, Wenzheng and Li, Yang and Yan, Junchi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {42130--42164}, 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/ma25r/ma25r.pdf}, url = {https://proceedings.mlr.press/v267/ma25r.html}, abstract = {Despite rapid progress in neural combinatorial optimization (NCO) for solving CO problems (COPs), as the problem scale grows, several bottlenecks persist: 1) solvers in the Global Prediction (GP) paradigm struggle in long-range decisions where the overly smooth intermediate heatmaps impede effective decoding, and 2) solvers in the Local Construction (LC) paradigm are time-consuming and incapable of tackling large instances due to the onerous auto-regressive process. Observing these challenges, we propose a new paradigm named Adaptive Expansion AE with its instantiation COExpander, positioned to leverage both advantages of GP and LC. COExpander utilizes informative heatmaps generated by a global predictor, which is learned under the guidance of locally determined partial solutions, to in turn direct the expansion of determined decision variables with adaptive step-sizes. To ensure transparent evaluation, we further take the lead to canonicalize 29 benchmarks spanning 6 popular COPs (MIS, MCl, MVC, MCut, TSP, ATSP) and various scales (50-10K nodes), upon which experiments demonstrate concrete SOTA performance of COExpander over these tasks. Source code and our standardized datasets will be made public.} }
Endnote
%0 Conference Paper %T COExpander: Adaptive Solution Expansion for Combinatorial Optimization %A Jiale Ma %A Wenzheng Pan %A Yang Li %A Junchi Yan %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-ma25r %I PMLR %P 42130--42164 %U https://proceedings.mlr.press/v267/ma25r.html %V 267 %X Despite rapid progress in neural combinatorial optimization (NCO) for solving CO problems (COPs), as the problem scale grows, several bottlenecks persist: 1) solvers in the Global Prediction (GP) paradigm struggle in long-range decisions where the overly smooth intermediate heatmaps impede effective decoding, and 2) solvers in the Local Construction (LC) paradigm are time-consuming and incapable of tackling large instances due to the onerous auto-regressive process. Observing these challenges, we propose a new paradigm named Adaptive Expansion AE with its instantiation COExpander, positioned to leverage both advantages of GP and LC. COExpander utilizes informative heatmaps generated by a global predictor, which is learned under the guidance of locally determined partial solutions, to in turn direct the expansion of determined decision variables with adaptive step-sizes. To ensure transparent evaluation, we further take the lead to canonicalize 29 benchmarks spanning 6 popular COPs (MIS, MCl, MVC, MCut, TSP, ATSP) and various scales (50-10K nodes), upon which experiments demonstrate concrete SOTA performance of COExpander over these tasks. Source code and our standardized datasets will be made public.
APA
Ma, J., Pan, W., Li, Y. & Yan, J.. (2025). COExpander: Adaptive Solution Expansion for Combinatorial Optimization. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:42130-42164 Available from https://proceedings.mlr.press/v267/ma25r.html.

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