{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/solving-np-hard-problems-on-graphs-by","title":"Solving NP-Hard Problems on Graphs with Extended AlphaGo Zero","arxiv_id":"1905.11623","date":"2019-05-28","proceeding":null,"authors":["Kenshin Abe","Zijian Xu","Issei Sato","Masashi Sugiyama"],"abstract":"There have been increasing challenges to solve combinatorial optimization problems by machine learning. Khalil et al. proposed an end-to-end reinforcement learning framework, S2V-DQN, which automatically learns graph embeddings to construct solutions to a wide range of problems. To improve the generalization ability of their Q-learning method, we propose a novel learning strategy based on AlphaGo Zero which is a Go engine that achieved a superhuman level without the domain knowledge of the game. Our framework is redesigned for combinatorial problems, where the final reward might take any real number instead of a binary response, win/lose. In experiments conducted for five kinds of NP-hard problems including {\\sc MinimumVertexCover} and {\\sc MaxCut}, our method is shown to generalize better to various graphs than S2V-DQN. Furthermore, our method can be combined with recently-developed graph neural network (GNN) models such as the \\emph{Graph Isomorphism Network}, resulting in even better performance. This experiment also gives an interesting insight into a suitable choice of GNN models for each task.","url_abs":"https://arxiv.org/abs/1905.11623v2","url_pdf":"https://arxiv.org/pdf/1905.11623v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"solving-np-hard-problems-on-graphs-by","repo_url":"https://github.com/colindbrown/columbia-deep-learning-project","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"solving-np-hard-problems-on-graphs-by","repo_url":"https://github.com/xuzijian629/combopt-zero","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"},{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"},{"task_slug":"q-learning","task_name":"Q-Learning"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"}],"methods":[{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"},{"method_slug":"q-learning","method_name":"Q-Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.11623","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.11623"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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