{"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/controlling-continuous-relaxation-for","title":"Controlling Continuous Relaxation for Combinatorial Optimization","arxiv_id":"2309.16965","date":"2023-09-29","proceeding":null,"authors":["Yuma Ichikawa"],"abstract":"Unsupervised learning (UL)-based solvers for combinatorial optimization (CO) train a neural network that generates a soft solution by directly optimizing the CO objective using a continuous relaxation strategy. These solvers offer several advantages over traditional methods and other learning-based methods, particularly for large-scale CO problems. However, UL-based solvers face two practical issues: (I) an optimization issue, where UL-based solvers are easily trapped at local optima, and (II) a rounding issue, where UL-based solvers require artificial post-learning rounding from the continuous space back to the original discrete space, undermining the robustness of the results. This study proposes a Continuous Relaxation Annealing (CRA) strategy, an effective rounding-free learning method for UL-based solvers. CRA introduces a penalty term that dynamically shifts from prioritizing continuous solutions, effectively smoothing the non-convexity of the objective function, to enforcing discreteness, eliminating artificial rounding. Experimental results demonstrate that CRA significantly enhances the performance of UL-based solvers, outperforming existing UL-based solvers and greedy algorithms in complex CO problems. Additionally, CRA effectively eliminates artificial rounding and accelerates the learning process.","url_abs":"https://arxiv.org/abs/2309.16965v4","url_pdf":"https://arxiv.org/pdf/2309.16965v4.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":"controlling-continuous-relaxation-for","repo_url":"https://github.com/Yuma-Ichikawa/CRA4CO","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause-Clear"}}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"},{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2309.16965","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2309.16965"}},"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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