{"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/reinforced-lin-kernighan-helsgaun-algorithms","title":"Reinforced Lin-Kernighan-Helsgaun Algorithms for the Traveling Salesman Problems","arxiv_id":"2207.03876","date":"2022-07-08","proceeding":null,"authors":["Jiongzhi Zheng","Kun He","Jianrong Zhou","Yan Jin","Chu-min Li"],"abstract":"TSP is a classical NP-hard combinatorial optimization problem with many practical variants. LKH is one of the state-of-the-art local search algorithms for the TSP. LKH-3 is a powerful extension of LKH that can solve many TSP variants. Both LKH and LKH-3 associate a candidate set to each city to improve the efficiency, and have two different methods, $\\alpha$-measure and POPMUSIC, to decide the candidate sets. In this work, we first propose a Variable Strategy Reinforced LKH (VSR-LKH) algorithm, which incorporates three reinforcement learning methods (Q-learning, Sarsa, Monte Carlo) with LKH, for the TSP. We further propose a new algorithm called VSR-LKH-3 that combines the variable strategy reinforcement learning method with LKH-3 for typical TSP variants, including the TSP with time windows (TSPTW) and Colored TSP (CTSP). The proposed algorithms replace the inflexible traversal operations in LKH and LKH-3 and let the algorithms learn to make a choice at each search step by reinforcement learning. Both LKH and LKH-3, with either $\\alpha$-measure or POPMUSIC, can be significantly improved by our methods. Extensive experiments on 236 widely-used TSP benchmarks with up to 85,900 cities demonstrate the excellent performance of VSR-LKH. VSR-LKH-3 also significantly outperforms the state-of-the-art heuristics for TSPTW and CTSP.","url_abs":"https://arxiv.org/abs/2207.03876v2","url_pdf":"https://arxiv.org/pdf/2207.03876v2.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":"reinforced-lin-kernighan-helsgaun-algorithms","repo_url":"https://github.com/jhl-hust/vsr-lkh-v2","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"},{"task_slug":"q-learning","task_name":"Q-Learning"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"traveling-salesman-problem","task_name":"Traveling Salesman Problem"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[{"method_slug":"sarsa","method_name":"Sarsa"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2207.03876","atlas_url":"https://app.syntology.ai/?focus=2207.03876","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}