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Article Dans Une Revue Knowledge-Based Systems Année : 2023

Reinforced Lin–Kernighan–Helsgaun algorithms for the traveling salesman problems

Résumé

The Traveling Salesman Problem (TSP) is a classical NP-hard combinatorial optimization problem with many practical variants. The Lin–Kernighan–Helsgaun (LKH) algorithm 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 use the candidate sets to improve their efficiency, and have two different methods, -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, and 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 the 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 the -measure or the POPMUSIC method, 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 the TSPTW and CTSP.

Dates et versions

hal-04124984 , version 1 (11-06-2023)

Identifiants

Citer

Jiongzhi Zheng, Kun He, Jianrong Zhou, Yan Jin, Chu-Min Li. Reinforced Lin–Kernighan–Helsgaun algorithms for the traveling salesman problems. Knowledge-Based Systems, 2023, 260, pp.110144. ⟨10.1016/j.knosys.2022.110144⟩. ⟨hal-04124984⟩
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