2010/03/31 by Daniel Karapetyan, Gregory Gutin · 100 citations
Computer Science · Engineering · Mathematics · #2-opt #Adaptation (eye) #Algorithm #Artificial intelligence #Biology #Computer science #Heuristic #Heuristics #Lin–Kernighan heuristic #Mathematical optimization #Mathematics #Metaheuristic Optimization Algorithms Research #Optimization and Packing Problems #Travelling salesman problem #Vehicle Routing Optimization Methods #cs.DS
paper · pdf · doi:10.1016/j.ejor.2010.08.011
published in European Journal of Operational Research 208(3), 221-232 (Elsevier BV) · 25 pages
arxiv created 2010/06/23 · openalex publication_date 2010/08/18 · arxiv updated 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search.