Hybrid Ejection Chain Methods for the Traveling Salesman Problem

  • Weichen Liu
  • Thomas Weise
  • Yuezhong Wu
  • Raymond Chiong
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 562)


Local search such as Ejection Chain Methods (ECMs) based on the stem-and-cycle (S&C) reference structure, Lin-Kernighan (LK) heuristics, as well as the recently proposed Multi-Neighborhood Search (MNS), are among the most competitive algorithms for the Traveling Salesman Problem (TSP). In this paper, we carry out a large-scale experiment with all 110 symmetric instances from the TSPLib to investigate the performances of these algorithms. Our study is different from previous work along this line of research in that we consider the entire runtime behavior of the algorithms, not just their end results. This leads to one of the most comprehensive comparisons of these algorithms to date. We introduce a new, improved S&C-ECM that can outperform LK and MNS. We then develop new hybrid versions of our ECM implementations by combining them with Evolutionary Algorithms and Population-based Ant Colony Optimization (PACO). We compare them to similar hybrids of LK and MNS. Our results show that hybrid PACO-S&C, PACO-LK and PACO-MNS are all very efficient. We also find that the full runtime behavior comparison provides deeper and clearer insights, while focusing on end results only would have led to a misleading conclusion.


Traveling salesman problem Ejection chain methods  Lin-Kernighan heuristic Multi-neighborhood search Hybrid algorithms 



We acknowledge support from the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China No. 61150110488, Special Financial Grant 201104329 from the China Postdoctoral Science Foundation, the Chinese Academy of Sciences (CAS) Fellowship for Young International Scientists 2011Y1GB01, and the European Union 7th Framework Program under Grant 247619. The experiments reported in this paper were executed on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Weichen Liu
    • 1
  • Thomas Weise
    • 1
  • Yuezhong Wu
    • 1
  • Raymond Chiong
    • 2
  1. 1.Joint USTC-Birmingham Research Institute in Intelligent Computation and Its Applications (UBRI), School of Computer Science and TechnologyUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of Design, Communication and IT, Faculty of Science and ITThe University of NewcastleCallaghanAustralia

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