Soft Computing

, Volume 22, Issue 5, pp 1669–1685 | Cite as

A parallel cooperative hybrid method based on ant colony optimization and 3-Opt algorithm for solving traveling salesman problem

  • Şaban Gülcü
  • Mostafa Mahi
  • Ömer Kaan Baykan
  • Halife Kodaz
Methodologies and Application


This article presented a parallel cooperative hybrid algorithm for solving traveling salesman problem. Although heuristic approaches and hybrid methods obtain good results in solving the TSP, they cannot successfully avoid getting stuck to local optima. Furthermore, their processing duration unluckily takes a long time. To overcome these deficiencies, we propose the parallel cooperative hybrid algorithm (PACO-3Opt) based on ant colony optimization. This method uses the 3-Opt algorithm to avoid local minima. PACO-3Opt has multiple colonies and a master–slave paradigm. Each colony runs ACO to generate the solutions. After a predefined number of iterations, each colony primarily runs 3-Opt to improve the solutions and then shares the best tour with other colonies. This process continues until the termination criterion meets. Thus, it can reach the global optimum. PACO-3Opt was compared with previous algorithms in the literature. The experimental results show that PACO-3Opt is more efficient and reliable than the other algorithms.


Ant colony optimization Parallel algorithm 3-Opt algorithm Traveling salesman problem Master–slave paradigm 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Şaban Gülcü
    • 1
  • Mostafa Mahi
    • 2
  • Ömer Kaan Baykan
    • 3
  • Halife Kodaz
    • 3
  1. 1.Department of Computer EngineeringNecmettin Erbakan UniversityKonyaTurkey
  2. 2.Department of Computer Engineering and Information TechnologyPayame Noor UniversityTehranIran
  3. 3.Department of Computer Engineering, Faculty of EngineeringSelcuk UniversityKonyaTurkey

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