Annals of Operations Research

, Volume 272, Issue 1–2, pp 273–287 | Cite as

Ascent–descent variable neighborhood decomposition search for community detection by modularity maximization

  • Dušan DžamićEmail author
  • Daniel Aloise
  • Nenad Mladenović
Advances in Theoretical and Applied Combinatorial Optimization


In this paper we propose a new variant of the Variable Neighborhood Decomposition Search (VNDS) heuristic for solving global optimization problems. We call it Ascent-Descent VNDS since it performs “boundary effect”, or local search step, even if the improvement in solving the subproblem has not been obtained. We apply it in detecting communities in large networks by modularity maximization, the criterion which is, despite of some recent criticism, most widely used. Computational analysis is performed on 22 instances from the 10th DIMACS Implementation Challenge. On 13 instances where optimal solutions were not known, we got the improved best known solutions on 9 instances and on 4 instances the solution was equal to the best known. Thus, the proposed new heuristic outperforms the current state-of-the-art algorithms from the literature.


Clustering Community detection Modularity maximization Variable neighborhood search Decomposition 



This research was partially supported by CNPq-Brazil Grants 308887/2014-0 and 400350/ 2014-9, and Serbian Ministry of Education and Science Grant 174010.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia
  2. 2.Departamento de Engenharia de Computação e AutomaçãoUniversidade Federal do Rio Grande do NorteNatalBrazil
  3. 3.Mathematical InstituteSerbian Academy of SciencesBelgradeSerbia

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