Ascent–descent variable neighborhood decomposition search for community detection by modularity maximization
- 166 Downloads
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.
KeywordsClustering 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.
- Alpert, CJ., Yao, SZ. (1995). Spectral partitioning: the more eigenvectors, the better. In Proceedings of the 32nd annual ACM/IEEE design automation conference ( pp. 195–200). ACMGoogle Scholar
- Bader, D. A., Meyerhenke, H., Sanders, P., & Wagner, D. (Eds.). (2013). Graph partitioning and graph clustering – 10th DIMACS implementation challenge, contemporary mathematics (Vol. 588). Boston: AMS.Google Scholar
- Carrizosa, E., Mladenovic, N., Todosijevic, R. (2011). Sum-of-squares clustering on networks. Yugoslav Journal of Operations Research ISSN: 0354–0243 EISSN:2334–6043 21(2)Google Scholar
- Djidjev, HN. (2006). A scalable multilevel algorithm for graph clustering and community structure detection. In International workshop on algorithms and models for the web-graph (pp. 117–128) SpringerGoogle Scholar
- Goldschmidt, O., & Hochbaum, D. S. (1988). Polynomial algorithm for the k-cut problem. In 29th annual symposium on foundations of computer science (pp. 444–451). IEEE.Google Scholar
- Hansen, P., Mladenović, N., Todosijević, R., & Hanafi, S. (2016). Variable neighborhood search: basics and variants. EURO Journal on Computational Optimization. doi: 10.1007/s13675-016-0075-x.
- Reichardt, J., & Bornholdt, S. (2006). Statistical mechanics of community detection. Physical Review E, 74(1), 016–110.Google Scholar
- Su, J., Havens, TC. (2014). Fuzzy community detection in social networks using a genetic algortihm. In 2014 IEEE international conference on fuzzy systems (FUZZ-IEEE) (pp. 2039–2046). IEEEGoogle Scholar