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An Experimental Evaluation of Multi-objective Evolutionary Algorithms for Detecting Critical Nodes in Complex Networks

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Applications of Evolutionary Computation (EvoApplications 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9028))

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Abstract

Identifying critical nodes in complex networks has become an important task across a variety of application domains. In this paper we propose a multi-objective version of the critical node detection problem, which aims to minimize pairwise connectivity in a graph by removing a subset of \(K\) nodes. Interestingly, while it has been recognized that this problem is inherently multi-objective since it was formulated, until now only single-objective algorithms have been proposed. After explicitly stating the new multi-objective problem variant, we then give a brief comparison of six common multi-objective evolutionary algorithms using sixteen common benchmark problem instances. A comparison of the results attained by viewing the algorithm as a single versus multi-objective problem is also conducted. We find that of the examined algorithms, NSGAII generally produces the most desirable approximation fronts. We also demonstrate that while related, the best multi-objective solutions do not translate into the best single-objective solutions.

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References

  1. MOEA Framework, version 2.1 (2014). http://www.moeaframework.org

  2. Addis, B., Di Summa, M., Grosso, A.: Identifying critical nodes in undirected graphs: complexity results and polynomial algorithms for the case of bounded treewidth. Discret. Appl.Math. 161(16–17), 2349–2360 (2013)

    Article  MATH  Google Scholar 

  3. Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 222–231 (2004)

    Google Scholar 

  4. Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Aspnes, J., Chang, K., Yampolskiy, A.: Inoculation strategies for victims of viruses and the sum-of-squares partition problem. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005. Society for Industrial and Applied Mathematics, pp. 43–52 (2005)

    Google Scholar 

  6. Boginski, V., Commander, C.: Identifying critical nodes in protein-protein interaction networks. In: Benson, M. (ed.) Clustering Challenges in Biological Networks, pp. 153–166. Springer, Berlin (2009)

    Chapter  Google Scholar 

  7. Chen, P., David, M., Kempe, D.: Better vaccination strategies for better people. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp. 179–188. ACM (2010)

    Google Scholar 

  8. Corne, D., Jerram, N., Knowles, J., Oates, M.: PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (2001)

    Google Scholar 

  9. Deb, K., Mohan, M., Mishra, S.: A fast multi-objective evolutionary algorithm for finding well-spread pareto-optimal solutions. Technical report, IIT-Kanpur (2003)

    Google Scholar 

  10. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  11. Di Summa, M., Grosso, A., Locatelli, M.: Complexity of the critical node problem over trees. Comput. Oper. Res. 38(12), 1766–1774 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dinh, T.N., Xuan, Y., Thai, M.T., Pardalos, P.M., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE/ACM Trans. Netw. 20(2), 609–619 (2012)

    Article  Google Scholar 

  13. Dinh, T.N., Xuan, Y., Thai, M.T., Park, E.K., Znati, T.: On approximation of new optimization methods for assessing network vulnerability. In: INFOCOM, pp. 2678–2686 (2010)

    Google Scholar 

  14. DiSumma, M., Grosso, A., Locatelli, M.: Branch and cut algorithms for detecting critical nodes in undirected graphs. Comput. Optim. Appl. 53(3), 649–680 (2012)

    Article  MathSciNet  Google Scholar 

  15. Engelberg, R., Könemann, J., Leonardi, S., (Seffi) Naor, J.: Cut problems in graphs with a budget constraint. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 435–446. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Garg, N., Vazirani, V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18, 3–20 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Joyce, K.E., Laurienti, P.J., Burdette, J.H., Hayasaka, S.: A new measure of centrality for brain networks. PLoS ONE 5(8), e12200 (2010)

    Article  Google Scholar 

  18. Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence in a social network. In: Proceedings of the 9th International Conference on Knowledge Discovery and Data Mining, pp. 137–146 (2003)

    Google Scholar 

  19. Knowles, J., Corne, D.: The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. In: Proceedings of the 1999 Congress on Evolutionary Computation, vol. 1, pp. 98–105 (1999)

    Google Scholar 

  20. Kollat, J., Reed, P.: Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design. Adv. Water Resour. 29(6), 792–807 (2006)

    Article  Google Scholar 

  21. Kumar, V.S.A., Rajaraman, R., Sun, Z., Sundaram, R.: Existence theorems and approximation algorithms for generalized network security games. In: Proceedings of the 2010 IEEE 30th International Conference on Distributed Computing Systems, pp. 348–357 (2010)

    Google Scholar 

  22. Nebro, A., Alba, E., Molina, G., Chicano, F., Luna, F., Durillo, J.: Optimal antenna placement using a new multi-objective CHC algorithm. In: 9th Annual Conference on Genetic and Evolutionary Computation, pp. 876–883 (2007)

    Google Scholar 

  23. Nguyen, D., Shen, Y., Thai, M.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid 4(1), 151–159 (2013)

    Article  Google Scholar 

  24. Saran, H., Vazirani, V.: Finding k-cuts within twice the optimal. SIAM J. Comput. 24, 101–108 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  25. Schott, J.: Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s thesis, Massachusetts Institute of Technology (1995)

    Google Scholar 

  26. Ventresca, M.: Global search algorithms using a combinatorial unranking-based problem representation for the critical node detection problem. Comput. Oper. Res. 39(11), 2763–2775 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ventresca, M., Aleman, D.: Evaluation of strategies to mitigate contagion spread using social network characteristics. Soc. Netw. 35(1), 75–88 (2013)

    Article  Google Scholar 

  28. Ventresca, M., Aleman, D.: A derandomized approximation algorithm for the critical node detection problem. Comput. Oper. Res. 43, 261–270 (2014)

    Article  MathSciNet  Google Scholar 

  29. Ventresca, M., Aleman, D.: a fast greedy algorithm for the critical node detection problem. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) COCOA 2014. LNCS, vol. 8881, pp. 603–612. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  30. Ventresca, M., Aleman, D.: A randomized algorithm with local search for containment of pandemic disease spread. Comput. Oper. Res. 48, 11–19 (2014)

    Article  MathSciNet  Google Scholar 

  31. Veremyev, A., Boginski, V., Pasiliao, E.L.: Exact identification of critical nodes in sparse networks via new compact formulations. Optim. Lett. 8(4), 1245–1259 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  32. Veremyev, A., Prokopyev, O.A., Pasiliao, E.L.: An integer programming framework for critical elements detection in graphs. J. Comb. Optim. 28(1), 233–273 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  33. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., Da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)

    Article  Google Scholar 

  34. Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, West Lafayette, IN, USA

    Mario Ventresca

  2. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Kyle Robert Harrison & Beatrice M. Ombuki-Berman

Authors
  1. Mario Ventresca
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  2. Kyle Robert Harrison
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  3. Beatrice M. Ombuki-Berman
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Correspondence to Mario Ventresca .

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Editors and Affiliations

  1. Universidad de Granada, Granada, Spain

    Antonio M. Mora

  2. Politecnico di Torino, Turin, Italy

    Giovanni Squillero

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Ventresca, M., Harrison, K.R., Ombuki-Berman, B.M. (2015). An Experimental Evaluation of Multi-objective Evolutionary Algorithms for Detecting Critical Nodes in Complex Networks. In: Mora, A., Squillero, G. (eds) Applications of Evolutionary Computation. EvoApplications 2015. Lecture Notes in Computer Science(), vol 9028. Springer, Cham. https://doi.org/10.1007/978-3-319-16549-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-16549-3_14

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  • Online ISBN: 978-3-319-16549-3

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