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The bi-objective critical node detection problem

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  • Ventresca, Mario
  • Harrison, Kyle Robert
  • Ombuki-Berman, Beatrice M.

Abstract

Identifying critical nodes in complex networks has become an important task across a variety of application domains. The Critical Node Detection Problem (CNDP) is an optimization problem that aims to minimize pairwise connectivity in a graph by removing a subset of K nodes. Despite the CNDP being recognized as a bi-objective problem, until now only single-objective problem formulations have been proposed. In this paper, we propose a bi-objective version of the problem that aims to maximize the number of connected components in a graph while simultaneously minimizing the variance of their cardinalities by removing a subset of K nodes. We prove that our bi-objective formulation is distinct from the CNDP, despite their common motivation. Finally, we give a brief comparison of six common multi-objective evolutionary algorithms using sixteen common benchmark problem instances, including for the node-weighted CNDP. We find that of the examined algorithms, NSGAII generally produces the most desirable approximation fronts.

Suggested Citation

  • Ventresca, Mario & Harrison, Kyle Robert & Ombuki-Berman, Beatrice M., 2018. "The bi-objective critical node detection problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 895-908.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:3:p:895-908
    DOI: 10.1016/j.ejor.2017.08.053
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    References listed on IDEAS

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    1. Marco Di Summa & Andrea Grosso & Marco Locatelli, 2012. "Branch and cut algorithms for detecting critical nodes in undirected graphs," Computational Optimization and Applications, Springer, vol. 53(3), pages 649-680, December.
    2. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    3. Karen E Joyce & Paul J Laurienti & Jonathan H Burdette & Satoru Hayasaka, 2010. "A New Measure of Centrality for Brain Networks," PLOS ONE, Public Library of Science, vol. 5(8), pages 1-13, August.
    4. Jose L. Walteros & Panos M. Pardalos, 2012. "Selected Topics in Critical Element Detection," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Military Science, edition 127, chapter 0, pages 9-26, Springer.
    5. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    6. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
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    Cited by:

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    2. Wu, Gongyu & Li, Meiyan & Li, Zhaojun Steven, 2021. "A Gene Importance based Evolutionary Algorithm (GIEA) for identifying critical nodes in Cyber–Physical Power Systems," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    3. Erfan Khosravani Moghadam & Mohammad Sharifi & Shahin Rafiee & Young Ki Chang, 2019. "Time–Cost–Quality Trade-Off in a Broiler Production Project Using Meta-Heuristic Algorithms: A Case Study," Agriculture, MDPI, vol. 10(1), pages 1-18, December.

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