Abstract
Robustness is one of the most important properties to consider when designing networked infrastructure systems such as the road network, airline network, and the electric power grid. A critical concern with such systems is that functionality must be maintained during the occurrence of natural disasters or deliberate attacks on their components. Multiple network robustness measures, each capturing different features of interest, have been formulated to evaluate the capability of a system to withstand such failures or attacks. These previously proposed robustness measures are sometimes uncorrelated or negatively correlated; hence, optimizing a single measure may not improve the overall robustness of the network. In this chapter, we propose a new approach addressing the budget-constrained multi-objective optimization problem of determining the set of new edges (of given size) that maximally improve multiple robustness measures. Experimental results show that adding the edges suggested by our approach significantly improves the network robustness, compared to previously proposed algorithms. The networks improved by our approach also maintain high robustness during random or targeted node attacks.
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Notes
- 1.
Similar results were obtained when the experiments were carried out for 100 generated scale-free networks by: (1) fixing the number of nodes and changing power law parameter in the aforementioned range, and (2) changing the number of nodes in the aforementioned range and fixing the power law parameter.
- 2.
We have experimented with other crossover operators such as two-point crossover, and the results were similar compared to the one-point crossover. Hence, the results with one-point crossover are reported here.
References
M.J. Alenazi, J.P. Sterbenz, Comprehensive comparison and accuracy of graph metrics in predicting network resilience, in 2015 11th International Conference on the Design of Reliable Communication Networks (DRCN) (IEEE, 2015), pp. 157–164
S. Bechikh, L.B. Said, K. Ghédira, Searching for knee regions of the pareto front using mobile reference points. Soft Comput. 15(9), 1807–1823 (2011)
P.J. Bentley, J.P. Wakefield, in Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms (Springer London, 1998), pp 231–240. https://doi.org/10.1007/978-1-4471-0427-8_25
A. Bigdeli, A. Tizghadam, A. Leon-Garcia, Comparison of network criticality, algebraic connectivity, and other graph metrics, in Proceedings of the 1st Annual Workshop on Simplifying Complex Network for Practitioners (ACM, 2009), p. 4
P. Boldi, M. Rosa, Robustness of social and web graphs to node removal. Soc. Netw. Anal. Min. 3(4), 829–842 (2013)
P. Boldi, M. Rosa, S. Vigna, Robustness of Social Networks: Comparative Results Based on Distance Distributions (Springer, 2011)
D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, C. Faloutsos, Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. (TISSEC) 10(4), 1 (2008)
H. Chan, L. Akoglu, in Optimizing network robustness by edge rewiring: A general framework. Data Mining and Knowledge Discovery (DAMI), 2016
H. Chan, L. Akoglu, H. Tong, Make it or break it: manipulating robustness in large networks, in Proceedings of the 2014 SIAM Data Mining Conference (SIAM, 2004), pp. 325–333
P. Chaudhari, R. Dharaskar, V. Thakare, Computing the most significant solution from pareto front obtained in multi-objective evolutionary. Int. J. Adv. Comput. Sci. Appl. 1(4), 63–68 (2010)
M. Cheikh, B. Jarboui, T. Loukil, P. Siarry, A method for selecting pareto optimal solutions in multiobjective optimization. J. Inf. Math. Sci. 2(1), 51–62 (2010)
D.W. Corne, J.D. Knowles, Techniques for highly multiobjective optimisation: some nondominated points are better than others, in Proceedings of the 9th annual conference on Genetic and evolutionary computation (ACM, 2007), pp 773–780
K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-ii, in Parallel Problem Solving from Nature PPSN VI, (Springer, 2000), pp. 849–858
F. di Pierro, Many-objective evolutionary algorithms and applications to water resources engineering. Ph.D. thesis, University of Exeter, 2006
N. Drechsler, R. Drechsler, B. Becker, Multi-objective optimisation based on relation favour, in International Conference on Evolutionary Multi-criterion Optimization (Springer, 2001), pp. 154–166
W. Ellens, Effective resistance and other graph measures for network robustness. Ph.D. thesis, Master thesis, Leiden University, 2011, https://www.math.leidenuniv.nl/scripties/EllensMaster.pdf
W. Ellens, R.E. Kooij, Graph Measures and Network Robustness, 2013. arXiv:13115064
M. Farina, P. Amato, On the optimal solution definition for many-criteria optimization problems, in Fuzzy Information Processing Society, 2002. Proceedings. NAFIPS. 2002 Annual Meeting of the North American, 2002, pp. 233–238. https://doi.org/10.1109/NAFIPS.2002.1018061
M. Fiedler, Algebraic connectivity of graphs. Czechoslov. Math. J 23(2), 298–305 (1973)
M. Garza-Fabre, G.T. Pulido, C.A.C. Coello, Ranking methods for many-objective optimization, in Mexican International Conference on Artificial Intelligence, (Springer, 2009), pp. 633–645
A. Ghosh, S. Boyd, A. Saberi, Minimizing effective resistance of a graph. SIAM Rev. 50(1), 37–66 (2008)
J.A. Hartigan, M.A. Wong, Algorithm as 136: a k-means clustering algorithm. J. R. Stat. Soc. Ser. C (Applied Statistics) 28(1), 100–108 (1979)
H.J. Herrmann, C.M. Schneider, AA.. Moreira, J.S. Andrade Jr., S. Havlin, Onion-like network topology enhances robustness against malicious attacks. J. Stat. Mech. Theory Exp. 2011(01), 01–027 (2011)
A. Jamakovic, P. van Mieghem, On the Robustness of Complex Networks by using the Algebraic Connectivity (Springer, 2008)
W. Jun, M. Barahona, T. Yue-Jin, D. Hong-Zhong, Natural connectivity of complex networks. Chin. Phys. Lett. 27(7), 078–902 (2010)
L.T. Le, T. Eliassi-Rad, H. Tong, Met: a fast algorithm for minimizing propagation in large graphs with small eigen-gaps, in Proceedings of the 2015 SIAM International Conference on Data Mining, SDM, SIAM, vol. 15, 2015, pp. 694–702
F.D. Malliaros, V. Megalooikonomou, C. Faloutsos, Fast robustness estimation in large social graphs: communities and anomaly detection. SDM, SIAM 12, 942–953 (2012)
M. Marchiori, V. Latora, Harmony in the small-world. Phys. A Stat. Mech. Appl. 285(3), 539–546 (2000)
G.S. Peng, J. Wu, Optimal network topology for structural robustness based on natural connectivity. Phys. Stati. Mech. Appl. 443, 212–220 (2016)
P.J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)
C.M. Schneider, A.A. Moreira, J.S. Andrade, S. Havlin, H.J. Herrmann, Mitigation of malicious attacks on networks. Proc. Nat. Acad. Sci. 108(10), 3838–3841 (2011)
N. Srinivas, K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)
G. Stewart, J.G. Sun, Matrix Perturbation Theory (computer science and scientific computing), 1990
S. Sudeng, N. Wattanapongsakorn, Post pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance. Eng. Appl. Artif. Intell. 38, 221–236 (2015)
A. Sydney, C. Scoglio, D. Gruenbacher, Optimizing algebraic connectivity by edge rewiring. Appl. Math. Comput. 219(10), 5465–5479 (2013)
T. Tanizawa, S. Havlin, H.E. Stanley, Robustness of onionlike correlated networks against targeted attacks. Phys. Rev. E 85(4), 046–109 (2012)
A. Tizghadam, A. Leon-Garcia, Autonomic traffic engineering for network robustness. IEEE J. Sel. Areas Commun. 28(1), 39–50 (2010)
H. Tong, B.A. Prakash, C. Tsourakakis, T. Eliassi-Rad, C. Faloutsos, D.H. Chau, On the vulnerability of large graphs, in 2010 IEEE 10th International Conference on Data Mining (ICDM) (IEEE, 2010), pp. 1091–1096
H. Tong, B.A. Prakash, T. Eliassi-Rad, M. Faloutsos, C. Faloutsos, Gelling, and melting, large graphs by edge manipulation, in Proceedings of the 21st ACM International Conference on Information and knowledge Management (ACM, 2012), pp 245–254
H. Wang, P. van Mieghem, Algebraic connectivity optimization via link addition, in Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems, ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), 2008, p. 22
T. Watanabe, N. Masuda, Enhancing the spectral gap of networks by node removal. Phys. Rev. E 82(4), 046–102 (2010)
D.J. Watts, S.H. Strogatz, Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)
L.J. Wismans, T. Brands, E.C. Van Berkum, M.C. Bliemer, Pruning and ranking the pareto optimal set, application for the dynamic multi-objective network design problem. J. Adv. Transp. 48(6), 588–607 (2014)
Z.X. Wu, P. Holme, Onion structure and network robustness. Phys. Rev. E 84(2), 026–106 (2011)
A. Yazdani, R.A. Otoo, P. Jeffrey, Resilience enhancing expansion strategies for water distribution systems: a network theory approach. Environ. Model. Softw. 26(12), 1574–1582 (2011)
A. Zeng, W. Liu, Enhancing network robustness against malicious attacks. Phys. Rev. E 85(6), 066–130 (2012)
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Gunasekara, R.C., Mohan, C.K., Mehrotra, K. (2018). Multi-objective Optimization to Improve Robustness in Networks. In: Mandal, J., Mukhopadhyay, S., Dutta, P. (eds) Multi-Objective Optimization. Springer, Singapore. https://doi.org/10.1007/978-981-13-1471-1_5
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