A multiobjective box-covering algorithm for fractal modularity on complex networks
[Display omitted] •Fractal modularity has been considered as an optimization objective for box-covering problem on complex networks and a multiobjective optimization function is formulized.•A multiobjective discrete PSO algorithm for box-covering problem is proposed.•A discrete particle status updat...
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| Published in: | Applied soft computing Vol. 61; pp. 294 - 313 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.12.2017
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| ISSN: | 1568-4946, 1872-9681 |
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| Abstract | [Display omitted]
•Fractal modularity has been considered as an optimization objective for box-covering problem on complex networks and a multiobjective optimization function is formulized.•A multiobjective discrete PSO algorithm for box-covering problem is proposed.•A discrete particle status updating rule is designed according to the knowledge from former generations, and a mutation operator is proposed to promote the diversity and help the algorithm escape from local optima.•The experimental studies compared with 12 state-of-the-art algorithms demonstrate that the proposed algorithm is effective and promising.
The box-covering method is widely used on measuring the fractal property on complex networks. The problem of finding the minimum number of boxes to tile a network is known as a NP-hard problem. Many algorithms have been proposed to solve this problem. All the current box-covering algorithms regard the box number minimization as the only objective. However, the fractal modularity of the network partition divided by the box-covering method, has been proved to be strongly related to the information transportation in complex networks. Maximizing the fractal modularity is also important in the box-covering method, which can be divided into two objectives: maximization of ratio association and minimization of ratio cut. In this paper, to solve the dilemma of minimizing the box number and maximizing the fractal modularity at the same time, a multiobjective discrete particle swarm optimization box-covering (MOPSOBC) algorithm is proposed. The MOPSOBC algorithm applies the decomposition approach on the two objectives to approximate the Pareto front. The proposed MOPSOBC algorithm has been applied to six benchmark networks and compared with the state-of-the-art algorithms, including two classical box-covering algorithms, four single objective optimization algorithms and six multiobjective optimization algorithms. The experimental results show that the MOPSOBC algorithm can get similar box numbers with the current best algorithm, and it outperforms the state-of-the-art algorithms on the fractal modularity and normalized mutual information. |
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| AbstractList | [Display omitted]
•Fractal modularity has been considered as an optimization objective for box-covering problem on complex networks and a multiobjective optimization function is formulized.•A multiobjective discrete PSO algorithm for box-covering problem is proposed.•A discrete particle status updating rule is designed according to the knowledge from former generations, and a mutation operator is proposed to promote the diversity and help the algorithm escape from local optima.•The experimental studies compared with 12 state-of-the-art algorithms demonstrate that the proposed algorithm is effective and promising.
The box-covering method is widely used on measuring the fractal property on complex networks. The problem of finding the minimum number of boxes to tile a network is known as a NP-hard problem. Many algorithms have been proposed to solve this problem. All the current box-covering algorithms regard the box number minimization as the only objective. However, the fractal modularity of the network partition divided by the box-covering method, has been proved to be strongly related to the information transportation in complex networks. Maximizing the fractal modularity is also important in the box-covering method, which can be divided into two objectives: maximization of ratio association and minimization of ratio cut. In this paper, to solve the dilemma of minimizing the box number and maximizing the fractal modularity at the same time, a multiobjective discrete particle swarm optimization box-covering (MOPSOBC) algorithm is proposed. The MOPSOBC algorithm applies the decomposition approach on the two objectives to approximate the Pareto front. The proposed MOPSOBC algorithm has been applied to six benchmark networks and compared with the state-of-the-art algorithms, including two classical box-covering algorithms, four single objective optimization algorithms and six multiobjective optimization algorithms. The experimental results show that the MOPSOBC algorithm can get similar box numbers with the current best algorithm, and it outperforms the state-of-the-art algorithms on the fractal modularity and normalized mutual information. |
| Author | Rao, Qi Wu, Hongrun Gong, Maoguo Kuang, Li Li, Yuanxiang Wang, Feng |
| Author_xml | – sequence: 1 givenname: Hongrun surname: Wu fullname: Wu, Hongrun organization: State Key Laboratory of Software Engineering, Computer School, Wuhan University, Wuhan 430072, China – sequence: 2 givenname: Li surname: Kuang fullname: Kuang, Li organization: State Key Laboratory of Software Engineering, Computer School, Wuhan University, Wuhan 430072, China – sequence: 3 givenname: Feng surname: Wang fullname: Wang, Feng email: fengwang@whu.edu.cn organization: State Key Laboratory of Software Engineering, Computer School, Wuhan University, Wuhan 430072, China – sequence: 4 givenname: Qi surname: Rao fullname: Rao, Qi organization: Institute of Computational Linguistics, Peking University, Beijing 100871, China – sequence: 5 givenname: Maoguo surname: Gong fullname: Gong, Maoguo organization: Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an 710071, China – sequence: 6 givenname: Yuanxiang surname: Li fullname: Li, Yuanxiang organization: State Key Laboratory of Software Engineering, Computer School, Wuhan University, Wuhan 430072, China |
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| Cites_doi | 10.1103/PhysRevE.89.042809 10.1126/science.156.3775.636 10.1103/PhysRevLett.104.025701 10.1109/TEVC.2005.857610 10.1016/j.physa.2006.10.025 10.1038/30918 10.1038/srep03049 10.1177/0731684411417198 10.1137/S003614450342480 10.1063/1.2732162 10.1109/TIFS.2016.2590944 10.1109/TEVC.2007.900837 10.1016/j.knosys.2016.10.016 10.1073/pnas.122653799 10.1073/pnas.1106612109 10.1016/S0141-9331(02)00053-4 10.1002/sec.1582 10.1109/TEVC.2011.2161090 10.1007/s00265-003-0651-y 10.1007/s11721-008-0022-4 10.1016/j.cie.2006.09.002 10.1109/TEVC.2004.826069 10.1038/nature03248 10.1109/CC.2016.7559082 10.1088/1367-2630/9/6/177 10.1016/j.physa.2012.03.021 10.1038/nphys266 10.1103/PhysRevLett.96.018701 10.1016/j.asoc.2014.08.019 10.1007/s11432-014-5115-7 10.1103/RevModPhys.74.47 10.1016/j.asoc.2011.10.005 10.1109/TEVC.2013.2260862 10.1126/science.1073374 10.1038/35036627 10.1103/PhysRevE.86.016707 10.1162/106365600568167 10.1109/TEVC.2004.826067 10.1109/4235.797969 10.1109/TEVC.2007.892759 10.1103/PhysRevE.69.026113 10.1038/35011540 10.1109/TEVC.2009.2030331 10.1088/1742-5468/2008/10/P10008 10.1073/pnas.0601602103 10.1073/pnas.0700250104 10.1103/PhysRevE.65.036123 10.1140/epjb/e2004-00125-x 10.1109/CC.2016.7559071 10.1126/science.286.5439.509 10.1109/4235.996017 10.1109/TSE.2010.26 |
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| Keywords | Box-covering algorithm Fractal dimension Particle swarm optimization Multiobjective optimization |
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| References | Liu, Cai, Shen, Fu, Liu, Linge (bib0150) 2016; 9 Zitzler, Thiele (bib0345) 1999; 3 Kennedy (bib0095) 2010 Newman (bib0180) 2003; 45 Chen, Zhang, Chung, Zhong, Wu, Shi (bib0030) 2010; 14 Peng, Chen, Guo (bib0200) 2010 Goldberg, Richardson (bib0065) 1987 Salman, Ahmad, Al-Madani (bib0240) 2002; 26 Gallos, Song, Havlin, Makse (bib0050) 2007; 104 Kim, Goh, Kahng, Kim (bib0105) 2007; 9 Pizzuti (bib0205) 2008 Lusseau, Schneider, Boisseau, Haase, Slooten, Dawson (bib0165) 2003; 54 Réka Albert (bib0230) 2002; 74 Bandyopadhyay, Saha, Maulik, Deb (bib0020) 2008; 12 Deb, Pratap, Agarwal, Meyarivan (bib0040) 2002; 6 Knowles, Corne (bib0115) 2000; 8 Mandelbrot (bib0170) 1967; 156 Newman, Girvan (bib0190) 2004; 69 Blondel, Guillaume, Lambiotte, Lefebvre (bib0025) 2008; 10 Song, Havlin, Makse (bib0265) 2005; 433 Kuang, Zhao, Wang, Li, Yu, Li (bib0135) 2014 Gong, Cai, Chen, Ma (bib0070) 2014; 18 Jeong, Tombor, Albert, Oltvai, Barabási (bib0090) 2000; 407 Kong, Zhang, Ye (bib0120) 2016; 115 Ravasz, Somera, Mongru, Oltvai, Barabási (bib0225) 2002; 297 Michael, David (bib0175) 1979 Sun, Zhao (bib0275) 2014; 89 Praditwong, Harman, Yao (bib0215) 2011; 37 Zitzler, Thiele (bib0340) 1998 Angus, Woodward (bib0015) 2009; 3 Girvan, Newman (bib0055) 2002; 99 Qu, Keeney, Robitzsch, Wang (bib0325) 2016; 13 Xia, Wang, Zhang, Qin, Sun, Ren (bib0300) 2016; 11 Locci, Concas, Tonelli, Turnu (bib0160) 2010; 7 Angelini, Boccaletti, Marinazzo, Pellicoro, Stramaglia (bib0010) 2007; 17 Kuang, Zheng, Li, Li, Sun (bib0140) 2015; 58 Zitzler, Laumanns, Thiele (bib0335) 2002 Gallos, Makse, Sigman (bib0045) 2012; 109 Watts, Strogatz (bib0285) 1998; 393 Wei, Liu, Zhang, Hu, Deng, Mahadevan (bib0290) 2013; 3 Krebs (bib0125) 2008 Song, Gallos, Havlin, Makse (bib0260) 2007; 3 Xue, Jiang, Zhao, Ma (bib0305) 2017 Kennedy, Eberhart (bib0100) 1997 Klemm, Eguiluz (bib0110) 2002; 65 Palermo, Silvano, Zaccaria (bib0195) 2008 Rozenfeld, Song, Makse (bib0235) 2010; 104 Zhang, Hu, Lan, Mahadevan, Deng (bib0310) 2014; 25 Goh, Salvi, Kahng, Kim (bib0060) 2006; 96 Newman (bib0185) 2006; 103 Zhou, Jiang, Sornette (bib0330) 2007; 375 Albert-László Barabási (bib0005) 1999; 286 Hartwell, Hopfield, Leibler, Murray (bib0085) 1999; 402 Coello, Pulido, Lechuga (bib0035) 2004; 8 Song, Havlin, Makse (bib0270) 2006; 2 Zhang, Sun, Wang (bib0320) 2016; 13 Kuang, Wang, Li, Mao, Lin, Yu (bib0130) 2015 Rao, Lakshmi (bib0220) 2011; 30 Liu, Gong, Sun, Jin (bib0155) 2017; PP Liang, Qin, Suganthan, Baskar (bib0145) 2006; 10 Gong, Fu, Jiao, Du (bib0075) 2011; 84 Wu, Huberman (bib0295) 2004; 38 Gong, Ma, Zhang, Jiao (bib0080) 2012; 391 Zhang, Li (bib0315) 2007; 11 Sha, Hsu (bib0250) 2006; 51 Shi, Yan, Cai, Wu (bib0255) 2012; 12 Pizzuti (bib0210) 2012; 16 Schneider, Kesselring, Andrade, Herrmann (bib0245) 2012; 86 Van den Bergh, Engelbrecht (bib0280) 2004; 8 Gong (10.1016/j.asoc.2017.07.034_bib0080) 2012; 391 Salman (10.1016/j.asoc.2017.07.034_bib0240) 2002; 26 Zhang (10.1016/j.asoc.2017.07.034_bib0315) 2007; 11 Wu (10.1016/j.asoc.2017.07.034_bib0295) 2004; 38 Zitzler (10.1016/j.asoc.2017.07.034_bib0335) 2002 Schneider (10.1016/j.asoc.2017.07.034_bib0245) 2012; 86 Kuang (10.1016/j.asoc.2017.07.034_bib0140) 2015; 58 Hartwell (10.1016/j.asoc.2017.07.034_bib0085) 1999; 402 Mandelbrot (10.1016/j.asoc.2017.07.034_bib0170) 1967; 156 Palermo (10.1016/j.asoc.2017.07.034_bib0195) 2008 Xue (10.1016/j.asoc.2017.07.034_bib0305) 2017 Albert-László Barabási (10.1016/j.asoc.2017.07.034_bib0005) 1999; 286 Réka Albert (10.1016/j.asoc.2017.07.034_bib0230) 2002; 74 Michael (10.1016/j.asoc.2017.07.034_bib0175) 1979 Kennedy (10.1016/j.asoc.2017.07.034_bib0095) 2010 Newman (10.1016/j.asoc.2017.07.034_bib0185) 2006; 103 Ravasz (10.1016/j.asoc.2017.07.034_bib0225) 2002; 297 Kuang (10.1016/j.asoc.2017.07.034_bib0135) 2014 Coello (10.1016/j.asoc.2017.07.034_bib0035) 2004; 8 Pizzuti (10.1016/j.asoc.2017.07.034_bib0205) 2008 Zhang (10.1016/j.asoc.2017.07.034_bib0310) 2014; 25 Gallos (10.1016/j.asoc.2017.07.034_bib0045) 2012; 109 Rao (10.1016/j.asoc.2017.07.034_bib0220) 2011; 30 Van den Bergh (10.1016/j.asoc.2017.07.034_bib0280) 2004; 8 Jeong (10.1016/j.asoc.2017.07.034_bib0090) 2000; 407 Lusseau (10.1016/j.asoc.2017.07.034_bib0165) 2003; 54 Peng (10.1016/j.asoc.2017.07.034_bib0200) 2010 Girvan (10.1016/j.asoc.2017.07.034_bib0055) 2002; 99 Locci (10.1016/j.asoc.2017.07.034_bib0160) 2010; 7 Shi (10.1016/j.asoc.2017.07.034_bib0255) 2012; 12 Wei (10.1016/j.asoc.2017.07.034_bib0290) 2013; 3 Kong (10.1016/j.asoc.2017.07.034_bib0120) 2016; 115 Kennedy (10.1016/j.asoc.2017.07.034_bib0100) 1997 Chen (10.1016/j.asoc.2017.07.034_bib0030) 2010; 14 Deb (10.1016/j.asoc.2017.07.034_bib0040) 2002; 6 Song (10.1016/j.asoc.2017.07.034_bib0270) 2006; 2 Liu (10.1016/j.asoc.2017.07.034_bib0150) 2016; 9 Kim (10.1016/j.asoc.2017.07.034_bib0105) 2007; 9 Zitzler (10.1016/j.asoc.2017.07.034_bib0340) 1998 Goh (10.1016/j.asoc.2017.07.034_bib0060) 2006; 96 Kuang (10.1016/j.asoc.2017.07.034_bib0130) 2015 Klemm (10.1016/j.asoc.2017.07.034_bib0110) 2002; 65 Angus (10.1016/j.asoc.2017.07.034_bib0015) 2009; 3 Newman (10.1016/j.asoc.2017.07.034_bib0180) 2003; 45 Zhang (10.1016/j.asoc.2017.07.034_bib0320) 2016; 13 Bandyopadhyay (10.1016/j.asoc.2017.07.034_bib0020) 2008; 12 Qu (10.1016/j.asoc.2017.07.034_bib0325) 2016; 13 Knowles (10.1016/j.asoc.2017.07.034_bib0115) 2000; 8 Sun (10.1016/j.asoc.2017.07.034_bib0275) 2014; 89 Angelini (10.1016/j.asoc.2017.07.034_bib0010) 2007; 17 Krebs (10.1016/j.asoc.2017.07.034_bib0125) 2008 Praditwong (10.1016/j.asoc.2017.07.034_bib0215) 2011; 37 Watts (10.1016/j.asoc.2017.07.034_bib0285) 1998; 393 Gallos (10.1016/j.asoc.2017.07.034_bib0050) 2007; 104 Xia (10.1016/j.asoc.2017.07.034_bib0300) 2016; 11 Gong (10.1016/j.asoc.2017.07.034_bib0075) 2011; 84 Zhou (10.1016/j.asoc.2017.07.034_bib0330) 2007; 375 Zitzler (10.1016/j.asoc.2017.07.034_bib0345) 1999; 3 Liu (10.1016/j.asoc.2017.07.034_bib0155) 2017; PP Blondel (10.1016/j.asoc.2017.07.034_bib0025) 2008; 10 Pizzuti (10.1016/j.asoc.2017.07.034_bib0210) 2012; 16 Newman (10.1016/j.asoc.2017.07.034_bib0190) 2004; 69 Gong (10.1016/j.asoc.2017.07.034_bib0070) 2014; 18 Liang (10.1016/j.asoc.2017.07.034_bib0145) 2006; 10 Song (10.1016/j.asoc.2017.07.034_bib0260) 2007; 3 Sha (10.1016/j.asoc.2017.07.034_bib0250) 2006; 51 Goldberg (10.1016/j.asoc.2017.07.034_bib0065) 1987 Song (10.1016/j.asoc.2017.07.034_bib0265) 2005; 433 Rozenfeld (10.1016/j.asoc.2017.07.034_bib0235) 2010; 104 |
| References_xml | – volume: 51 start-page: 791 year: 2006 end-page: 808 ident: bib0250 article-title: A hybrid particle swarm optimization for job shop scheduling problem publication-title: Comput. Ind. Eng. – volume: 10 start-page: P10008 year: 2008 ident: bib0025 article-title: Fast unfolding of communities in large networks publication-title: J. Stat. Mech. Theory Exp. – volume: 3 start-page: 257 year: 1999 end-page: 271 ident: bib0345 article-title: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach publication-title: IEEE Trans. Evol. Comput. – start-page: 41 year: 1987 end-page: 49 ident: bib0065 article-title: Genetic algorithms with sharing for multimodal function optimization publication-title: Proceedings of the Second International Conference on Genetic Algorithms – start-page: 693 year: 2014 end-page: 699 ident: bib0135 article-title: A differential evolution box-covering algorithm for fractal dimension on complex networks publication-title: Proceedings of 2014 IEEE Congress on Evolutionary Computation – start-page: 1081 year: 2008 end-page: 1090 ident: bib0205 article-title: Ga-net: a genetic algorithm for community detection in social networks publication-title: Parallel Problem Solving From Nature – PPSN X, International Conference Dortmund – volume: 103 start-page: 8577 year: 2006 end-page: 8582 ident: bib0185 article-title: Modularity and community structure in networks publication-title: Proc. Natl. Acad. Sci. U.S.A. – volume: PP start-page: 1 year: 2017 end-page: 14 ident: bib0155 article-title: A many-objective evolutionary algorithm using a one-by-one selection strategy publication-title: IEEE Trans. Cybernet. – volume: 9 start-page: 177 year: 2007 ident: bib0105 article-title: Fractality and self-similarity in scale-free networks publication-title: N. J. Phys. – volume: 99 start-page: 7821 year: 2002 end-page: 7826 ident: bib0055 article-title: Community structure in social and biological networks publication-title: Proc. Natl. Acad. Sci. U.S.A. – volume: 58 start-page: 12111 year: 2015 ident: bib0140 article-title: A fractal and scale-free model of complex networks with hub attraction behaviors publication-title: Sci. China Inform. Sci. – volume: 3 start-page: 69 year: 2009 end-page: 85 ident: bib0015 article-title: Multiple objective ant colony optimisation publication-title: Swarm Intell. – volume: 13 start-page: 108 year: 2016 end-page: 116 ident: bib0325 article-title: Multilevel pattern mining architecture for automatic network monitoring in heterogeneous wireless communication networks publication-title: China Commun. – volume: 393 start-page: 440 year: 1998 end-page: 442 ident: bib0285 article-title: Collective dynamics of ‘small-world’ networks publication-title: Nature – start-page: 1 year: 2017 end-page: 18 ident: bib0305 article-title: A self-adaptive artificial bee colony algorithm based on global best for global optimization publication-title: Soft Comput. – volume: 8 start-page: 256 year: 2004 end-page: 279 ident: bib0035 article-title: Handling multiple objectives with particle swarm optimization publication-title: IEEE Trans. Evol. Comput. – start-page: 292 year: 1998 end-page: 301 ident: bib0340 article-title: Multiobjective optimization using evolutionary algorithms – a comparative case study publication-title: International Conference on Parallel Problem Solving from Nature – volume: 14 start-page: 278 year: 2010 end-page: 300 ident: bib0030 article-title: A novel set-based particle swarm optimization method for discrete optimization problems publication-title: IEEE Trans. Evol. Comput. – volume: 26 start-page: 363 year: 2002 end-page: 371 ident: bib0240 article-title: Particle swarm optimization for task assignment problem publication-title: Microprocess. Microsyst. – volume: 286 start-page: 509 year: 1999 end-page: 512 ident: bib0005 article-title: Emergence of scaling in random networks publication-title: Science – volume: 7 start-page: 371 year: 2010 end-page: 380 ident: bib0160 article-title: Three algorithms for analyzing fractal software networks publication-title: WSEAS Trans. Inform. Sci. Appl. – volume: 69 start-page: 026113 year: 2004 ident: bib0190 article-title: Finding and evaluating community structure in networks publication-title: Phys. Rev. E – volume: 89 start-page: 182 year: 2014 end-page: 190 ident: bib0275 article-title: Overlapping-box-covering method for the fractal dimension of complex networks publication-title: Phys. Rev. E – start-page: 4104 year: 1997 end-page: 4108 ident: bib0100 article-title: A discrete binary version of the particle swarm algorithm publication-title: Proceedings of 1997 IEEE International Conference on Systems, Man, and Cybernetics, vol. 5 – volume: 11 start-page: 712 year: 2007 end-page: 731 ident: bib0315 article-title: MOEA/D: a multiobjective evolutionary algorithm based on decomposition publication-title: IEEE Trans. Evol. Comput. – start-page: 641 year: 2008 end-page: 644 ident: bib0195 article-title: Discrete particle swarm optimization for multi-objective design space exploration publication-title: Euromicro Conference on Digital System Design: Architectures, Methods and Tools, Dsd 2008 – volume: 433 start-page: 392 year: 2005 end-page: 395 ident: bib0265 article-title: Self-similarity of complex networks publication-title: Nature – volume: 6 start-page: 182 year: 2002 end-page: 197 ident: bib0040 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: IEEE Trans. Evol. Comput. – volume: 156 start-page: 636 year: 1967 end-page: 638 ident: bib0170 article-title: How long is the coast of Britain publication-title: Science – volume: 12 start-page: 850 year: 2012 end-page: 859 ident: bib0255 article-title: Multi-objective community detection in complex networks publication-title: Appl. Soft Comput. – volume: 3 start-page: 3049 year: 2013 ident: bib0290 article-title: Box-covering algorithm for fractal dimension of weighted networks publication-title: Sci. Rep. – volume: 84 start-page: 4146 year: 2011 end-page: 4152 ident: bib0075 article-title: Memetic algorithm for community detection in networks publication-title: Phys. Rev. E – volume: 37 start-page: 264 year: 2011 end-page: 282 ident: bib0215 article-title: Software module clustering as a multi-objective search problem publication-title: IEEE Trans. Soft. Eng. – volume: 11 start-page: 2594 year: 2016 end-page: 2608 ident: bib0300 article-title: A privacy-preserving and copy-deterrence content-based image retrieval scheme in cloud computing publication-title: IEEE Trans. Inform. Forensics Secur. – volume: 74 start-page: 47 year: 2002 end-page: 97 ident: bib0230 article-title: Statistical mechanics of complex networks publication-title: Rev. Mod. Phys. – volume: 17 year: 2007 ident: bib0010 article-title: Identification of network modules by optimization of ratio association publication-title: Chaos – volume: 86 start-page: 3461 year: 2012 end-page: 3463 ident: bib0245 article-title: Box-covering algorithm for fractal dimension of complex networks publication-title: Phys. Rev. E – volume: 297 start-page: 1551 year: 2002 end-page: 1555 ident: bib0225 article-title: Hierarchical organization of modularity in metabolic networks publication-title: Science – volume: 3 start-page: 297 year: 2007 end-page: 316 ident: bib0260 article-title: How to calculate the fractal dimension of a complex network: the box covering algorithm publication-title: J. Stat. Mech: Theory Exp. – volume: 375 start-page: 741 year: 2007 end-page: 752 ident: bib0330 article-title: Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling publication-title: Physica A – volume: 104 start-page: 358 year: 2010 end-page: 359 ident: bib0235 article-title: Small-world to fractal transition in complex networks: a renormalization group approach publication-title: Phys. Rev. Lett. – volume: 13 start-page: 16 year: 2016 end-page: 23 ident: bib0320 article-title: Efficient algorithm for k-barrier coverage based on integer linear programming publication-title: China Commun. – start-page: 1396 year: 2015 end-page: 1403 ident: bib0130 article-title: A discrete particle swarm optimization box-covering algorithm for fractal dimension on complex networks publication-title: IEEE Congress on Evolutionary Computation, CEC 2015 – volume: 9 start-page: 4002 year: 2016 end-page: 4012 ident: bib0150 article-title: A speculative approach to spatial-temporal efficiency with multi-objective optimization in a heterogeneous cloud environment publication-title: Secur. Commun. Netw. – volume: 8 start-page: 225 year: 2004 end-page: 239 ident: bib0280 article-title: A cooperative approach to particle swarm optimization publication-title: IEEE Trans. Evol. Comput. – volume: 407 start-page: 651 year: 2000 end-page: 654 ident: bib0090 article-title: The large-scale organization of metabolic networks publication-title: Nature – volume: 8 start-page: 149 year: 2000 end-page: 172 ident: bib0115 article-title: Approximating the nondominated front using the Pareto archived evolution strategy publication-title: Evol. Comput. – volume: 54 start-page: 396 year: 2003 end-page: 405 ident: bib0165 article-title: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations publication-title: Behav. Ecol. Sociobiol. – year: 2008 ident: bib0125 article-title: A Network of Books About Recent Us Politics Sold by the Online Bookseller amazon.com – start-page: 760 year: 2010 end-page: 766 ident: bib0095 article-title: Particle swarm optimization publication-title: Encyclopedia of Machine Learning – year: 1979 ident: bib0175 article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness – volume: 25 start-page: 514 year: 2014 end-page: 518 ident: bib0310 article-title: Fuzzy fractal dimension of complex networks publication-title: Appl. Soft Comput. – start-page: 92 year: 2002 end-page: 100 ident: bib0335 article-title: Spea2: improving the strength pareto evolutionary algorithm publication-title: Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems – volume: 391 start-page: 4050 year: 2012 end-page: 4060 ident: bib0080 article-title: Community detection in networks by using multiobjective evolutionary algorithm with decomposition publication-title: Physica A – volume: 45 start-page: 167 year: 2003 end-page: 256 ident: bib0180 article-title: The structure and function of complex networks publication-title: SIAM Rev. – volume: 104 start-page: 7746 year: 2007 end-page: 7751 ident: bib0050 article-title: Scaling theory of transport in complex biological networks publication-title: Proc. Natl. Acad. Sci. U.S.A. – volume: 12 start-page: 269 year: 2008 end-page: 283 ident: bib0020 article-title: A simulated annealing-based multiobjective optimization algorithm: AMOSA publication-title: IEEE Trans. Evol. Comput. – volume: 65 start-page: 036123 year: 2002 ident: bib0110 article-title: Highly clustered scale-free networks publication-title: Phys. Rev. E – volume: 115 start-page: 123 year: 2016 end-page: 132 ident: bib0120 article-title: A belief propagation-based method for task allocation in open and dynamic cloud environments publication-title: Knowl.-Based Syst. – volume: 96 start-page: 018701 year: 2006 ident: bib0060 article-title: Skeleton and fractal scaling in complex networks publication-title: Phys. Rev. Lett. – volume: 10 start-page: 281 year: 2006 end-page: 295 ident: bib0145 article-title: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions publication-title: IEEE Trans. Evol. Comput. – volume: 30 start-page: 1703 year: 2011 end-page: 1727 ident: bib0220 article-title: Discrete hybrid pso algorithm for design of laminate composites with multiple objectives publication-title: J. Reinforced Plast. Compos. – volume: 2 start-page: 275 year: 2006 end-page: 281 ident: bib0270 article-title: Origins of fractality in the growth of complex networks publication-title: Nat. Phys. – volume: 109 start-page: 2825 year: 2012 end-page: 2830 ident: bib0045 article-title: A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks publication-title: Proc. Natl. Acad. Sci. U.S.A. – volume: 402 start-page: C47 year: 1999 end-page: C52 ident: bib0085 article-title: From molecular to modular cell biology publication-title: Nature – volume: 38 start-page: 331 year: 2004 end-page: 338 ident: bib0295 article-title: Finding communities in linear time: a physics approach publication-title: Eur. Phys. J. B – volume: 16 start-page: 418 year: 2012 end-page: 430 ident: bib0210 article-title: A multiobjective genetic algorithm to find communities in complex networks publication-title: IEEE Trans. Evol. Comput. – start-page: 1 year: 2010 end-page: 4 ident: bib0200 article-title: A discrete PSO for partitioning in VLSI circuit publication-title: International Conference on Computational Intelligence and Software Engineering – volume: 18 start-page: 82 year: 2014 end-page: 97 ident: bib0070 article-title: Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition publication-title: IEEE Trans. Evol. Comput. – volume: 89 start-page: 182 issue: 4 year: 2014 ident: 10.1016/j.asoc.2017.07.034_bib0275 article-title: Overlapping-box-covering method for the fractal dimension of complex networks publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.042809 – volume: 156 start-page: 636 issue: 3775 year: 1967 ident: 10.1016/j.asoc.2017.07.034_bib0170 article-title: How long is the coast of Britain publication-title: Science doi: 10.1126/science.156.3775.636 – start-page: 41 year: 1987 ident: 10.1016/j.asoc.2017.07.034_bib0065 article-title: Genetic algorithms with sharing for multimodal function optimization – start-page: 760 year: 2010 ident: 10.1016/j.asoc.2017.07.034_bib0095 article-title: Particle swarm optimization – year: 1979 ident: 10.1016/j.asoc.2017.07.034_bib0175 – start-page: 1081 year: 2008 ident: 10.1016/j.asoc.2017.07.034_bib0205 article-title: Ga-net: a genetic algorithm for community detection in social networks – volume: 104 start-page: 358 issue: 2 year: 2010 ident: 10.1016/j.asoc.2017.07.034_bib0235 article-title: Small-world to fractal transition in complex networks: a renormalization group approach publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.104.025701 – start-page: 641 year: 2008 ident: 10.1016/j.asoc.2017.07.034_bib0195 article-title: Discrete particle swarm optimization for multi-objective design space exploration – volume: 10 start-page: 281 issue: 3 year: 2006 ident: 10.1016/j.asoc.2017.07.034_bib0145 article-title: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2005.857610 – volume: 375 start-page: 741 issue: 2 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0330 article-title: Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling publication-title: Physica A doi: 10.1016/j.physa.2006.10.025 – volume: 393 start-page: 440 issue: 6684 year: 1998 ident: 10.1016/j.asoc.2017.07.034_bib0285 article-title: Collective dynamics of ‘small-world’ networks publication-title: Nature doi: 10.1038/30918 – volume: 3 start-page: 3049 year: 2013 ident: 10.1016/j.asoc.2017.07.034_bib0290 article-title: Box-covering algorithm for fractal dimension of weighted networks publication-title: Sci. Rep. doi: 10.1038/srep03049 – volume: 30 start-page: 1703 issue: 20 year: 2011 ident: 10.1016/j.asoc.2017.07.034_bib0220 article-title: Discrete hybrid pso algorithm for design of laminate composites with multiple objectives publication-title: J. Reinforced Plast. Compos. doi: 10.1177/0731684411417198 – volume: 45 start-page: 167 issue: 2 year: 2003 ident: 10.1016/j.asoc.2017.07.034_bib0180 article-title: The structure and function of complex networks publication-title: SIAM Rev. doi: 10.1137/S003614450342480 – volume: 84 start-page: 4146 issue: 84 year: 2011 ident: 10.1016/j.asoc.2017.07.034_bib0075 article-title: Memetic algorithm for community detection in networks publication-title: Phys. Rev. E – volume: PP start-page: 1 issue: 99 year: 2017 ident: 10.1016/j.asoc.2017.07.034_bib0155 article-title: A many-objective evolutionary algorithm using a one-by-one selection strategy publication-title: IEEE Trans. Cybernet. – volume: 17 issue: 2 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0010 article-title: Identification of network modules by optimization of ratio association publication-title: Chaos doi: 10.1063/1.2732162 – volume: 11 start-page: 2594 issue: 11 year: 2016 ident: 10.1016/j.asoc.2017.07.034_bib0300 article-title: A privacy-preserving and copy-deterrence content-based image retrieval scheme in cloud computing publication-title: IEEE Trans. Inform. Forensics Secur. doi: 10.1109/TIFS.2016.2590944 – volume: 12 start-page: 269 issue: 3 year: 2008 ident: 10.1016/j.asoc.2017.07.034_bib0020 article-title: A simulated annealing-based multiobjective optimization algorithm: AMOSA publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2007.900837 – volume: 115 start-page: 123 year: 2016 ident: 10.1016/j.asoc.2017.07.034_bib0120 article-title: A belief propagation-based method for task allocation in open and dynamic cloud environments publication-title: Knowl.-Based Syst. doi: 10.1016/j.knosys.2016.10.016 – volume: 99 start-page: 7821 issue: 12 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0055 article-title: Community structure in social and biological networks publication-title: Proc. Natl. Acad. Sci. U.S.A. doi: 10.1073/pnas.122653799 – volume: 109 start-page: 2825 issue: 8 year: 2012 ident: 10.1016/j.asoc.2017.07.034_bib0045 article-title: A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks publication-title: Proc. Natl. Acad. Sci. U.S.A. doi: 10.1073/pnas.1106612109 – volume: 26 start-page: 363 issue: 8 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0240 article-title: Particle swarm optimization for task assignment problem publication-title: Microprocess. Microsyst. doi: 10.1016/S0141-9331(02)00053-4 – start-page: 693 year: 2014 ident: 10.1016/j.asoc.2017.07.034_bib0135 article-title: A differential evolution box-covering algorithm for fractal dimension on complex networks – volume: 9 start-page: 4002 issue: 17 year: 2016 ident: 10.1016/j.asoc.2017.07.034_bib0150 article-title: A speculative approach to spatial-temporal efficiency with multi-objective optimization in a heterogeneous cloud environment publication-title: Secur. Commun. Netw. doi: 10.1002/sec.1582 – volume: 16 start-page: 418 issue: 3 year: 2012 ident: 10.1016/j.asoc.2017.07.034_bib0210 article-title: A multiobjective genetic algorithm to find communities in complex networks publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2011.2161090 – volume: 54 start-page: 396 issue: 4 year: 2003 ident: 10.1016/j.asoc.2017.07.034_bib0165 article-title: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations publication-title: Behav. Ecol. Sociobiol. doi: 10.1007/s00265-003-0651-y – volume: 3 start-page: 69 issue: 1 year: 2009 ident: 10.1016/j.asoc.2017.07.034_bib0015 article-title: Multiple objective ant colony optimisation publication-title: Swarm Intell. doi: 10.1007/s11721-008-0022-4 – volume: 51 start-page: 791 issue: 4 year: 2006 ident: 10.1016/j.asoc.2017.07.034_bib0250 article-title: A hybrid particle swarm optimization for job shop scheduling problem publication-title: Comput. Ind. Eng. doi: 10.1016/j.cie.2006.09.002 – volume: 8 start-page: 225 issue: 3 year: 2004 ident: 10.1016/j.asoc.2017.07.034_bib0280 article-title: A cooperative approach to particle swarm optimization publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2004.826069 – volume: 433 start-page: 392 issue: 7024 year: 2005 ident: 10.1016/j.asoc.2017.07.034_bib0265 article-title: Self-similarity of complex networks publication-title: Nature doi: 10.1038/nature03248 – volume: 13 start-page: 108 issue: 7 year: 2016 ident: 10.1016/j.asoc.2017.07.034_bib0325 article-title: Multilevel pattern mining architecture for automatic network monitoring in heterogeneous wireless communication networks publication-title: China Commun. doi: 10.1109/CC.2016.7559082 – volume: 9 start-page: 177 issue: 6 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0105 article-title: Fractality and self-similarity in scale-free networks publication-title: N. J. Phys. doi: 10.1088/1367-2630/9/6/177 – volume: 391 start-page: 4050 issue: 15 year: 2012 ident: 10.1016/j.asoc.2017.07.034_bib0080 article-title: Community detection in networks by using multiobjective evolutionary algorithm with decomposition publication-title: Physica A doi: 10.1016/j.physa.2012.03.021 – start-page: 1396 year: 2015 ident: 10.1016/j.asoc.2017.07.034_bib0130 article-title: A discrete particle swarm optimization box-covering algorithm for fractal dimension on complex networks – volume: 2 start-page: 275 issue: 4 year: 2006 ident: 10.1016/j.asoc.2017.07.034_bib0270 article-title: Origins of fractality in the growth of complex networks publication-title: Nat. Phys. doi: 10.1038/nphys266 – volume: 96 start-page: 018701 issue: 1 year: 2006 ident: 10.1016/j.asoc.2017.07.034_bib0060 article-title: Skeleton and fractal scaling in complex networks publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.96.018701 – start-page: 292 year: 1998 ident: 10.1016/j.asoc.2017.07.034_bib0340 article-title: Multiobjective optimization using evolutionary algorithms – a comparative case study – volume: 25 start-page: 514 issue: C year: 2014 ident: 10.1016/j.asoc.2017.07.034_bib0310 article-title: Fuzzy fractal dimension of complex networks publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2014.08.019 – volume: 58 start-page: 12111 issue: 1 year: 2015 ident: 10.1016/j.asoc.2017.07.034_bib0140 article-title: A fractal and scale-free model of complex networks with hub attraction behaviors publication-title: Sci. China Inform. Sci. doi: 10.1007/s11432-014-5115-7 – volume: 74 start-page: 47 issue: 1 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0230 article-title: Statistical mechanics of complex networks publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.74.47 – volume: 12 start-page: 850 issue: 2 year: 2012 ident: 10.1016/j.asoc.2017.07.034_bib0255 article-title: Multi-objective community detection in complex networks publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2011.10.005 – volume: 18 start-page: 82 issue: 1 year: 2014 ident: 10.1016/j.asoc.2017.07.034_bib0070 article-title: Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2013.2260862 – volume: 297 start-page: 1551 issue: 5586 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0225 article-title: Hierarchical organization of modularity in metabolic networks publication-title: Science doi: 10.1126/science.1073374 – start-page: 1 year: 2010 ident: 10.1016/j.asoc.2017.07.034_bib0200 article-title: A discrete PSO for partitioning in VLSI circuit – volume: 407 start-page: 651 issue: 6804 year: 2000 ident: 10.1016/j.asoc.2017.07.034_bib0090 article-title: The large-scale organization of metabolic networks publication-title: Nature doi: 10.1038/35036627 – volume: 86 start-page: 3461 issue: 1 year: 2012 ident: 10.1016/j.asoc.2017.07.034_bib0245 article-title: Box-covering algorithm for fractal dimension of complex networks publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.86.016707 – volume: 3 start-page: 297 issue: 03 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0260 article-title: How to calculate the fractal dimension of a complex network: the box covering algorithm publication-title: J. Stat. Mech: Theory Exp. – volume: 8 start-page: 149 issue: 2 year: 2000 ident: 10.1016/j.asoc.2017.07.034_bib0115 article-title: Approximating the nondominated front using the Pareto archived evolution strategy publication-title: Evol. Comput. doi: 10.1162/106365600568167 – start-page: 92 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0335 article-title: Spea2: improving the strength pareto evolutionary algorithm – volume: 8 start-page: 256 issue: 3 year: 2004 ident: 10.1016/j.asoc.2017.07.034_bib0035 article-title: Handling multiple objectives with particle swarm optimization publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2004.826067 – year: 2008 ident: 10.1016/j.asoc.2017.07.034_bib0125 – volume: 3 start-page: 257 issue: 4 year: 1999 ident: 10.1016/j.asoc.2017.07.034_bib0345 article-title: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/4235.797969 – volume: 11 start-page: 712 issue: 6 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0315 article-title: MOEA/D: a multiobjective evolutionary algorithm based on decomposition publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2007.892759 – volume: 69 start-page: 026113 issue: 2 year: 2004 ident: 10.1016/j.asoc.2017.07.034_bib0190 article-title: Finding and evaluating community structure in networks publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.69.026113 – volume: 402 start-page: C47 year: 1999 ident: 10.1016/j.asoc.2017.07.034_bib0085 article-title: From molecular to modular cell biology publication-title: Nature doi: 10.1038/35011540 – volume: 14 start-page: 278 issue: 2 year: 2010 ident: 10.1016/j.asoc.2017.07.034_bib0030 article-title: A novel set-based particle swarm optimization method for discrete optimization problems publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/TEVC.2009.2030331 – start-page: 1 year: 2017 ident: 10.1016/j.asoc.2017.07.034_bib0305 article-title: A self-adaptive artificial bee colony algorithm based on global best for global optimization publication-title: Soft Comput. – volume: 10 start-page: P10008 year: 2008 ident: 10.1016/j.asoc.2017.07.034_bib0025 article-title: Fast unfolding of communities in large networks publication-title: J. Stat. Mech. Theory Exp. doi: 10.1088/1742-5468/2008/10/P10008 – volume: 103 start-page: 8577 issue: 23 year: 2006 ident: 10.1016/j.asoc.2017.07.034_bib0185 article-title: Modularity and community structure in networks publication-title: Proc. Natl. Acad. Sci. U.S.A. doi: 10.1073/pnas.0601602103 – volume: 7 start-page: 371 issue: 3 year: 2010 ident: 10.1016/j.asoc.2017.07.034_bib0160 article-title: Three algorithms for analyzing fractal software networks publication-title: WSEAS Trans. Inform. Sci. Appl. – volume: 104 start-page: 7746 issue: 19 year: 2007 ident: 10.1016/j.asoc.2017.07.034_bib0050 article-title: Scaling theory of transport in complex biological networks publication-title: Proc. Natl. Acad. Sci. U.S.A. doi: 10.1073/pnas.0700250104 – volume: 65 start-page: 036123 issue: 3 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0110 article-title: Highly clustered scale-free networks publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.65.036123 – start-page: 4104 year: 1997 ident: 10.1016/j.asoc.2017.07.034_bib0100 article-title: A discrete binary version of the particle swarm algorithm – volume: 38 start-page: 331 issue: 2 year: 2004 ident: 10.1016/j.asoc.2017.07.034_bib0295 article-title: Finding communities in linear time: a physics approach publication-title: Eur. Phys. J. B doi: 10.1140/epjb/e2004-00125-x – volume: 13 start-page: 16 issue: 7 year: 2016 ident: 10.1016/j.asoc.2017.07.034_bib0320 article-title: Efficient algorithm for k-barrier coverage based on integer linear programming publication-title: China Commun. doi: 10.1109/CC.2016.7559071 – volume: 286 start-page: 509 issue: 5439 year: 1999 ident: 10.1016/j.asoc.2017.07.034_bib0005 article-title: Emergence of scaling in random networks publication-title: Science doi: 10.1126/science.286.5439.509 – volume: 6 start-page: 182 issue: 2 year: 2002 ident: 10.1016/j.asoc.2017.07.034_bib0040 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: IEEE Trans. Evol. Comput. doi: 10.1109/4235.996017 – volume: 37 start-page: 264 issue: 2 year: 2011 ident: 10.1016/j.asoc.2017.07.034_bib0215 article-title: Software module clustering as a multi-objective search problem publication-title: IEEE Trans. Soft. Eng. doi: 10.1109/TSE.2010.26 |
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