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A novel discrete ICO algorithm for influence maximization in complex networks

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Abstract

It is axiomatic that influence maximization is one of the major issues of the Internet today. In this paper a novel specialized metaheuristic algorithm is proposed to efficiently deal with it. The purpose of influence maximization is to select a subset of seed nodes in the network in order to influence other nodes maximally. The greedy methods present good results for influence maximization, but these algorithms involve very high computational time. Unlike greedy algorithms, meta-heuristic algorithms have acceptable efficiency. The ICO algorithm is just recently proposed as an ensign of meta-heuristic algorithms to solve continuous optimization problems in 2022. In this paper, a discrete version of ICO, called DICO, is proposed. The contribution of the proposed method is to present a new intelligent operator based on the nodes’ degree and logistic mapping for initialization of solutions. In addition, novel approaches are proposed to reproduce each parent discretely. Another innovation of the proposed method is to present a new local search operator based on the network topology. In this operator, a tabu list is suggested to decrease the selection probability of nodes influenced by those nodes selected previously. The proposed method is evaluated on 6 real- world networks, and it is compared to the state-of-the-art and conventional methods. The evaluation results prove that the proposed method has the higher influence than most of other methods. Also, it has an acceptable performance in terms of computational time making it prominent in comparison with existing methods.

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Notes

  1. http://networkrepository.com/ca-netscience.php.

  2. https://www.cc.gatech.edu/dimacs10/archive/clustering.shtml.

  3. https://snap.stanford.edu/data/ca-GrQc.html.

  4. https://snap.stanford.edu/data/ca-HepTh.html.

  5. https://snap.stanford.edu/data/p2p-Gnutella08.html.

  6. http://networkrepository.com/tech-pgp.php.

References

  1. Kempe D, Kleinberg, J, and Tardos É (2003) Maximizing the spread of influence through a social network,. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, Washington, D.C. [Online]. https://doi.org/10.1145/956750.956769

  2. Chen W, Lakshmanan LVS, Castillo C (2013) Information and influence propagation in social networks. Synth Lect Data Manag 5(4):1–177. https://doi.org/10.2200/S00527ED1V01Y201308DTM037

    Article  Google Scholar 

  3. Goldenberg J, Libai B, Muller E (2001) Talk of the network: a complex systems look at the underlying process of word-of-mouth. Market Lett 12(3):211–223

    Article  Google Scholar 

  4. Leskovec J, Adamic LA, Huberman BA (2007) The dynamics of viral marketing. ACM Trans Web. https://doi.org/10.1145/1232722.1232727

    Article  Google Scholar 

  5. Wu P, Pan L (2017) Scalable influence blocking maximization in social networks under competitive independent cascade models. Comput Netw 123:38–50. https://doi.org/10.1016/j.comnet.2017.05.004

    Article  Google Scholar 

  6. Ye M, Liu X, and Lee W-C (2012) Exploring social influence for recommendation: a generative model approach. In: Proceedings of the 35th international ACM SIGIR conference on research and development in information retrieval, Portland, Oregon, USA [Online]. https://doi.org/10.1145/2348283.2348373

  7. Song X, Tseng B, Lin C-Y, Sun M-T (2006) Personalized recommendation driven by information flow. In: Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval, pp 509–516

  8. Sahargahi V, Majidnezhad V, Afshord ST, Jafari Y (2022) An intelligent chaotic clonal optimizer. Appl Soft Comput 115:108126

    Article  Google Scholar 

  9. Ali IM, Essam D, Kasmarik K (2019) A novel differential evolution mapping technique for generic combinatorial optimization problems. Appl Soft Comput 80:297–309

    Article  Google Scholar 

  10. Feng Z-K, Niu W-J, Liu S (2021) Cooperation search algorithm: a novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems. Appl Soft Comput 98:106734

    Article  Google Scholar 

  11. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190

    Article  Google Scholar 

  12. Asef F, Majidnezhad V, Feizi-Derakhshi M-R, Parsa S (2021) Heat transfer relation-based optimization algorithm (HTOA). Soft Comput 25(13):8129–8158

    Article  Google Scholar 

  13. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    Article  MathSciNet  MATH  Google Scholar 

  14. Kivi ME, Majidnezhad V (2021) A novel swarm intelligence algorithm inspired by the grazing of sheep. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02809-y

    Article  Google Scholar 

  15. Chu X et al (2020) An artificial bee colony algorithm with adaptive heterogeneous competition for global optimization problems. Appl Soft Comput 93:106391

    Article  Google Scholar 

  16. Kumar N, Singh N, Vidyarthi DP (2021) Artificial lizard search optimization (ALSO): a novel nature-inspired meta-heuristic algorithm. Soft Comput 25(8):6179–6201

    Article  Google Scholar 

  17. Bogar E, Beyhan S (2020) Adolescent identity search algorithm (AISA): a novel metaheuristic approach for solving optimization problems. Appl Soft Comput 95:106503

    Article  Google Scholar 

  18. Zhao S, Zhang T, Ma S, Chen M (2022) Dandelion Optimizer: a nature-inspired metaheuristic algorithm for engineering applications. Eng Appl Artif Intell 114:105075

    Article  Google Scholar 

  19. Zhang P, Du J, Wang L, Fei M, Yang T, Pardalos PM (2022) A human learning optimization algorithm with reasoning learning. Appl Soft Comput 122:108816

    Article  Google Scholar 

  20. Meng Z, Li G, Wang X, Sait S, Yildiz A (2012) A comparative study of metaheuristic algorithms for reliability-based design optimization problems. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-020-09443-z

    Article  Google Scholar 

  21. Gupta S, Abderazek H, Yłldłz BS, Yildiz AR, Mirjalili S, Sait SM (2021) Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems. Expert Syst Appl 183:115351

    Article  Google Scholar 

  22. Yłldłz BS, Pholdee N, Bureerat S, Erdaş MU, Yłldłz AR, Sait SM (2021) Comparision of the political optimization algorithm, the Archimedes optimization algorithm and the Levy flight algorithm for design optimization in industry. Mater Test 63(4):356–359

    Article  Google Scholar 

  23. Yłldłz BS, Patel V, Pholdee N, Sait SM, Bureerat S, Yłldłz AR (2021) Conceptual comparison of the ecogeography-based algorithm, equilibrium algorithm, marine predators algorithm and slime mold algorithm for optimal product design. Mater Test 63(4):336–340

    Article  Google Scholar 

  24. Panagant N, Pholdee N, Bureerat S, Yildiz AR, Mirjalili S (2021) A comparative study of recent multi-objective metaheuristics for solving constrained Truss optimisation problems. Arch Comput Methods Eng 28(5):4031–4047

    Article  Google Scholar 

  25. Zhang J, Gao Z, Li S, Zhao J, Song W (2022) Improved intelligent clonal optimizer based on adaptive parameter strategy. Math Biosci Eng 19(10):10275–10315

    Article  MATH  Google Scholar 

  26. Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, and Glance N (2007) Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, San Jose, California, USA [Online]. https://doi.org/10.1145/1281192.1281239

  27. Chen W, Wang Y, and Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, Paris, France [Online]. https://doi.org/10.1145/1557019.1557047

  28. Zhang S, Zeng X, Tang B (2021) RCELF: a residual-based approach for influence maximization problem. Inf Syst 102:101828. https://doi.org/10.1016/j.is.2021.101828

    Article  Google Scholar 

  29. Cui L et al (2017) DDSE: a novel evolutionary algorithm based on degree-descending search strategy for influence maximization in social networks. J Netw Comput Appl 103:119–130. https://doi.org/10.1016/j.jnca.2017.12.003

    Article  Google Scholar 

  30. Jiang Q, Song G, Cong G, Wang Y, Si W, and Xie K (2011) Simulated annealing based influence maximization in social networks. In: Proceedings of the twenty-fifth AAAI conference on artificial intelligence, San Francisco, California

  31. Zareie A, Sheikhahmadi A, Jalili M (2020) Identification of influential users in social network using gray wolf optimization algorithm. Expert Syst Appl 142:112971. https://doi.org/10.1016/j.eswa.2019.112971

    Article  Google Scholar 

  32. Simsek A, Resul KARA (2018) Using swarm intelligence algorithms to detect influential individuals for influence maximization in social networks. Expert Syst Appl 114:224–236. https://doi.org/10.1016/j.eswa.2018.07.038

    Article  Google Scholar 

  33. Bucur D, Iacca G (2016) Influence maximization in social networks with genetic algorithms. In: Squillero G, Burelli P (eds) Applications of evolutionary computation. Springer International Publishing, Cham, pp 379–392

    Chapter  Google Scholar 

  34. Tsai C-W, Liu S-J (2019) SEIM: search economics for influence maximization in online social networks. Future Gener Comput Syst 93:1055–1064. https://doi.org/10.1016/j.future.2018.08.033

    Article  Google Scholar 

  35. Cantini R, Marozzo F, Mazza S, Talia D, Trunfio P (2021) A weighted artificial bee colony algorithm for influence maximization. Online Soc Netw Media 26:100167. https://doi.org/10.1016/j.osnem.2021.100167

    Article  Google Scholar 

  36. Zhang K, Du H, Feldman MW (2017) Maximizing influence in a social network: improved results using a genetic algorithm. Phys A Stat Mech Appl 478:20–30. https://doi.org/10.1016/j.physa.2017.02.067

    Article  MATH  Google Scholar 

  37. Wang Y, Zhang Y, Yang F, Li D, Sun X, Ma J (2021) Time-sensitive positive influence maximization in signed social networks. Phys A Stat Mech Appl 584:126353. https://doi.org/10.1016/j.physa.2021.126353

    Article  Google Scholar 

  38. Jabari Lotf J, Abdollahi Azgomi M, Dishabi MRE (2022) An improved influence maximization method for social networks based on genetic algorithm. Phys A Stat Mech Appl 586:126480. https://doi.org/10.1016/j.physa.2021.126480

    Article  Google Scholar 

  39. Qiu L, Tian X, Zhang J, Gu C, Sai S (2021) LIDDE: a differential evolution algorithm based on local-influence-descending search strategy for influence maximization in social networks. J Netw Comput Appl 178:102973. https://doi.org/10.1016/j.jnca.2020.102973

    Article  Google Scholar 

  40. Li W, Zhong K, Wang J, Chen D (2021) A dynamic algorithm based on cohesive entropy for influence maximization in social networks. Expert Syst Appl 169:114207. https://doi.org/10.1016/j.eswa.2020.114207

    Article  Google Scholar 

  41. Xie X, Li J, Sheng Y, Wang W, Yang W (2021) Competitive influence maximization considering inactive nodes and community homophily. Knowl-Based Syst 233:107497. https://doi.org/10.1016/j.knosys.2021.107497

    Article  Google Scholar 

  42. Li W, Li Z, Luvembe AM, Yang C (2021) Influence maximization algorithm based on Gaussian propagation model. Inf Sci 568:386–402. https://doi.org/10.1016/j.ins.2021.04.061

    Article  MathSciNet  Google Scholar 

  43. Nguyen MT, Kim K (2020) Genetic convolutional neural network for intrusion detection systems. Future Gener Comput Syst 113:418–427. https://doi.org/10.1016/j.future.2020.07.042

    Article  Google Scholar 

  44. Iacca G, Konotopska K, Bucur D, Tonda A (2021) An evolutionary framework for maximizing influence propagation in social networks. Softw Impacts 9:100107. https://doi.org/10.1016/j.simpa.2021.100107

    Article  Google Scholar 

  45. Kumar A, Misra RK, Singh D, Mishra S, Das S (2019) The spherical search algorithm for bound-constrained global optimization problems. Appl Soft Comput 85:105734. https://doi.org/10.1016/j.asoc.2019.105734

    Article  Google Scholar 

  46. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  47. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  48. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Article  Google Scholar 

  49. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  50. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  51. Fausto F, Cuevas E, Valdivia A, González A (2017) A global optimization algorithm inspired in the behavior of selfish herds. Biosystems 160:39–55. https://doi.org/10.1016/j.biosystems.2017.07.010

    Article  Google Scholar 

  52. Hashim FA, Houssein EH, Mabrouk MS, Al-Atabany W, Mirjalili S (2019) Henry gas solubility optimization: a novel physics-based algorithm. Future Gener Comput Syst 101:646–667. https://doi.org/10.1016/j.future.2019.07.015

    Article  Google Scholar 

  53. Price K, Storn R, Lampinen JA (2005) Differential evolution, a practical approach to global optimization (natural computing series). Springer-Verlag, Berlin

    MATH  Google Scholar 

  54. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, 27 Nov–1 Dec 1995, vol 4, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968

  55. Elsayed S, Sarker R, and Essam D (2011) GA with a new multi-parent crossover for solving IEEE-CEC2011 competition problems, pp 1034–1040

  56. Tanabe R and Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE congress on evolutionary computation (CEC), 6-11 Jul 2014, pp 1658–1665. https://doi.org/10.1109/CEC.2014.6900380

  57. Awad NH, Ali MZ, and Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In: 2017 IEEE congress on evolutionary computation (CEC), 5–8 Jun 2017, pp 372–379. https://doi.org/10.1109/CEC.2017.7969336

  58. Mohamed AW, Hadi AA, Fattouh AM, and Jambi KM (2017) LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems In: 2017 IEEE congress on evolutionary computation (CEC), 5-8 June 2017, pp. 145–152. https://doi.org/10.1109/CEC.2017.7969307

  59. Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104. https://doi.org/10.1103/PhysRevE.74.036104

    Article  MathSciNet  Google Scholar 

  60. Guimerà R, Danon L, Díaz-Guilera A, Giralt F, Arenas A (2003) Self-similar community structure in a network of human interactions. Phys Rev E 68(6):065103. https://doi.org/10.1103/PhysRevE.68.065103

    Article  Google Scholar 

  61. Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discov Data 10(1145/1217299):1217301. https://doi.org/10.1145/1217299.1217301

    Article  Google Scholar 

  62. Lu F, Zhang W, Shao L, Jiang X, Xu P, Jin H (2017) Scalable influence maximization under independent cascade model. J Netw Comput Appl 86:15–23. https://doi.org/10.1016/j.jnca.2016.10.020

    Article  Google Scholar 

  63. Gregory S (2009) Finding overlapping communities using disjoint community detection algorithms. Springer, Berlin, pp 47–61

    Google Scholar 

  64. Gong M, Yan J, Shen B, Ma L, Cai Q (2016) Influence maximization in social networks based on discrete particle swarm optimization. Inf Sci 367–368:600–614. https://doi.org/10.1016/j.ins.2016.07.012

    Article  Google Scholar 

  65. Brin S, Page L (1998) The anatomy of a large-scale hypertextual Web search engine. Comput Netw ISDN Syst 30(1):107–117. https://doi.org/10.1016/S0169-7552(98)00110-X

    Article  Google Scholar 

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  1. Department of Computer Engineering, Shabestar Branch, Islamic Azad University, Shabestar, Iran

    Vahideh Sahargahi, Vahid Majidnezhad, Saeid Taghavi Afshord & Yasser Jafari

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  1. Vahideh Sahargahi
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Sahargahi, V., Majidnezhad, V., Taghavi Afshord, S. et al. A novel discrete ICO algorithm for influence maximization in complex networks. Computing 105, 1523–1546 (2023). https://doi.org/10.1007/s00607-023-01157-x

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