Zombie politics: evolutionary algorithms to counteract the spread of negative opinions

  • Ronald HochreiterEmail author
  • Christoph Waldhauser
Methodologies and Application


This paper is about simulating the spread of opinions in a society and about finding ways to counteract that spread. To abstract away from potentially emotionally laden opinions, we instead simulate the spread of a zombie outbreak in a society. The virus causing this outbreak is different from traditional approaches: It not only causes a binary outcome (healthy vs. infected) but rather a continuous outcome. To counteract the outbreak, a discrete number of infection-level-specific treatments are available. This corresponds to acts of mild persuasion or the threats of legal action in the opinion spreading use case. This paper offers a genetic and a cultural algorithm that find the optimal mixture of treatments during the run of the simulation. They are assessed in a number of different scenarios. It is shown that albeit far from being perfect, the cultural algorithm delivers superior performance at lower computational expense.


Dynamic optimization Opinion propagation Epidemiology Evolutionary computing 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Acemoglu D, Ozdaglar A (2011) Opinion dynamics and learning in social networks. Dyn Games Appl 1(1):3–49MathSciNetCrossRefGoogle Scholar
  2. Adar E, Adamic L (2005) Tracking information epidemics in blogspace. In: Proceedings of the 2005 IEEE/WIC/ACM international conference on web intelligence, 2005, IEEE, pp 207–214Google Scholar
  3. Adjemian JC, Girvetz EH, Beckett L, Foley JE (2006) Analysis of genetic algorithm for rule-set production (GARP) modeling approach for predicting distributions of fleas implicated as vectors of plague, yersinia pestis, California. J Med Entomol 43(1):93–103Google Scholar
  4. Amaral L, Scala A, Barthélémy M, Stanley H (2000) Classes of small-world networks. Proc Natl Acad Sci 97(21):11149–11152CrossRefGoogle Scholar
  5. Amaral MA, Arenzon JJ (2018) Rumor propagation meets skepticism: a parallel with zombies. EPL (Europhys Lett) 124(1):18007CrossRefGoogle Scholar
  6. Amelkin V, Singh AK (2019) Fighting opinion control in social networks via link recommendation. In: ACM SIGKDD conference of knowledge discovery and data mining, ACMGoogle Scholar
  7. Askarizadeh M, Ladani BT, Manshaei MH (2019) An evolutionary game model for analysis of rumor propagation and control in social networks. Phys A: Stat Mech Appl 523:21–39MathSciNetCrossRefGoogle Scholar
  8. Branke J (2002) Evolutionary optimization in dynamic environments. Kluwer, NorwellCrossRefGoogle Scholar
  9. Brauer F, Castillo-Chavez C (2011) Mathematical models in population biology and epidemiology. Springer, New YorkzbMATHGoogle Scholar
  10. Bucur D, Iacca G, Marcelli A, Squillero G, Tonda A (2017) Multi-objective evolutionary algorithms for influence maximization in social networks. In: European conference on the applications of evolutionary computation, Springer, Berlin, pp 221–233Google Scholar
  11. Bucur D, Iacca G, Marcelli A, Squillero G, Tonda A (2018) Improving multi-objective evolutionary influence maximization in social networks. In: International conference on the applications of evolutionary computation, Springer, Berlin, pp 117–124Google Scholar
  12. Calderhead B, Girolami M, Higham D (2010) Is it safe to go out yet? statistical inference in a zombie outbreak model. University of Strathclyde, Department of Mathematics and Statistics, PreprintGoogle Scholar
  13. Castiglione F, Pappalardo F, Bernaschi M, Motta S (2007) Optimization of HAART with genetic algorithms and agent-based models of HIV infection. Bioinformatics 23(24):3350–3355CrossRefGoogle Scholar
  14. Chen W, Collins A, Cummings R, Ke T, Liu Z, Rincon D, Sun X, Wang Y, Wei W, Yuan Y (2011) Influence maximization in social networks when negative opinions may emerge and propagate. In: Proceedings of the 11th SIAM international conference on data mining (SDM 2011), vol 11, pp 379–390Google Scholar
  15. Crossley M, Amos M (2011) Simzombie: a case-study in agent-based simulation construction. Technologies and applications, agent and multi-agent systems, pp 514–523Google Scholar
  16. Cruz C, González JR, Pelta DA (2011) Optimization in dynamic environments: a survey on problems, methods and measures. Soft Comput Fus Found Methodol Appl 15(7):1427–1448Google Scholar
  17. Eubank S, Guclu H, Kumar V, Marathe M, Srinivasan A, Toroczkai Z, Wang N (2004) Modelling disease outbreaks in realistic urban social networks. Nature 429(6988):180–184CrossRefGoogle Scholar
  18. Fu X, Liew C, Soh H, Lee G, Hung T, Ng LC (2007) Time-series infectious disease data analysis using SVM and genetic algorithm. In: IEEE congress on evolutionary computation 2007 (CEC 2007), pp 1276–1280Google Scholar
  19. Yn Guo, Cheng J, Yy Cao, Lin Y (2011) A novel multi-population cultural algorithm adopting knowledge migration. Soft Comput Fus Found Methodol Appl 15(5):897–905Google Scholar
  20. He Z, Cai Z, Yu J, Wang X, Sun Y, Li Y (2016) Cost-efficient strategies for restraining rumor spreading in mobile social networks. IEEE Trans Veh Technol 66(3):2789–2800CrossRefGoogle Scholar
  21. Hochreiter R, Waldhauser C (2013) Solving dynamic optimisation problems with revolutionary algorithms. Int J Innov Comput Appl 5(1):17–25Google Scholar
  22. Hosseini-Pozveh M, Zamanifar K, Naghsh-Nilchi AR, Dolog P (2016) Maximizing the spread of positive influence in signed social networks. Intell Data Anal 20(1):199–218CrossRefGoogle Scholar
  23. Java A, Kolari P, Finin T, Oates T (2006) Modeling the spread of influence on the blogosphere. In: Proceedings of the 15th international world wide web conference, pp 22–26Google Scholar
  24. Kaiser C, Kröckel J, Bodendorf F (2013) Simulating the spread of opinions in online social networks when targeting opinion leaders. Inf Syst e-Bus Manag 11(4):597–621CrossRefGoogle Scholar
  25. Kaur H, He J (2017) Blocking negative influential node set in social networks: from host perspective. Trans Emerg Telecommun Technol 28(4):e3007CrossRefGoogle Scholar
  26. Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining, ACM, pp 137–146Google Scholar
  27. Kleywegt AJ, Papastavrou JD (1998) The dynamic and stochastic knapsack problem. Oper Res 46(1):17–35MathSciNetCrossRefGoogle Scholar
  28. Krömer P, Nowaková J (2017) Guided genetic algorithm for the influence maximization problem. In: International computing and combinatorics conference, Springer, Berlin, pp 630–641Google Scholar
  29. Lahiri M, Cebrian M (2010) The genetic algorithm as a general diffusion model for social networks. In: Proceedings of the 24th AAAI conference on artifical intelligence, pp 494–499Google Scholar
  30. Levine RS, Peterson AT, Benedict MQ (2004) Geographic and ecologic distributions of the anopheles gambiae complex predicted using a genetic algorithm. Am J Trop Med Hyg 70(2):105–109CrossRefGoogle Scholar
  31. Lin D, Li S, Cao D (2010) Making intelligent business decisions by mining the implicit relation from bloggers’ posts. Soft Comput Fus Found Methodol Appl 14(12):1317–1327Google Scholar
  32. Lynch A (1998) Thought contagion: How belief spreads through society: the new science of memes. Basic Books, New YorkGoogle Scholar
  33. Martello S, Toth P (1990) Knapsack problems. Wiley, New YorkzbMATHGoogle Scholar
  34. Miller W, Holmberg S, Pierce R (eds) (1999) Policy representation in Western democracies. Oxford University Press, OxfordGoogle Scholar
  35. Moore T, Finley P, Linebarger J, Outkin A, Verzi S, Brodsky N, Cannon D, Zagonel A, Glass R (2011) Extending opinion dynamics to model public health problems and analyze public policy interventions. In: 8th International conference on complex systemsGoogle Scholar
  36. Munz P, Hudea I, Imad J, Smith R (2009) When zombies attack!: mathematical modelling of an outbreak of zombie infection. In: Infectious Disease Modelling Research Progress. Nova Science Publishers, Hauppauge, pp 133–150Google Scholar
  37. Papastavrou JD, Rajagopalan S, Kleywegt AJ (1996) The dynamic and stochastic knapsack problem with deadlines. Manag Sci 42(12):1706–1718CrossRefGoogle Scholar
  38. Patlolla P, Gunupudi V, Mikler A, Jacob R (2006) Agent-based simulation tools in computational epidemiology. Lecture notes in computer science 3473:212–223Google Scholar
  39. R Core Team (2012) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria., ISBN 3-900051-07-0
  40. Rahmandad H, Sterman J (2008) Heterogeneity and network structure in the dynamics of diffusion: comparing agent-based and differential equation models. Manag Sci 54(5):998–1014CrossRefGoogle Scholar
  41. Reynolds R (1994) An introduction to cultural algorithms. In: Evolutionary programming—proceedings of the 3rd annual conference. World Scientific, pp 131–139Google Scholar
  42. Reynolds R, Ali M (2008) Computing with the social fabric: the evolution of social intelligence within a cultural framework. Comput Intell Mag 3(1):18–30CrossRefGoogle Scholar
  43. Rodríguez Lucatero C, Alarcón L, Bernal Jaquez R, Schaum A (2012) Decision dynamics in complex networks subject to mass media and social contact transmission mechanisms. arXiv:1210.8193
  44. Rogers FB (1963) Medical subject headings. Bull Med Libr Assoc 51(1):114–116Google Scholar
  45. Sobkowicz P, Kaschesky M, Bouchard G (2012) Opinion formation in the social web: agent-based simulations of opinion convergence and divergence. Lecture notes in computer science 7103:288–303Google Scholar
  46. Sokolowski J, Banks C (2011) Principles of modeling and simulation: a multidisciplinary approach. Wiley, HobokenzbMATHGoogle Scholar
  47. Stockwell D (1999) The GARP modelling system: problems and solutions to automated spatial prediction. Int J Geogr Inf Sci 13(2):143–158CrossRefGoogle Scholar
  48. Tastle WJ, Wierman MJ (2007) Consensus and dissention: a measure of ordinal dispersion. Int J Approxim Reason 45(3):531–545MathSciNetCrossRefGoogle Scholar
  49. Teng P (1985) A comparison of simulation approaches to epidemic modeling. Ann Rev Phytopathol 23(1):351–379CrossRefGoogle Scholar
  50. Thomas R (2012) Knowledge aware and culturally sensitive sir models for infectious disease spread. Master’s thesis, University of WindsorGoogle Scholar
  51. Waldhauser C (2013) Revil: zombie outbreak simulator for the analysis of opinion propagation., R package version 0.1
  52. Wessels B, Miller W (1999) System characteristics matter: empirical evidence from ten representation studies. In: Miller W, Holmberg S, Pierce R (eds) Policy representation in Western democracies. Oxford University Press, Oxford, pp 137–161Google Scholar
  53. Wickham H (2009) ggplot2: elegant graphics for data analysis. Springer, New York. Accessed 1 June 2019
  54. Xiao Y, Chen D, Wei S, Li Q, Wang H, Xu M (2019) Rumor propagation dynamic model based on evolutionary game and anti-rumor. Nonlinear Dyn 95(1):523–539CrossRefGoogle Scholar
  55. Yan S, Tang S, Pei S, Jiang S, Zhang X, Ding W, Zheng Z (2013) The spreading of opposite opinions on online social networks with authoritative nodes. Phys A: Stat Mech Appl 392(17):3846–3855MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Business and ManagementWebster Vienna Private UniversityViennaAustria
  2. 2.Raiffeisen Bank International AGViennaAustria

Personalised recommendations