Skip to main content
Log in

A New Evolutionary Model Based on Cellular Learning Automata and Chaos Theory

  • Published:
New Generation Computing Aims and scope Submit manuscript

Abstract

In this paper, a new fine-grained evolutionary model, called CCLA-EM, is proposed for solving the optimization problems, which greatly overcomes the premature convergence problem of the existing evolutionary algorithms. In the proposed model, a combination of an evolutionary algorithm with a cellular learning automaton is used. The population individuals are distributed on the cells of a cellular learning automaton. Each individual interacts and cooperates with the individuals of neighboring cells to reach the global optimum. Distributing the population individuals on the cells of a cellular learning automaton allows the parallel implementation of the proposed model. Also, in different stages of the proposed model, numbers generated by a chaotic process are used instead of random ones. The use of numbers generated by a chaotic process leads to a complete search of the search space and hence avoids being trapped in local optima. Experiments on various benchmarks of the community structure detection problem indicate the superiority of the proposed model to the well-known algorithms GA-net and ICLA-net.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes

  1. The process described in previous paragraph is performed only for active cells. In other words, only active cells update their status and action probability distribution.

References

  1. Zelinka, I., Snasael, V., Abraham, A.: Handbook of optimization: from classical to modern approach. Springer (2012)

    Google Scholar 

  2. Tenne, Y., Goh, C.-K.: Computational intelligence in expensive optimization problems. Springer (2010)

    Book  Google Scholar 

  3. Alba, E., Blum, C., Asasi, P., Leon, C., Gomez, J.A.: Optimization techniques for solving complex problems. Wiley (2009)

    Book  Google Scholar 

  4. Korte, B., Vygen, J., Korte, B., Vygen, J.: Combinatorial optimization. Springer (2012)

    Book  Google Scholar 

  5. Blum, C., Roli, A.: Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput. Surv. 35(3), 268–308 (2003)

    Article  Google Scholar 

  6. Liu, J., Zhong, W., Jiao, L.: A multiagent evolutionary algorithm for combinatorial optimization problems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 40(1), 229–240 (2009)

    Google Scholar 

  7. Liu, J., Zhong, W., Jiao, L.: A multiagent evolutionary algorithm for constraint satisfaction problems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 36(1), 54–73 (2006)

    Article  Google Scholar 

  8. Zhong, W., Liu, J., Xue, M., Jiao, L.: A multiagent genetic algorithm for global numerical optimization. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 34(2), 1128–1141 (2004)

    Article  Google Scholar 

  9. Juan, L., Zixing, C., Jianqin, L.: Premature convergence in genetic algorithm: analysis and prevention based on chaos operator. In: Proceedings of the 3rd World congress on intelligent control and automation (Cat. No. 00EX393), vol. 1. IEEE, pp. 495–499 (2000)

  10. Caponetto, R., Fortuna, L., Fazzino, S., Xibilia, M.G.: Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans. Evol. Comput. 7(3), 289–304 (2003)

    Article  Google Scholar 

  11. Zarei, B., Meybodi, M.R., Masoumi, B.: Chaotic memetic algorithm and its application for detecting community structure in complex networks. Chaos 30(1), 013125 (2020)

    Article  MathSciNet  Google Scholar 

  12. Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601 (1983)

    Article  MathSciNet  Google Scholar 

  13. Narendra, K.S., Thathachar, M.A.: Learning automata: an introduction. Courier corporation (2012)

    Google Scholar 

  14. Santharam, G., Sastry, P., Thathachar, M.: Continuous action set learning automata for stochastic optimization. J. Franklin Inst. 331(5), 607–628 (1994)

    Article  MathSciNet  Google Scholar 

  15. Beigy, H., Meybodi, M.R.: A mathematical framework for cellular learning automata. Adv. Complex Syst. 7(03n04), 295–319 (2004)

    Article  MathSciNet  Google Scholar 

  16. Lorenzelli, F.: The essence of chaos. CRC Press (2014)

    Book  Google Scholar 

  17. Smith, P.: Explaining chaos. Cambridge University Press (1998)

    Book  Google Scholar 

  18. Williams, G.: Chaos theory tamed. CRC Press (1997)

    Book  Google Scholar 

  19. Ausloos, M., Dirickx, M.: The logistic map and the route to chaos: From the beginnings to modern applications. Springer (2006)

    Book  Google Scholar 

  20. Hilborn, R.C.: Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press (2000)

    Book  Google Scholar 

  21. Alba, E., Dorronsoro, B.: Cellular genetic algorithms. Springer (2009)

    MATH  Google Scholar 

  22. Li, X., Wu, J., Li, X.: Theory of practical cellular automaton. Springer (2018)

    Book  Google Scholar 

  23. Sudholt, D.: Parallel evolutionary algorithms. In: Springer handbook of computational intelligence, pp. 929–959. Springer (2015)

    Chapter  Google Scholar 

  24. Tomassini, M.: Parallel and distributed evolutionary algorithms: A review. In: Miettinen, K., Makela, M., Neittaanmaki, P., Periaux, J. (eds.) Evolutionary Algorithms in Engineering and Computer Science, pp. 113–131. John Wiley & Sons, LTD, New York (1999)

    Google Scholar 

  25. Chellapilla, K.: Combining mutation operators in evolutionary programming. IEEE Trans. Evol. Comput. 2(3), 91–96 (1998)

    Article  Google Scholar 

  26. Marin, J., Sole, R.V.: Macroevolutionary algorithms: a new optimization method on fitness landscapes. IEEE Trans. Evol. Comput. 3(4), 272–286 (1999)

    Article  Google Scholar 

  27. Jiao, L., Wang, L.: A novel genetic algorithm based on immunity. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 30(5), 552–561 (2000)

    Article  Google Scholar 

  28. Leung, Y.-W., Wang, Y.: An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans. Evol. Comput. 5(1), 41–53 (2001)

    Article  Google Scholar 

  29. Kazarlis, S.A., Papadakis, S.E., Theocharis, J., Petridis, V.: Microgenetic algorithms as generalized hill-climbing operators for GA optimization. IEEE Trans. Evol. Comput. 5(3), 204–217 (2001)

    Article  Google Scholar 

  30. Pizzuti, C.: GA-net: a genetic algorithm for community detection in social networks. In: International conference on parallel problem solving from nature, Springer, pp. 1081–1090 (2008)

  31. Zhao, Y., Jiang, W., Li, S., Ma, Y., Su, G., Lin, X.: A cellular learning automata based algorithm for detecting community structure in complex networks. Neurocomputing 151, 1216–1226 (2015)

    Article  Google Scholar 

  32. Newman, M.: Networks. Oxford University Press (2018)

    Book  Google Scholar 

  33. Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)

    Article  Google Scholar 

  34. Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3–5), 75–174 (2010)

    Article  MathSciNet  Google Scholar 

  35. Fortunato, S., Hric, D.: Community detection in networks: a user guide. Phys. Rep. 659, 1–44 (2016)

    Article  MathSciNet  Google Scholar 

  36. Tang, L., Liu, H.: Community detection and mining in social media. Synth. Lect. Data Min. Knowl. Discov. 2(1), 1–137 (2010)

    Article  MathSciNet  Google Scholar 

  37. Brandes, U., et al.: On finding graph clusterings with maximum modularity. In: International workshop on graph-theoretic concepts in computer science, Springer, pp. 121–132 (2007)

  38. Bui, T.N., Jones, C.: Finding good approximate vertex and edge partitions is NP-hard. Inf. Process. Lett. 42(3), 153–159 (1992)

    Article  MathSciNet  Google Scholar 

  39. Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete problems. In: Proceedings of the sixth annual ACM symposium on theory of computing, pp. 47–63 (1974)

  40. Park, Y., Song, M.: A genetic algorithm for clustering problems. In: Proceedings of the third annual conference on genetic programming, pp. 568–575 (1998)

  41. Danon, L., Diaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. J. Stat. Mech: Theory Exp. 2005(09), P09008 (2005)

    Article  Google Scholar 

  42. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bagher Zarei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarei, B., Meybodi, M.R. & Masoumi, B. A New Evolutionary Model Based on Cellular Learning Automata and Chaos Theory. New Gener. Comput. 40, 285–310 (2022). https://doi.org/10.1007/s00354-022-00159-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00354-022-00159-1

Keywords

Navigation