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Self-organizing Coalitions for Managing Complexity pp 139–169Cite as

Optimization Models with Coalitional Cellular Automata

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Part of the book series: Emergence, Complexity and Computation ((ECC,volume 29))

Abstract

This chapter analyzes the use of adaptive neighborhoods based on coalitions in evolutionary optimization frameworks. First, we introduce the concepts of evolutionary algorithms, population topologies and coalitions. We integrate all these topics to study how to avoid some of the drawbacks of previous evolutionary algorithms and to remove their typically required parameters. The main contribution of the chapter is a redefinition of the Evolutionary Algorithm with Coalitions (EACO), which uses cellular approaches with neighborhoods, allowing the formation of coalitions among cells as a way to create islands of evolution in order to preserve diversity. This idea speeds up the evolution of individuals grouped in high-quality coalitions that are quickly converging to promising solutions. In the results section, we successfully compare EACO with a canonical cGA (Cellular Genetic Algorithm), and provide evidences about the statistical significance of our results. We also analyze the influence of parameters in order to tune them up accordingly; and finally, we evaluate the performance of EACO under different complex network topologies.

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Notes

  1. 1.

    Like mutations in genetic evolution, \(P_{reb}\) alters the state of a cell within a coalition; and implicitly the whole coalition structure.

  2. 2.

    The problem order is: 0. ECC, 1. MAXCUT100, 2. MAXCUT20_01, 3. MAXCUT20_09, 4. MMDP, 5. MTTP100, 6. MTTP200 and 7. P-PEAKS.

  3. 3.

    The most computation demanding problem is P-PEAKS, which takes around 100 milliseconds per run to be solved by both algorithms with a population of 25 cells, and using a standard Intel dual-core computer with 8 GB of RAM. However, the same problem takes about ten times longer with a population of 1600 cells.

  4. 4.

    Note that Avgfitness in the formulae must be positive when we are maximizing, but negative if we minimize.

  5. 5.

    The best neighbor means the cell with the best functional value.

References

  1. Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley, New York (2005)

    Book  MATH  Google Scholar 

  2. Alba, E., Troya, J.M.: Cellular evolutionary algorithms: evaluating the influence of ratio. In: Schoenauer, M. et al. (eds.) PPSN-6. Lecture Notes in Computer Science, vol. 1917, pp. 29–38. Springer, Berlin (2000)

    Google Scholar 

  3. Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. IEEE Trans. Evol. Comput. 6(5), 443–462 (2002)

    Article  Google Scholar 

  4. Alba, E., Troya, J.M.: Improving flexibility and efficiency by adding parallelism to genetic algorithms. Soft Comput. 12(2), 91–114 (2002)

    MathSciNet  Google Scholar 

  5. Alba, E., Dorronsoro, B.: The exploration/exploitation tradeoff in dynamic cellular evolutionary algorithms. IEEE Trans. Evol. Comput. 9(2), 126–142 (2005)

    Article  Google Scholar 

  6. Alba, E., Dorronsoro, B.: Cellular Genetic Algorithms. Operations Research/Compuer Science Interfaces. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  7. Alba, E., Dorronsoro, B., Giacobini, M., Tomassini, M.: Decentralized cellular evolutionary algorithms. Handbook of Bioinspired Algorithms and Applications, pp. 103–120. CRC Press, Boca Raton (2006)

    Google Scholar 

  8. Alba, E., Madera, J., Dorronsoro, B., Ochoa, A., Soto, M.: Theory and practice of cellular UMDA for discrete optimization. In: Runarsson, T.P. et al. (eds.) Proceedings of the International Conference on Parallel Problem Solving from Nature IX (PPSN-IX), Reykjavik, Iceland. Lecture Notes in Computer Science, vol. 4193, pp. 242–251. Springer, Berlin (2006)

    Google Scholar 

  9. Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation. Oxford University Press, Oxford (1997)

    Google Scholar 

  10. Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence. From Natural to Artificial Systems. Oxford University Press, Oxford (1999)

    MATH  Google Scholar 

  11. Bremermann, H.: Optimization trough evolution and resombination. Self-Organizing Systems, pp. 93–106. Spartan Books, Washington DC (1962)

    Google Scholar 

  12. Cantor, G., Gómez, J.: Maintaining genetic diversity in fine-grained parallel genetic algorithms by combining cellular automata, cambrian explosions and massive extinctions. In: Proceedings of the IEEE International Conference on Evolutionary Computation (CEC), pp. 1–8 (2010)

    Google Scholar 

  13. Cantú-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Book Series on Genetic Algorithms and Evolutionary Computation, vol. 1, 2nd edn. Kluwer Academic Publishers, Dordrecht (2000)

    MATH  Google Scholar 

  14. Chen, H., Flann, N.S., Watson, D.W.: Parallel genetic simulated annealing: a massively parallel SIMD algorithm. IEEE Trans. Parallel Distrib. Syst. 9(2), 126–136 (1998)

    Article  Google Scholar 

  15. Clerc, M.: Particle Swarm Optimization. ISTE (International Scientific and Technical Encyclopedia) (2006)

    Google Scholar 

  16. Cramer, N.: A representation for the adaptive generation of simple sequential programs. In: Grefenstette, J. (ed.) Proceedings of the First International Conference on Genetic Algorithms and their Applications, Carnegie-Mellon University, Pittsburgh, PA, USA, 24–26 July 1985, pp. 183–187 (1985)

    Google Scholar 

  17. Darwin, C.: On the Origin of Species by Means of Natural Selection. John Murray, Londres (1859)

    Google Scholar 

  18. De Jong, K.A., Potter, M.A., Spears, W.M.: Using problem generators to explore the effects of epistasis. In: Bäck, T. (ed.) Proceedings of the 7th International Conference of Genetic Algorithms, Morgan Kaufman, pp. 338–345 (1997)

    Google Scholar 

  19. Dorigo, M., Stützle, T.: Ant Colony Optimization. The MIT Press, Cambridge (2004)

    MATH  Google Scholar 

  20. Dorronsoro, B., Bouvry, P.: Adaptive neighborhoods for cellular genetic algorithms. In: Nature Inspired Distributed Computing (NIDISC) Sessions of the International Parallel and Distributed Processing Symposium (IPDPS) 2011 Workshop, pp. 383–389 (2011)

    Google Scholar 

  21. Dorronsoro, B., Bouvry, P.: Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Trans. Evol. Comput. 15(1), 67–98 (2011)

    Article  Google Scholar 

  22. Dorronsoro, B., Bouvry, P.: On the use of small-world population topologies for genetic algorithms. In: EVOLVE 2011, A Bridge Between Probability, Set Oriented Numerics and Evolutionary Computation, e–proceedings (2011)

    Google Scholar 

  23. Dorronsoro, B., Bouvry, P.: Cellular genetic algorithms without additional parameters. J. Supercomput. 63(3), 816–835 (2012)

    Article  Google Scholar 

  24. Dorronsoro, B., Burguillo, J.C., Peleteiro, A., Bouvry, P.: Evolutionary algorithms based on game theory and cellular automata with coalitions. Handbook of Optimization, pp. 481–503. Springer, Berlin (2013)

    Chapter  Google Scholar 

  25. Elshamy, W., Emara, H.M., Bahgat, A.: Clubs-based particle swarm optimization. In: Proceedings of the IEEE Swarm Intelligence Symposium (SIS), pp. 289–296 (2007)

    Google Scholar 

  26. Fogel, L.: Autonomous automata. Ind. Res. 4, 14–19 (1962)

    Google Scholar 

  27. Fraser, A.: Simulation of genetic systems by automatic digital computers II: effects of linkage on rates under selection. Aust. J. Biol. Sci. 10, 492–499 (1957)

    Article  Google Scholar 

  28. Giacobini, M.T.M., Preuss, M.: Effects of scale-free and small-world topologies on binary coded self-adaptive CEA. In: Evolutionary Computation in Combinatorial Optimization (EvoCOP). Lecture Notes in Computer Science (LNCS), vol. 3906. Springer, Berlin (2006)

    Google Scholar 

  29. Giacobini, M., Tomassini, M., Tettamanzi, A.: Takeover time curves in random and small-world structured populations. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), Washington D.C. USA, 25–29 June 2005, pp. 1333–1340. ACM Press (2005)

    Google Scholar 

  30. Glover, F.W., Kochenberger, G.A. (eds.): Handbook of Metaheuristics. International Series in Operations Research Management Science. Kluwer, Dordrecht (2003)

    MATH  Google Scholar 

  31. Godoy, A., Von Zuben, F.J.: A complex neighborhood based particle swarm optimization. In: Proceedings of the IEEE International Conference on Evolutionary Computation (CEC), pp. 720–727 (2009)

    Google Scholar 

  32. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Reading (1989)

    MATH  Google Scholar 

  33. Goldberg, D., Deb, K., Horn, J.: Massively multimodality, deception, and genetic algorithms. In: Proceedings of the International Conference on Parallel Problem Solving from Nature II, pp. 37–46 (1992)

    Google Scholar 

  34. Holland, J.: Outline for a logical theory of adaptive systems. J. ACM 9(3), 297–314 (1962)

    Article  MATH  Google Scholar 

  35. Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  36. Hussain, T.: An introduction to evolutionary computation. Tutorial presentation, CITO Researcher Retreat, 12–14 May 1998, Hamilton, Ontario (1998)

    Google Scholar 

  37. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Implementation of cellular genetic algorithms with two neighborhood structures for single-objective and multi-objective optimization. Soft Comput. 15(9), 1749–1767 (2011)

    Article  Google Scholar 

  38. Janson, S., Middendorf, M.: A hierarchical particle swarm optimizer and its adaptive variant. IEEE Syst. Man Cybern. Part B 35(6), 1272–1282 (2005)

    Article  Google Scholar 

  39. Janson, S., Alba, E., Dorronsoro, B., Middendorf, M.: Hierarchical cellular genetic algorithm. In: Gottlieb, J., Raidl, G. (eds.) Evolutionary Computation in Combinatorial Optimization (EvoCOP), Budapest, Hungary. Lecture Notes in Computer Science (LNCS), vol. 3906, pp. 111–122. Springer, Berlin (2006)

    Google Scholar 

  40. Kennedy, J.: Stereotyping: improving particle swarm performance with cluster analysis. In: Proceedings of the IEEE International Conference on Evolutionary Computation (CEC), vol. 2, pp. 1507–1512 (2000)

    Google Scholar 

  41. Kennedy, J., Mendes, R.: Population structure and particle swarm performance. In: Proceedings of the IEEE International Conference on Evolutionary Computation (CEC), pp. 1671–1676. IEEE Press (2002)

    Google Scholar 

  42. Kennedy, J., Mendes, R.: Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 36(4), 515–519 (2006)

    Article  Google Scholar 

  43. Khuri, S., Bäck, T., Heitkötter, J.: An evolutionary approach to combinatorial optimization problems. In: Proceedings of the ACM Press Computer Science Conference, Phoenix, Arizona, pp. 66–73. ACM Press (1994)

    Google Scholar 

  44. Koza, J.: Genetic programming. In: Williams, J., Kent, A. (eds.) Encyclopedia of Computer Science and Technology, vol. 39, pp. 29–43. Marcel-Dekker, New York (1998)

    Google Scholar 

  45. Larrañaga, P., Lozano, J. (eds.): Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  46. Li, X.: Adaptively choosing neighbourhood bests using species in a particle swarm optimizer for multimodal function optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO). Lecture Notes in Computer Science (LNCS), vol. 3102, pp. 105–116. Springer, Berlin (2004)

    Google Scholar 

  47. Li, X., Sutherland, S.: A cellular genetic algorithm simulating predator-prey interactions. In: Proceedings of the Third International Conference on Genetic Algorithms (ICGA), Morgan Kaufmann, pp. 416–421 (2002)

    Google Scholar 

  48. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  49. Manderick, B., Spiessens, P.: Fine-grained parallel genetic algorithm. In: Schaffer, J. (ed.) Third International Conference on Genetic Algorithms ICGA-3, pp. 428–433. Morgan-Kaufmann (1989)

    Google Scholar 

  50. Mendel, G.: Versuche über Pflanzen-Hybriden. Verhandlungen des Naturforschedes Vereines in Brünn 4 (1865)

    Google Scholar 

  51. Mendes, R., Kennedy, J., Neves, J.: The fully informed particle swarm: simpler, may be better. IEEE Trans. Evol. Comput. 8(3), 204–210 (2004)

    Article  Google Scholar 

  52. Nedjah, N., Alba, E., de Macedo Mourelle, L.: Parallel Evolutionary Computations. Studies in Computational Intelligence. Springer, Berlin (2006)

    Book  MATH  Google Scholar 

  53. Neri, F., Cotta, C., Moscato, P.: Handbook of Memetic Algorithms. Studies in Computational Intelligence, vol. 379. Springer, Berlin (2012)

    Google Scholar 

  54. Olariu, S., Zomaya, A.Y. (eds.): Handbook of Bioinspired Algorithms and Applications. CRC Press, Boca Raton (2006)

    MATH  Google Scholar 

  55. Payne, J.L., Eppstein, M.J.: Emergent mating topologies in spatially structured genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), Seattle, Washington, USA, pp. 207–214. ACM Press (2006)

    Google Scholar 

  56. Payne, J.L., Eppstein, M.J.: The influence of scaling and assortativity on takeover times in scale-free topologies. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), Atlanta, Georgia, USA, pp. 241–248. ACM Press (2008)

    Google Scholar 

  57. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)

    MATH  Google Scholar 

  58. Rechenberg, I.: Cybernetic solution path of an experimental problem. Technical report, Royal Aircraft Establishment, Library translation No. 1122, Farnborough, Hants., UK, 1965

    Google Scholar 

  59. Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme und Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart (1973)

    Google Scholar 

  60. Schwefel, H.-P.: Kybernetische Evolution als Strategie der Experimentellen Forschung in der Strömungstechnik. Ph.D. thesis, Technical University of Berlin, 1965

    Google Scholar 

  61. Simoncini, D., Verel, S., Collard, P., Clergue, M.: Anisotropic selection in cellular genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), Seattle, Washington, USA, pp. 559–566. ACM Press (2006)

    Google Scholar 

  62. Standard Particle Swarm Optimization, Particle Swarm Central website

    Google Scholar 

  63. Stender, J.: Parallel Genetic Algorithms: Theory and Applications. IOS Press, Amsterdam (1993)

    MATH  Google Scholar 

  64. Stinson, D.R.: An Introduction to the Design and Analysis of Algorithms. The Charles Babbage Research Center, Winnipeg, Manitoba, Canada, 1985 (second edition, 1987)

    Google Scholar 

  65. Suganthan, P.N.: Particle swarm optimiser with neighborhood operator. In: Proceedings of the IEEE International Conference on Evolutionary Computation (CEC), vol. 3, pp. 1958–1962 (1999)

    Google Scholar 

  66. Talbi, E.: Parallel Combinatorial Optimization. Wiley, New York (2006)

    Book  Google Scholar 

  67. Tomassini, M.: Spatially Structured Evolutionary Algorithms: Artificial Evolution in Space and Time. Natural Computing Series. Springer, Berlin (2005)

    MATH  Google Scholar 

  68. Whitacre, J.M., Sarker, R.A., Pham, T.T.: The self-organization of interaction networks for nature-inspired optimization. IEEE Trans. Evol. Comput. 12(2), 220–230 (2008)

    Article  Google Scholar 

  69. Whitley, D.: Cellular genetic algorithms. In: Forrest, S. (ed.) Fifth International Conference on Genetic Algorithms ICGA-5, California, CA, USA, p. 658. Morgan-Kaufmann (1993)

    Google Scholar 

  70. Whitley, D., Rana, S., Dzubera, J., Mathias, K.E.: Evaluating evolutionary algorithms. Artif. Intell. 85, 245–276 (1997)

    Article  Google Scholar 

  71. Wright, S.: Isolation by distance. Genetics 28, 114–138 (1943)

    Google Scholar 

  72. Yumind, L., Ming, L., Ling, L.: Cellular genetic algorithms with evolutional rule. In: International Workshop on Intelligent Systems and Applications (ISA), pp. 1–4. IEEE (2009)

    Google Scholar 

  73. Zelinka, I., Oplatkova, Z., Nolle, L.: Analytic programming-symbolic regression by means of arbitrary evolutionary algorithms. Int. J. Simul. Syst. Sci. Technol. 6(9), 44–56 (2005)

    Google Scholar 

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Acknowledgements

This work was partially supported by the European Regional Development Fund (ERDF) together with the Galician Regional Government under agreement for funding the Atlantic Research Center for Information and Communication Technologies (AtlantTIC).

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  1. Department of Telematics Engineering, School of Telecommunications Engineering, University of Vigo, 36310, Vigo, Spain

    Juan C. Burguillo

  2. Computer Science Engineering Department, University of Cadiz, 11519, Cadiz, Spain

    Bernabé Dorronsoro

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Correspondence to Juan C. Burguillo .

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Burguillo, J.C., Dorronsoro, B. (2018). Optimization Models with Coalitional Cellular Automata. In: Self-organizing Coalitions for Managing Complexity. Emergence, Complexity and Computation, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-69898-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-69898-4_8

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