Soft Computing

, Volume 20, Issue 4, pp 1549–1563 | Cite as

Surrogate modeling based on an adaptive network and granular computing

  • Israel Cruz-Vega
  • Hugo Jair Escalante
  • Carlos A. Reyes
  • Jesus A. Gonzalez
  • Alejandro Rosales
Methodologies and Application

Abstract

Reducing the number of evaluations of expensive fitness functions is one of the main concerns in evolutionary algorithms, especially when working with instances of contemporary engineering problems. As an alternative to this efficiency constraint, surrogate-based methods are grounded in the construction of approximate models that estimate the solutions’ fitness by modeling the relationships between solution variables and their performance. This paper proposes a methodology based on granular computing for the construction of surrogate models for evolutionary algorithms. Under the proposed method, granules are associated with representative solutions of the problem under analysis. New solutions are evaluated with the expensive (original) fitness function only if they are not already covered by an existing granule. The parameters defining granules are periodically adapted as the search goes on using a neuro-fuzzy network that does not only reduce the number of fitness function evaluations, but also provides better convergence capabilities. The proposed method is evaluated on classical benchmark functions and on a recent benchmark created to test large-scale optimization models. Our results show that the proposed method considerably reduces the actual number of fitness function evaluations without significantly degrading the quality of solutions.

Keywords

Surrogate modeling Genetic algorithms Neuro-fuzzy networks 

References

  1. Aja-Fernández S, Alberola-López C (2004) Fuzzy granules as a basic word representation for computing with words. In: 9th conference speech and computerGoogle Scholar
  2. Akbarzadeh-T MR, Davarynejad M, Pariz N (2008) Adaptive fuzzy fitness granulation for evolutionary optimization. Int J Approx Reason 49(3):523–538CrossRefGoogle Scholar
  3. Akbarzadeh-T MR, Mosavat I, Abbasi S (2003) Friendship modeling for cooperative co-evolutionary fuzzy systems: a hybrid ga-gp algorithm. In: 22nd international conference of the North American Fuzzy Information Processing Society, 2003 (NAFIPS 2003). IEEE, pp 61–66Google Scholar
  4. Bertsimas D, Tsitsiklis J et al (1993) Simulated annealing. Stat Sci 8(1):10–15CrossRefMATHGoogle Scholar
  5. Castellano G, Fanelli AM, Mencar C (2003) Fuzzy information granules: a compact, transparent and efficient representation. JACIII 7(2):160–168Google Scholar
  6. Clarke SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. J Mech Des 127(6):1077–1087CrossRefGoogle Scholar
  7. Cruz-Vega I, Escalante HJ (2015) A note on: adaptive fuzzy fitness granulation for evolutionary optimization. Int J Approx Reason 57:40–43CrossRefGoogle Scholar
  8. Cruz-Vega I, Garcia-Limon M, Escalante HJ (2014) Adaptive-surrogate based on a neuro-fuzzy network and granular computing. In: Proceedings of the 2014 conference on genetic and evolutionary computation. ACM, pp 761–768Google Scholar
  9. De Jong KA (1975) An analysis of the behavior of a class of genetic adaptive systems. Ph.D. Dissertation. University of Michigan, Ann Arbor, MI, USA, AAI7609381Google Scholar
  10. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18CrossRefGoogle Scholar
  11. Digalakis JG, Margaritis KG (2002) An experimental study of benchmarking functions for genetic algorithms. Int J Comput Math 79(4):403–416MathSciNetCrossRefMATHGoogle Scholar
  12. Do Wan Kim HJL, Park JB, Joo YH (2006) Ga-based construction of fuzzy classifiers using information granulesGoogle Scholar
  13. Farina M (2002) A neural network based generalized response surface multiobjective evolutionary algorithm. In: Proceedings of the 2002 congress on evolutionary computation, 2002 (CEC’02), vol 1. IEEE, pp 956–961Google Scholar
  14. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99CrossRefGoogle Scholar
  15. Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3–12CrossRefGoogle Scholar
  16. Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1(2):61– 70CrossRefGoogle Scholar
  17. Karakasis MK, Giannakoglou KC (2004) On the use of surrogate evaluation models in multi-objective evolutionary algorithms. In: Proceedings of European congress on computational methods in applied sciences and engineering (ECCOMAS 2004)Google Scholar
  18. Leite D, Gomide F, Ballini R, Costa P (2011) Fuzzy granular evolving modeling for time series prediction. In: 2011 IEEE international conference on fuzzy systems (FUZZ). IEEE, pp 2794–2801Google Scholar
  19. Li X, Tang K, Omidvar MN, Yang Z, Qin K, China H (2013) Benchmark functions for the CEC 2013 special session and competition on large-scale global optimization. Gene 7:33 (2013)Google Scholar
  20. Morse PM (1929) Diatomic molecules according to the wave mechanics. ii. Vibrational levels. Phys Rev 34(1):57CrossRefMATHGoogle Scholar
  21. Myers WR, Montgomery DC (2003) Response surface methodology. Encycl Biopharm Stat 1:858–869Google Scholar
  22. Panoutsos G, Mahfouf M (2010) A neural-fuzzy modelling framework based on granular computing: concepts and applications. Fuzzy Sets Syst 161(21):2808–2830MathSciNetCrossRefGoogle Scholar
  23. Park KJ, Pedrycz W, Oh SK (2007) A genetic approach to modeling fuzzy systems based on information granulation and successive generation-based evolution method. Simul Model Pract Theory 15(9):1128–1145CrossRefGoogle Scholar
  24. Pedrycz W (2014) Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing. Eur J Oper Res 232(1):137–145MathSciNetCrossRefGoogle Scholar
  25. Pedrycz W, Song M (2012) A genetic reduction of feature space in the design of fuzzy models. Appl Soft Comput 12(9):2801–2816CrossRefGoogle Scholar
  26. Pintér JD (2006) Global optimization: scientific and engineering case studies, vol 85. Springer, BerlinGoogle Scholar
  27. Puris A, Bello R, Molina D, Herrera F (2012) Variable mesh optimization for continuous optimization problems. Soft Comput 16(3):511–525CrossRefGoogle Scholar
  28. Roberts C, Johnston RL, Wilson NT (2000) A genetic algorithm for the structural optimization of morse clusters. Theor Chem Acc 104(2):123–130CrossRefGoogle Scholar
  29. Roh SB, Pedrycz W, Ahn TC (2014) A design of granular fuzzy classifier. Expert Syst Appl 41(15):6786–6795Google Scholar
  30. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–423Google Scholar
  31. Velasco J, Saucedo-Espinosa MA, Escalante HJ, Mendoza K, Villarreal-Rodrıguez CE, Chacón-Mondragón OL, Rodrıguez A, Berrones A (2014) An adaptive random search for unconstrained global optimization. Computacion y Sistemas 18(2):243–257Google Scholar
  32. Yao JT, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989Google Scholar
  33. Yao Y (2005) Perspectives of granular computing. In: 2005 IEEE international conference on granular computing, vol 1. IEEE, pp 85–90Google Scholar
  34. Yao YY (2004) Granular computing. In: Proceedings of the 4th Chinese national conference on rough sets and soft computing, vol 31, pp 1–5Google Scholar
  35. Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127MathSciNetCrossRefMATHGoogle Scholar
  36. Zhang J, Chowdhury S, Messac A (2012) An adaptive hybrid surrogate model. Struct Multidiscip Optim 46(2):223–238CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Israel Cruz-Vega
    • 1
  • Hugo Jair Escalante
    • 1
  • Carlos A. Reyes
    • 1
  • Jesus A. Gonzalez
    • 1
  • Alejandro Rosales
    • 1
  1. 1.Computer Science DepartmentInstituto Nacional de Astrofísica, Óptica y ElectrónicaPueblaMexico

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