Skip to main content
SpringerLink
Log in

Chaos Embedded Metaheuristic Algorithms

  • Chapter
  • First Online:
Advances in Metaheuristic Algorithms for Optimal Design of Structures

  • 1274 Accesses

Abstract

In nature complex biological phenomena such as the collective behavior of birds, foraging activity of bees or cooperative behavior of ants may result from relatively simple rules which however present nonlinear behavior being sensitive to initial conditions. Such systems are generally known as “deterministic nonlinear systems” and the corresponding theory as “chaos theory”. Thus real world systems that may seem to be stochastic or random, may present a nonlinear deterministic and chaotic behavior. Although chaos and random signals share the property of long term unpredictable irregular behavior and many of random generators in programming softwares as well as the chaotic maps are deterministic; however chaos can help order to arise from disorder. Similarly, many metaheuristics optimization algorithms are inspired from biological systems where order arises from disorder. In these cases disorder often indicates both non-organized patterns and irregular behavior, whereas order is the result of self-organization and evolution and often arises from a disorder condition or from the presence of dissymmetries. Self-organization and evolution are two key factors of many metaheuristic optimization techniques. Due to these common properties between chaos and optimization algorithms, simultaneous use of these concepts can improve the performance of the optimization algorithms [1]. Seemingly the benefits of such combination is a generic for other stochastic optimization and experimental studies confirmed this; although, this has not mathematically been proven yet [2].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Sheikholeslami R, Kaveh A (2013) A survey of chaos embedded metaheuristic algorithms. Int J Optim Civil Eng 3:617–633

    Google Scholar 

  2. Tavazoei MS, Haeri M (2007) An optimization algorithm based on chaotic behavior and fractal nature. J Comput Appl Math 206:1070–1081

    Article  MATH  MathSciNet  Google Scholar 

  3. Bucolo M, Caponetto R, Fortuna L, Frasca M, Rizzo A (2002) Does chaos work better than noise? IEEE Circ Syst Mag 2(3):4–19

    Article  Google Scholar 

  4. Liu B, Wang L, Jin YH, Tang F, Huang DX (2005) Improved particle swarm optimization combined with chaos. Chaos Solitons Fractals 25(5):1261–1271

    Article  MATH  Google Scholar 

  5. Liu S, Hou Z (2002) Weighted gradient direction based chaos optimization algorithm for nonlinear programming problem. Proceedings of the 4th world congress on intelligent control and automation, pp 1779–1783

    Google Scholar 

  6. Li TY, Yorke JA (1975) Period three implies chaos. Am Math Mon 82:985–992

    Article  MATH  MathSciNet  Google Scholar 

  7. Tatsumi K, Obita Y, Tanino T (2009) Chaos generator exploiting a gradient model with sinusoidal perturbations for global optimization. Chaos Solitons Fractals 42:1705–1723

    Article  MATH  MathSciNet  Google Scholar 

  8. Hilborn RC (2000) Chaos and nonlinear dynamics. Oxford University Press, New York

    Book  MATH  Google Scholar 

  9. Heidari-Bateni G, McGillem CD (1994) A chaotic direct-sequence spread spectrum communication system. IEEE Trans Commun 42(2–4):1524–1527

    Article  Google Scholar 

  10. May R (1976) Mathematical models with very complicated dynamics. Nature 261:459–467

    Article  Google Scholar 

  11. Peitgen H, Jurgens H, Saupe D (1992) Chaos and fractals. Springer, Berlin

    Book  Google Scholar 

  12. Zheng WM (1994) Kneading plane of the circle map. Chaos Solitons Fractals 4(7):1221–1233

    Article  MATH  Google Scholar 

  13. Dressler U, Farmer JD (1992) Generalized Lyapunov exponents corresponding to higher derivatives. Physica D 59:365–377

    Article  MATH  MathSciNet  Google Scholar 

  14. Zaslavskii GM (1987) The simplest case of a strange attractor. Phys Lett A69(3):145–147

    MathSciNet  Google Scholar 

  15. Glover F, Kochenberger GA (2003) Handbook of metaheuristic. Kluwer Academic, Boston

    Google Scholar 

  16. Talbi EG (2009) Metaheuristics: from design to implementation. Wiley, New Jersey

    Book  Google Scholar 

  17. Dorigo M (2009) Metaheuristics network website (2000). http://www.metaheuristics.net/. Visited in January

  18. Schuster HG (1988) Deterministic chaos: an introduction (2nd Revised edn). Physick-Verlag GmnH, Weinheim, Federal Republic of Germany

    Google Scholar 

  19. Coelho L, Mariani V (2008) Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization. Expert Syst Appl 34:1905–1913

    Article  Google Scholar 

  20. Alatas B (2010) Chaotic harmony search algorithm. Appl Math Comput 29(4):2687–2699

    Article  Google Scholar 

  21. Alatas B, Akin E, Ozer AB (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals 40:1715–1734

    Article  MATH  MathSciNet  Google Scholar 

  22. Alatas B (2010) Chaotic bee colony algorithms for global numerical optimization. Expert Syst Appl 37:5682–5687

    Article  Google Scholar 

  23. Alatas B (2011) Uniform big bang-chaotic big crunch optimization. Commun Nonlinear Sci Numer Simul 16(9):3696–3703

    Article  MATH  Google Scholar 

  24. Talatahari S, Farahmand Azar B, Sheikholeslami R, Gandomi AH (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simul 17:1312–1319

    Article  MATH  MathSciNet  Google Scholar 

  25. Talataharis S, Kaveh A, Sheikholeslami R (2011) An efficient charged system search using chaos for global optimization problems. Int J Optim Civil Eng 1(2):305–325

    Google Scholar 

  26. Talatahari S, Kaveh A, Sheikholeslami R (2012) Chaotic imperialist competitive algorithm for optimum design of truss structures. Struct Multidiscip Optim 46:355–367

    Article  Google Scholar 

  27. Talatahari S, Kaveh A, Sheikholeslami R (2012) Engineering design optimization using chaotic enhanced charged system search algorithms. Acta Mech 223:2269–2285

    Article  MATH  Google Scholar 

  28. Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315

    Article  Google Scholar 

  29. Yang D, Li G, Cheng G (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34:1366–1375

    Article  Google Scholar 

  30. Wu TB, Cheng Y, Zhou TY, Yue Z (2009) Optimization control of PID based on chaos genetic algorithm. Comput Simul 26:202–204

    Google Scholar 

  31. Guo ZL, Wang SA (2005) The comparative study of performance of three types of chaos immune optimization combination algorithms. J Syst Simul 17:307–309

    Google Scholar 

  32. Ji MJ, Tang HW (2004) Application of chaos in simulated annealing. Chaos Solitons Fractals 21:933–941

    Article  MATH  Google Scholar 

  33. Wang Y, Liu JH (2010) Chaotic particle swarm optimization for assembly sequence planning. Robot Cim-Int Manuf 26:212–222

    Article  MATH  Google Scholar 

  34. Gao L, Liu X (2009) A resilient particle swarm optimization algorithm based on chaos and applying it to optimize the fermentation process. Int J Inf Syst Sci 5:380–391

    MathSciNet  Google Scholar 

  35. He Y, Zhou J, Li C, Yang J, Li Q (2008) A precise chaotic particle swarm optimization algorithm based on improved tent map. In Proceedings of the 4th international conference on natural computation, pp 569–573

    Google Scholar 

  36. Baykasoglu A (2012) Design optimization with chaos embedded great deluge algorithm. Appl Soft Comput 12(3):1055–1067

    Article  Google Scholar 

  37. Kaveh A, Sheikholeslami R, Talatahari S, Keshvari-Ilkhichi M (2014) Chaotic swarming of particles: a new method for size optimization of truss structures. Adv Eng Softw 67:136–147

    Article  Google Scholar 

  38. Lamberti L (2008) An efficient simulated annealing algorithm for design optimization of truss structures. Comput Struct 86:1936–1953

    Article  Google Scholar 

  39. Togan V, Daloglu AT (2008) An improved genetic algorithm with initial population strategy and self-adaptive member grouping. Comput Struct 86:1204–1218

    Article  Google Scholar 

  40. Degertekin SO (2012) Improved harmony search algorithms for sizing optimization of truss structures. Comput Struct 92–93:229–241

    Article  Google Scholar 

  41. Kaveh A, Talatahari S (2009) Size optimization of space trusses using big bang-big crunch algorithm. Comput Struct 87:1129–1140

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Tehran, Iran

    A. Kaveh

Authors
  1. A. Kaveh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kaveh, A. (2014). Chaos Embedded Metaheuristic Algorithms. In: Advances in Metaheuristic Algorithms for Optimal Design of Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-05549-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-05549-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05548-0

  • Online ISBN: 978-3-319-05549-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation