Acta Mechanica

, Volume 229, Issue 7, pp 2883–2907 | Cite as

Chaotic enhanced colliding bodies algorithms for size optimization of truss structures

  • A. Kaveh
  • A. Dadras
  • A. H. Montazeran
Original Paper


Colliding bodies optimization (CBO) is a recently developed population-based metaheuristic algorithm that mimics the collision between two bodies, where the momentum conservation law is utilized to determine the new positions of the agents in the search space. To overcome some deficiencies in the CBO like slow convergence and getting trapped in local minima, an enhanced version of the algorithm, ECBO, is proposed. One of the efficient techniques to improve the performances of the metaheuristic algorithms is adding chaos to their structure. In this paper, chaos is incorporated into the ECBO through three types of embeddings and ten chaotic maps. Proposing different chaotic versions, finding the best version among chaotic versions and improving the efficiency of the standard CBO and ECBO are the main achievements of this study. The results of examining some mathematical and engineering problems show how some chaotic ECBO variants can enhance the performance of the standard ECBO.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

707_2018_2149_MOESM1_ESM.xlsx (47 kb)
Supplementary Materials: Supplementary data associated with this article containing all optimal design variables for different structures, chaotic maps and scenarios can be found in the online version. (pdf 47.3KB)


  1. 1.
    Talbi, E.-G.: Metaheuristics: From Design to Implementation, vol. 74. Wiley, Hoboken (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Kaveh, A.: Advances in Metaheuristic Algorithms for Optimal Design of Structures, 2nd edn. Springer, Switzerland (2017)CrossRefzbMATHGoogle Scholar
  3. 3.
    Goldberg, D.E., Holland, J.H.: Genetic algorithms and machine learning. Mach. Learn. 3(2), 95–99 (1988)CrossRefGoogle Scholar
  4. 4.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 1995. MHS’95, pp. 39–43. IEEE (1995)Google Scholar
  5. 5.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Geem, Z.W., Kim, J.H., Loganathan, G.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)CrossRefGoogle Scholar
  7. 7.
    Geem, Z.W.: Recent Advances in Harmony Search Algorithm, vol. 270. Springer, Berlin (2010)zbMATHGoogle Scholar
  8. 8.
    Kaveh, A., Talatahari, S.: A novel heuristic optimization method: charged system search. Acta Mech. 213(3), 267–289 (2010)CrossRefzbMATHGoogle Scholar
  9. 9.
    Kaveh, A.: Ray optimization algorithm. In: Advances in Metaheuristic Algorithms for Optimal Design of Structures, pp. 233–276. Springer, Cham (2014)Google Scholar
  10. 10.
    Kaveh, A., Farhoudi, N.: A new optimization method: dolphin echolocation. Adv. Eng. Softw. 59, 53–70 (2013)CrossRefGoogle Scholar
  11. 11.
    Kaveh, A., Mahdavi, V.R.: Colliding bodies optimization: a novel meta-heuristic method. Comput. Struct. 139, 18–27 (2014). CrossRefGoogle Scholar
  12. 12.
    Blum, C., Roli, A., Sampels, M.: Hybrid Metaheuristics: An Emerging Approach to Optimization, vol. 114. Springer, Berlin (2008)zbMATHGoogle Scholar
  13. 13.
    Blum, C., Puchinger, J., Raidl, G.R., Roli, A.: Hybrid metaheuristics in combinatorial optimization: a survey. Appl. Soft Comput. 11(6), 4135–4151 (2011)CrossRefzbMATHGoogle Scholar
  14. 14.
    Gharooni-fard, G., Moein-darbari, F., Deldari, H., Morvaridi, A.: Scheduling of scientific workflows using a chaos-genetic algorithm. Procedia Comput. Sci. 1(1), 1445–1454 (2010)CrossRefGoogle Scholar
  15. 15.
    Mingjun, J., Huanwen, T.: Application of chaos in simulated annealing. Chaos Solitons Fractals 21(4), 933–941 (2004)CrossRefzbMATHGoogle Scholar
  16. 16.
    Alatas, B., Akin, E., Ozer, A.B.: Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals 40(4), 1715–1734 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kaveh, A., Sheikholeslami, R., Talatahari, S., Keshvari-Ilkhichi, M.: Chaotic swarming of particles: a new method for size optimization of truss structures. Adv. Eng. Softw. 67, 136–147 (2014)CrossRefGoogle Scholar
  18. 18.
    Alatas, B.: Chaotic harmony search algorithms. Appl. Math. Comput. 216(9), 2687–2699 (2010)zbMATHGoogle Scholar
  19. 19.
    Gandomi, A., Yang, X.-S., Talatahari, S., Alavi, A.: Firefly algorithm with chaos. Commun. Nonlinear Sci. Numer. Simul. 18(1), 89–98 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Kohli, M., Arora, S.: Chaotic grey wolf optimization algorithm for constrained optimization problems. J. Comput. Des. Eng. (2017).
  21. 21.
    Talatahari, S., Kaveh, A., Sheikholeslami, R.: Chaotic imperialist competitive algorithm for optimum design of truss structures. Struct. Multidiscip. Optim. 46(3), 355–367 (2012)CrossRefGoogle Scholar
  22. 22.
    Talatahari, S., Kaveh, A., Sheikholeslami, R.: Engineering design optimization using chaotic enhanced charged system search algorithms. Acta Mech. 223(10), 2269–2285 (2012)CrossRefzbMATHGoogle Scholar
  23. 23.
    Sheikholeslami, R., Kaveh, A.: A survey of chaos embedded meta-heuristic algorithms. Int. J. Optim. Civ. Eng. 3(4), 617–633 (2013)Google Scholar
  24. 24.
    Kaveh, A., Ilchi Ghazaan, M.: Enhanced colliding bodies optimization for design problems with continuous and discrete variables. Adv. Eng. Softw. 77, 66–75 (2014)CrossRefGoogle Scholar
  25. 25.
    Kaveh, A., Mahdavi, V.R.: Colliding Bodies Optimization: Extensions and Applications. Springer, Cham (2015)CrossRefzbMATHGoogle Scholar
  26. 26.
    He, D., He, C., Jiang, L.-G., Zhu, H.-W., Hu, G.R.: Chaotic characteristics of a one-dimensional iterative map with infinite collapses. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(7), 900–906 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Devaney, R.L., Eckmann, J.-P.: An introduction to chaotic dynamical systems. Phys. Today 40, 72 (1987)CrossRefGoogle Scholar
  28. 28.
    Bucolo, M., Caponetto, R., Fortuna, L., Frasca, M., Rizzo, A.: Does chaos work better than noise? IEEE Circuit Syst. Mag. 2(3), 4–19 (2002)CrossRefGoogle Scholar
  29. 29.
    Erramilli, A., Singh, R., Pruthi, P.: Modeling Packet Traffic with Chaotic Maps. KTH, Stockholm (1994)zbMATHGoogle Scholar
  30. 30.
    Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (2002)CrossRefzbMATHGoogle Scholar
  31. 31.
    Peitgen, H.-O., Jürgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer, Berlin (2006)zbMATHGoogle Scholar
  32. 32.
    Kaveh, A., Ilchi Ghazaan, M.: Computer codes for colliding bodies optimization and its enhanced version. Int. J. Optim. Civ. Eng. 4(3), 321–332 (2014)Google Scholar
  33. 33.
    Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design: With Applications, vol. 1. McGraw-Hill, New York (1984)zbMATHGoogle Scholar
  34. 34.
    LRFD, A.: American Institute of Steel Construction (AISC). Load and Resistance Factor Design. AISC, Chicago (1994)Google Scholar
  35. 35.
    Construction, A.: Manual of Steel Construction: Allowable Stress Design. American Institute of Steel Construction (AISC) Chicago (1989)Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre of Excellence for Fundamental Studies in Structural EngineeringIran University of Science and TechnologyTehranIran
  2. 2.School of Civil EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations