Genetic Algorithms for Optimization of 3D Truss Structures

  • Vedat Toğan
  • Ayşe Turhan DaloğluEmail author
Part of the Modeling and Optimization in Science and Technologies book series (MOST, volume 7)


Various optimization techniques have been applied to find the optimum solutions of structural design problems in the last 50 or 60 years. Simple structural optimization problems with continuous design variables have been solved initially using mathematically diverse techniques. New approaches called meta-heuristic techniques have been emerging along with the progress of traditional methods. This chapter first introduces the mathematical formulations of optimization problems and then gives a summary and development process of the preliminary techniques such as genetic algorithm (GA) in obtaining the optimum solutions. The mathematical formulations of the structural optimization problems are associated with the design variables, loads, structural responses, and constraints. Strategies are proposed to improve the performance of the technique to reduce the number of search and the size of the problem. Finally, some examples related to 3D truss structures are presented.


  1. 1.
    Horst, R., Pardolos, P.M.: Handbook of global optimization. Kluwer Academic Publishers, Dordrecht (1995)CrossRefGoogle Scholar
  2. 2.
    Nocedal, J., Wright, J.S.: Numerical optimization. Springer, New York (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chong, E.K.P., Zak, S.H.: Introduction to Optimization. Wiley, New York (2002)zbMATHGoogle Scholar
  4. 4.
    Paton, R.: Computing with Biological Metaphors. Chapman & Hall, London (1994)Google Scholar
  5. 5.
    Adami, C.: An Introduction to Artificial Life. Springer, New York (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Matheck, C.: Design in Nature: Learning from Trees. Springer, Berlin (1998)CrossRefGoogle Scholar
  7. 7.
    Mitchell, M.: An Introduction to Genetic Algorithms. The MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  8. 8.
    Flake, G.W.: The Computational Beauty of Nature. MIT Press, Cambridge (2000)Google Scholar
  9. 9.
    Kennedy, J., Eberhart, R., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  10. 10.
    Glover, F., Kochenberger, G.A.: Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht (2003)CrossRefzbMATHGoogle Scholar
  11. 11.
    Dreo, J., Petrowski, A., Siarry, P., Taillard, E.: Meta-Heuristics for Hard Optimization. Springer, Berlin (2006)zbMATHGoogle Scholar
  12. 12.
    Sean, L.: Essentials of Metaheuristics (2015).
  13. 13.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Co., Reading (1989)Google Scholar
  14. 14.
    Rajeev, S., Krishnamoorthy, C.S.: Discrete Optimization of Structures Using Genetic Algorithms. J. Struct. Eng. 118(5), 1233–1250 (1992)CrossRefGoogle Scholar
  15. 15.
    Tang, X.,·Bassir, D.H., Zhang, W.: Shape, Sizing Optimization and Material Selection Based on Mixed Variables and Genetic Algorithm. Optim Eng 12, 111–128 (2011)Google Scholar
  16. 16.
    Ahmadi, M., Arabi, M., Hoag, D.L., Engel, B.A.: A mixed discrete-continuous variable multiobjective genetic algorithm for targeted implementation of nonpoint source pollution control practices. Water Resour. Res. 49, 8344–8356 (2013)CrossRefGoogle Scholar
  17. 17.
    Yuan, Q.K., Li, S.J., Jiang, L.L., Tang, W.Y.: A mixed-coding genetic algorithm and its application on gear reducer optimization. Fuzzy Info. Eng. 2(AISC 62), 753–759 (2009)Google Scholar
  18. 18.
    Rao, S.S., Xiong, T.: A hybrid genetic algorithm for mixed-discrete design optimization. J. Mech. Des. 127(6), 1100–1112 (2004)CrossRefGoogle Scholar
  19. 19.
    Kumar, A.: Encoding scheme in genetic algorithm. Int. J. Adv. Res. IT Eng. 2(3), 1–7 (2013)Google Scholar
  20. 20.
    Kumar R, Jyotishree (2012) Novel encoding scheme in genetic algorithms for better fitness. Int. J. Eng. Adv. Tech. 1(6), 214–218Google Scholar
  21. 21.
    Zhu, J., Zhou, D., Li, F., Fu, T.: Improved real coded genetic algorithm and its simulation. J. Softw. 9(2), 389–397 (2014)CrossRefGoogle Scholar
  22. 22.
    Nanakorn, P., Meesomklin, K.: An adaptive function in genetic algorithms for structural design optimization. Comp. Struct. 79(29–30), 2527–2539 (2001)CrossRefGoogle Scholar
  23. 23.
    Kramer, O., Schwefel, H.P.: On three new approaches to handle constraints within evolution strategies. Nat. Comp. 5, 363–385 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Lemonge, A.C.C., Barbosa, H.J.C.: An adaptive penalty scheme for genetic algorithms in structural optimization. Int. J. Numer. Meth. Eng. 59, 703–736 (2004)CrossRefzbMATHGoogle Scholar
  25. 25.
    Coello, C.A.C.: Use of a self-adaptive penalty approach for engineering optimization problems. Comp. Ind. 41, 113–127 (2000)CrossRefGoogle Scholar
  26. 26.
    Lin, C.H.: A rough penalty genetic algorithm for constrained optimization. Inform. Sci. 241, 119–137 (2013)CrossRefGoogle Scholar
  27. 27.
    Lemonge, A.C.C., Barbosa, H.J.C., Bernardino, H.S.: A family of adaptive penalty schemes for steady-state genetic algorithms. Proceeding in WCCI 2012, June, pp. 10–15. Brisbane, Australia (2012)Google Scholar
  28. 28.
    Kaya, M.: The effects of two new crossover operators on genetic algorithm performance. Appl. Soft Comput. 11, 881–890 (2011)CrossRefGoogle Scholar
  29. 29.
    Thanh, P.D., Binh H.T.T., Lam, B.T.: New mechanism of combination crossover operators in genetic algorithm for solving the traveling salesman problem. Knowl. Syst. Eng. (AISC 326), 753–759 (2015)Google Scholar
  30. 30.
    Deep, K., Thakur, M.: A new mutation operator for real coded genetic algorithms. Appl. Math. Comput. 193(1), 211–230 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Toğan, V., Daloğlu, A.T.: Optimization of 3d trusses with adaptive approach in genetic algorithms. Eng. Struct. 28, 1019–1027 (2006)CrossRefGoogle Scholar
  32. 32.
    Jenkins, W.M.: A decimal-coded evolutionary algorithm for constrained optimization. Comput. Struct. 80(5–6), 471–480 (2002)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Srivinas, M., Patnaik, L.M.: Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans. Syst. Man Cybern. 24(4), 656–667 (1994)CrossRefGoogle Scholar
  34. 34.
    Toğan, V., Daloğlu, A.: An improved genetic algorithm with initial population and selfadaptive member grouping. Comput. Struct. 86, 1204–1218 (2008)CrossRefGoogle Scholar
  35. 35.
    Toğan, V., Daloğlu, A.: Adaptive approaches in genetic algorithms to catch the global optimum. Proceeding in ACE 2006, October, pp. 11–13. İstanbul, Turkey (2006)Google Scholar
  36. 36.
    Toğan, V., Daloğlu, A.: optimization of truss systems with metaheuristic algorithms and automatically member grouping. Proceeding in 4th National Steel Structures Symposium, October, pp. 24–26. İstanbul, Turkey (2011)Google Scholar
  37. 37.
    Bekiroğlu, S.: Optimum design of steel frame with genetic algorithm (in Turkish). M.Sc. thesis, Karadeniz Technical University (2003)Google Scholar
  38. 38.
    Krishnamoorthy, C.S., Venkatesh, P.P., Sudarshan, R.: Object-oriented framework for genetic algorithms with application to space truss optimization. J. Comput. Civil Eng. 16, 66–75 (2002)CrossRefGoogle Scholar
  39. 39.
    Sudarshan, R.: Genetic algorithms and application to the optimization of space trusses. A Project Report, Madras (India), Indian Institute of Technology (2000)Google Scholar
  40. 40.
    Galante, M.: Genetic algorithms as an approach to optimize real-world trusses. Int. J. Numer. Meth. Eng. 39, 361–382 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    American Institute of Steel Construction (AISC).: Manual of steel construction-allowable stress design, 9th edn. Chicago (1989)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Civil EngineeringKaradeniz Technical UniversityTrabzonTurkey

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