Structural and Multidisciplinary Optimization

, Volume 25, Issue 4, pp 261–269 | Cite as

Sizing design of truss structures using particle swarms

  • J.F. Schutte
  • A.A. Groenwold
Research paper


The optimal sizing design of truss structures is studied using the recently proposed particle swarm optimization algorithm (PSOA). The algorithm mimics the social behavior of birds. Individual birds in the flock exchange information about their position, velocity and fitness, and the behavior of the flock is then influenced to increase the probability of migration to regions of high fitness.

A simple approach is presented to accommodate the stress and displacement constraints in the initial stages of the swarm searches. Increased social pressure, at the cost of cognitive learning, is exerted on infeasible birds to increase their rate of migration to feasible regions. Numerical results are presented for a number of well-known test functions, with dimensionality of up to 21.


particle swarm optimization algorithm sizing design truss structure  


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  1. 1.
    Carlisle, A.; Dozier, G. 2000: Adapting particle swarm optimization to dynamic environments. In: Int. Conf. Artificial Intelligence, Vol. I (held in Las Vegas), pp. 429–434 Google Scholar
  2. 2.
    Carlisle, A.; Dozier, G. 2001: An off-the-shelf pso. In: Proc. Workshop on Particle Swarm Optimization (held in Indianapolis) Google Scholar
  3. 3.
    Clerc, M. 1999: The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization. In: Angeline, P.; Michalewicz, Z.; Schoenauer, M.; Yao, X.; Zalzala, A. (eds.) Proc. Congr. Evolutionary Computation, Vol. 3 (held in Washington DC), pp. 1951–1957. Piscataway, NJ, USA: IEEE Press Google Scholar
  4. 4.
    Eberhart, R. C.; Shi, Y. 2001: Tracking and optimizing dynamic systems with particle swarms. In: Proc. 2001 Congr. Evolutionary Computation CEC2001, pp. 94–100. Piscataway, NJ, USA: IEEE Press Google Scholar
  5. 5.
    Eberhart, R.; Hu, X. 1999: Human tremor analysis using particle swarm optimization. In: Angeline, P.J.; Michalewicz, Z.; Schoenauer, M.; Yao, X.; Zalzala, A. (eds.) Proc. Congr. Evolutionary Computation, Vol. 3 (held in Washington DC), pp. 1927–1930. Piscataway, NJ, USA: IEEE Press Google Scholar
  6. 6.
    Eberhart, R.; Shi, Y. 2000: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proc. 2000 Congr. Evolutionary Computation, pp. 84–88. Piscataway: IEEE Service Center Google Scholar
  7. 7.
    Fourie, P.; Groenwold, A. 2000: Particle swarms in size and shape optimization. In: Snyman, J.; Craig, K. (eds.) Proc. Workshop on Multidisciplinary Design Optimization (held in Pretoria), pp. 97–106 Google Scholar
  8. 8.
    Fourie, P.; Groenwold, A. 2001a: The particle swarm algorithm in topology optimization. In: Proc. 4th World Congr. Structural and Multidisciplinary Optimization (held in Dalian); paper no. 154, May 2001 Google Scholar
  9. 9.
    Fourie, P.; Groenwold, A. 2001b: The particle swarm optimization algorithm in size and shape optimization. Struct. Multidisc. Optim.; 23, 259–267 Google Scholar
  10. 10.
    Goldberg, D. 1989: Genetic Algorithms in Search, Optimization, and Machine Learning. New York: Addison-Wesley Google Scholar
  11. 11.
    Groenwold, A.; Stander, N.; Snyman, J. 1996: A pseudo-discrete rounding method for structural optimization. Struct. Optim. 11, 218–227 Google Scholar
  12. 12.
    Huiskes, R.; Weinans, H.; Grootenboer, H.; Dalstra, M.; Fudala, B.; Sloof, T. 1987: Adaptive bone-remodeling theory applied to prosthetic-design analysis. J. Biomech. 20, 1135–1150 Google Scholar
  13. 13.
    Kennedy, J. 2000: Stereotyping: improving particle swarm performance with cluster analysis. In: Proc. 2000 Congr. on Evolutionary Computation, pp. 1507–1512. Piscataway: IEEE Service Center Google Scholar
  14. 14.
    Kennedy, J.; Eberhart, R. 1995: Particle swarm optimization. In: Proc. 1995 IEEE Int. Conf. Neural Networks, Vol. 4 (held in Perth) pp. 1942–1948. Piscataway: IEEE Service Center Google Scholar
  15. 15.
    Løvbjerg, M.; Rasmussen, T.; Krink, T. 2001: Hybrid particle swarm optimiser with breeding and subpopulations. In: Proc. 3rd Genetic and Evolutionary Computation Conference (GECCO-2001) Google Scholar
  16. 16.
    Metropolis, N.; Rosenbluth, A.; Rosenbluth, M.; Teller, A.; Teller, E. 1953: Equation of state calculations by fast computing machine. Int. J. Fatigue 21, 1084–1092 Google Scholar
  17. 17.
    Ringertz, U. 1988: On methods for discrete structural optimization. Eng. Optim. 13, 47–64 Google Scholar
  18. 18.
    Schmit, L.; Fleury, C. 1980: Discrete-continuous variable structural synthesis using dual methods. AIAA J. 18, 1515–1524 Google Scholar
  19. 19.
    Schutte, J. 2001: Particle swarms in sizing and global optimization, Master’s thesis, University of Pretoria, Department of Mechanical Engineering; 2002 (in press) Google Scholar
  20. 20.
    Schutte, J.; Groenwold, A. 2001: A study of global optimization using particle swarms; submitted Google Scholar
  21. 21.
    Shi, Y.; Eberhart, R. 1998a: A modified particle swarm optimizer. In: Proc. IEEE Int. Conf. Evolutionary Computation, pp. 69–73. Piscataway: IEEE Press Google Scholar
  22. 22.
    Shi, Y.; Eberhart, R. 1998b: Parameter selection in particle swarm optimization. In: Porto, V.; Saravanan, N.; Waagen, D.; Eiben, A. (eds.) Evolutionary Programming VII, Lecture Notes in Computer Science 1447, pp. 591–600. Berlin: Springer Google Scholar
  23. 23.
    Sunar, M.; Belegundu, A. 1991: Trust region methods for structural optimization using exact second order sensitivity. Int. J. Numer. Methods Eng. 32, 275–293 Google Scholar
  24. 24.
    van den Bergh, F.; Engelbrecht, A. 2001: Training product unit networks using cooperative particle swarm optimizers. In: Proc. Int. Joint Conf. Neural Networks 2001, IJCNN2001 (held in Washington DC) Google Scholar
  25. 25.
    Wolpert, D.; Macready, W. 1997: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82Google Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of PretoriaPretoriaSouth Africa

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