Skip to main content
Log in

Solving truss topological optimization via Swarm Intelligence

  • Construction Management
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

Structural topological optimization is the most general form of structural optimization and requires a less detailed description of the concept. One of the most exciting and challenging problems in this field is to find optimized layouts with minimization of compliance (maximization of stiffness) for a given total mass of the structure discretized by truss members, which cannot be well solved by evolutionary algorithms. Particle Swarm Optimization (PSO) is a new paradigm of Swarm Intelligence which is inspired by concepts from ‘Social Psychology’ and ‘Artificial Life’. PSO is particularly a preferable candidate to solve highly nonlinear, non-convex and even discontinuous problems and has been applied to many different kinds of optimization problems. The motivation of this paper is to propose an enhanced Lbest based PSO and geometrical consistency check tightly connecting to the ground structure approach to break through in this optimization field. Through a popular benchmark test, two kinds of Modified Lbest based PSO (MLPSO) exhibited competitive performance due to improved global searching ability.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Achtziger, W. and Stolpe, M. (2007). “Truss topology optimization with discrete design variables-Guaranteed global optimality and benchmark examples.” Structural and Multidisciplinary Optimization, Vol. 34, No. 1, pp. 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  • Achtziger, W., Bendsøe, M. Ben-Tal, A., and Zowe, J. (1992). “Equivalent displacement based formulations for maximum strength Truss topology design.” IMPACT of Computing in Science and Engineering, Vol. 4, No. 4, pp. 315–345.

    Article  MATH  MathSciNet  Google Scholar 

  • Alatas, B., Akin, E. and Ozer, A. B. (2009). “Chaos embedded particle swarm optimization algorithms.” Chaos, Solitons & Fractals, Vol. 40, No. 4, pp. 1715–1734.

    Article  MATH  MathSciNet  Google Scholar 

  • Angeline, P. J. (1998). “Evolutionary optimization versus particle swarm optimization: philosophy and performance differences.” Evolutionary Programming VII, Springer, Berlin Heidelberg, pp. 601–610.

    Chapter  Google Scholar 

  • Ben-Tal, A. and Bendsøe, M. P. (1993). “A new method for optimal truss topology design.” SIAM Journal on Optimization, Vol. 3, No. 2, pp. 322–358.

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal, A. and Zibulevsky, M. (1997). “Penalty/barrier multiplier methods for convex programming problems.” Siam Journal of Optimization, Vol. 7, No. 2, pp. 347–366.

    Article  MATH  MathSciNet  Google Scholar 

  • Bendsøe, M. P. and Sigmund, O. (2003). Topology optimization: Theory, methods and applications, Spinger, Verlag.

    Google Scholar 

  • Bendsøe, M. P., Ben-Tal, A., and Zowe, J. (1994). “Optimization methods for truss geometry and topology design.” Structural and Multidisciplinary Optimization, Vol. 7, No. 3, pp. 141–159.

    Article  Google Scholar 

  • Bochenek, B. and Foryoe, P. (2006). “Structural optimization for postbuckling behavior using particle swarms.” Structural and Multidisciplinary Optimization, Vol. 32, No. 6, pp. 521–531.

    Article  Google Scholar 

  • Christensen, S. and Oppacher, F. (2001). “What can we learn from no free lunch? A first attempt to characterize the concept of a searchable function.” Proc. Genetic and Evolutionary Computation Conference, Vol. 2001, pp. 1219–1226.

    Google Scholar 

  • Clerc, M. (1999). “The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization.” Proc., The 1999 congress on Evolutionary Computation, CEC 99, IEEE, Vol. 3, pp. 1951–1957.

    Article  Google Scholar 

  • Cui, Z. and Zeng, J. (2004). “A guaranteed global convergence particle swarm optimizer.” Rough Sets and Current Trends in Computing, Springer, Berlin, Heidelberg, pp. 762–767.

    Chapter  Google Scholar 

  • Dorn, W. S., Gomory, R. S., and Greenberg, H. J. (1964). “Automatic design of optimal structures.” Journal de Mecanique, Vol. 3, No. 6, pp. 2552.

    Google Scholar 

  • Eberhart, R. C. and Kennedy, J. (1995). “A new optimizer using particle swarm theory.” Proc., 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, Vol. 1, pp. 39–43.

    Article  Google Scholar 

  • Eberhart, R. C., Kennedy, J., and Shi, Y. (2001). Swarm intelligence, Elsevier, Burlington, MA.

    Google Scholar 

  • Fiacco, A. V. and McCormick, G. P. (1964). “The sequential unconstrained minimization technique for nonlinear programing, a primal-dual method.” Management Science, Vol. 10, No. 2, pp. 360–366.

    Article  Google Scholar 

  • Fiacco, A. V. and McCormick, G. P. (1990). Nonlinear programming: Sequential unconstrained minimization techniques, Society for Industrial Mathematics, Vol. 4.

    Book  MATH  Google Scholar 

  • Fleron, P. (1964). “The minimum weight of trusses.” Bygningsstatiske Meddelelser, Vol. 35, No. 3, pp. 81–96.

    Google Scholar 

  • Fourie, P. C. and Groenwold, A. A. (2002). “The particle swarm optimization algorithm in size and shape optimization.” Structural and Multidisciplinary Optimization, Vol. 23, No. 4, pp. 259–267.

    Article  Google Scholar 

  • Giger, M. and Ermanni, P. (2006). “Evolutionary truss topology optimization using a graph-based parameterization concept.” Structural and Multidisciplinary Optimization, Vol. 32, No. 4, pp. 313–326.

    Article  MathSciNet  Google Scholar 

  • Hajela, P. and Lee, E. (1995). “Genetic algorithms in truss topological optimization.” International Journal of Solids and Structures, Vol. 32, No. 22, pp. 3341–3357.

    Article  MATH  MathSciNet  Google Scholar 

  • Hu, X. and Eberhart, R. C. (2002). “Adaptive particle swarm optimization: Detection and response todynamic systems.” Proc., Computational Intelligence, IEEE, Vol. 2, pp. 1666–1670.

    Google Scholar 

  • Jarre, F., Kocvara, M., and Zowe, J. (1998). “Optimal truss design by interior-point methods.” Siam Journal of Optimization, Vol. 8, No. 4, pp. 1084–1107.

    Article  MATH  MathSciNet  Google Scholar 

  • Kaoa, Y. T. and Zahara, E. (2008). “A hybrid genetic algorithm and particle swarm optimization for multimodal functions.” Applied Soft Computing, Vol. 8, No. 2, pp. 849–857.

    Article  Google Scholar 

  • Krink, T. and Løvbjerg, M. (2002). “The life cycle model: Combining particle swarm optimisation, genetic algorithms and hill climbers.” Proc. Parallel Problem Solving from Nature VII, Springer, Berlin Heidelberg, pp. 621–630.

    Google Scholar 

  • Levitin, G., Hu, X. H., and Dai, Y. S. (2007). “Particle swarm optimization in reliability engineering.” Computational Intelligence in Reliability Engineering, Springer Berlin Heidelberg, pp. 83–112.

    Chapter  Google Scholar 

  • Lewiński, T. and Rozvany, G. (2007). “Exact analytical solutions for some popular benchmark problems in topology optimization II: Three-sided polygonal supports.” Structural and Multidisciplinary Optimization, Vol. 33, No. 4, pp. 337–349.

    Article  MathSciNet  Google Scholar 

  • Lewiński, T. and Rozvany, G. (2008). “Exact analytical solutions for some popular benchmark problems in topology optimization III: Lshaped domains.” Structural and Multi-disciplinary Optimization, Vol. 35, No. 2, pp. 165–174.

    Article  Google Scholar 

  • Lewiński, T., Zhou, M., and Rozvany, Gin (1993). “Exact least-weight truss layouts for rectangular domains with various support conditions.” Structural and Multidisciplinary Optimization, Vol. 6, No. 1, pp. 65–67.

    Article  Google Scholar 

  • Masuda, K., Kurihara, K., and Aiyoshi, E. (2010). “A penalty approach to handle inequality constraints in particle swarm optimization.” Proc., Systems Man and Cybernetics (SMC), IEEE, pp. 2520–2525.

    Google Scholar 

  • Mendes, R., Kennedy, J., and Neves, J. (2004). “The fully informed particle swarm: Simpler, maybe better.” IEEE Transactions on Evolutionary Computation, Vol. 8, No. 3, pp. 204–210.

    Article  Google Scholar 

  • Michell, AGM. (1904). “The limits of economy of material in frame structures.” Phil. Mag., Vol. 8, No. 47, pp. 589–597.

    Article  MATH  Google Scholar 

  • Nocedal, J. and Wright, S. J. (1999). Numerical optimization, Springer, Vol. 2, New York.

    Book  MATH  Google Scholar 

  • Ohsaki, M. and Swan, C. C. (2002). “Topology and geometry optimization of trusses and frames.” Recent Advances in Optimal Structural Design, pp. 97–123.

    Google Scholar 

  • Poli, R. (2007). “An analysis of publications on particle swarm optimization applications.” Tech. Rep. CSM-469, Department of Computing and Electronic Systems, University of Essex, Colchester, Essex, UK.

    Google Scholar 

  • Prez, R. E. and Behdinan, K (2007). “Particle swarm approach for structural design optimization.” Computer and Structures, Vol. 85, Nos. 19–20, pp. 1579–1588.

    Article  Google Scholar 

  • Pulido, G. T. and Coello, C. A. C. (2004). “A constraint-handling mechanism for particle swarm optimization.” Evolutionary Computation, IEEE, Vol. 2, pp. 1396–1403.

    Google Scholar 

  • Rozvany, G. (1989). “Structural design via optimality criteria.” Mechanics of Elastic and Inelastic Solids, Vol. 8.

    Google Scholar 

  • Rozvany, G. (1996). “Difficulties in truss topology optimization with stress, local buckling and system stability constraints.” Structural and Multidisciplinary Optimization, Vol. 11, No. 3, pp. 213–217.

    Article  Google Scholar 

  • Rozvany, G. (1998). “Exact analytical solutions for some popular benchmark problems in topology optimization.” Structural and Multidisciplinary Optimization, Vol. 15, No. 1, pp. 42–48.

    Article  MATH  MathSciNet  Google Scholar 

  • Rule, W. K. (1994). “Automatic truss design by optimized growth.” Journal of Structural Engineering, Vol. 120, No. 10, pp. 3063–3070.

    Article  Google Scholar 

  • Shelokar, P., Siarry, P., Jayaraman, V., Kulkarni, B. (2007). “Particle swarm and ant colony algorithms hybridized for improved continuous optimization.” Applied Mathematics and Computation, Vol. 188, No. 1, pp. 129–142.

    Article  MATH  MathSciNet  Google Scholar 

  • Shi, Y., EDS Embedded System Team, Kokomo, and Eberhart, R. C. (2001). “Fuzzy adaptive particle swarm optimization.” Proc., the 2001 Congress on Evolutionary Computation, IEEE, Vol. 1, pp. 101–106.

    Article  Google Scholar 

  • Spillers, W. R. and MacBain, K. M. (2009). Structural optimization, Springer.

    MATH  Google Scholar 

  • Topping, B. H. V., Khan, A, I., and Leite, J. P. D. B. (1996). “Topological design of truss structures using simulated annealing.” Structural Engineering Review, Vol. 8, Nos. 2–3, pp. 301–314.

    Google Scholar 

  • Venter, G. and Sobieszczanski-Sobieski, J. (2004). “Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization.” Struct. Multidiscip. Optim., Vol. 26, No. 1–2, pp. 121–131.

    Article  Google Scholar 

  • Zhou, M. (1996). “Difficulties in truss topology optimization with stress and local buckling constraints.” Structural and Multidisciplinary Optimization, Vol. 11, No. 1, pp. 134–136.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bin Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, B., Zhang, Q. & Zhou, Z. Solving truss topological optimization via Swarm Intelligence. KSCE J Civ Eng 19, 1962–1972 (2015). https://doi.org/10.1007/s12205-015-0218-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-015-0218-2

Keywords

Navigation