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A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures

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Abstract

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front.

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References

  1. Dorn W., Gomory R., Greenberg H.: Automatic design of optimal structures. J. Mec. 3, 25–52 (1964)

    Google Scholar 

  2. Gou X., Cheng G., Yamazaki K.: A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints. Struct. Multidisc. Optim. 22, 364–372 (2001)

    Article  Google Scholar 

  3. Wang D., Zhang W.H., Jiang J.S.: Combined shape and sizing optimization of truss structures. Comput. Mech. 29, 307–312 (2002)

    Article  MATH  Google Scholar 

  4. Gou X., Liu W., Li H.: Simultaneous shape and topology optimization of truss under local and global stability constraints. Acta Mech. Solida. Sinica. 16, 95–101 (2003)

    Google Scholar 

  5. Rozvany G.I.N.: Stress ratio and compliance based methods in topology optimization-a critical review. Struct. Multidisc. Optim. 21, 109–119 (2001)

    Article  Google Scholar 

  6. Rozvany, G.I.N.: Aims, scope basic concepts and methods of topology optimization. In: Rozvany, G.I.N. (ed.) Topology Optimization in Structural Mechanics, CISM Courses and Lectures, vol. 374, pp. 1–55. Springer, Berlin (1997)

  7. Giger M., Ermanni P.: Evolutionary truss topology optimization using a graph-based parameterization concept. Struct. Multidisc. Optim. 32, 313–326 (2006)

    Article  Google Scholar 

  8. Su, R.Y., Gui, L.J., Fan, Z.: Topology and sizing optimization of truss structures using adaptive genetic algorithm with node matrix encoding. In: The 5th International Conference on Natural Computation, Tianjin, China (2009)

  9. Hajela P., Lee E.: Genetic algorithms in truss topological optimization. Int. J. Solid. Struct. 32, 3341–3357 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rajan S.D.: Sizing, shape, and topology design optimization of trusses using genetic algorithm. J. Struct. Eng. 121, 1480–1487 (1995)

    Article  Google Scholar 

  11. Soh C.K., Yang J.: Optimal layout of bridge trusses by genetic algorithms. Comput. Aided Civ. Inf. 13, 247–254 (1998)

    Article  Google Scholar 

  12. Balling R.J., Briggs R.R., Gillman K.: Multiple optimum size/shape/topology designs for skeletal structures using a genetic algorithm. J. Struct. Eng. 132, 1158–1165 (2006)

    Article  Google Scholar 

  13. Kaveh A., Kalatjari V.: Topology optimization of trusses using genetic algorithm, force method and graph theory. Int. J. Numer. Methods Eng. 58, 771–791 (2003)

    Article  MATH  Google Scholar 

  14. Kawamoto A., Bendsoe M.P., Sigmund O.: Planar articulated mechanism design by graph theoretical enumeration. Struct. Multidisc. Optim. 27, 295–299 (2004)

    Article  Google Scholar 

  15. Deb K., Pratap A., Agarwal S., Meyarivan T.: A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE. Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  16. Zitzler E., Laumanns M., Thiele L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Swiss Federal Institute Technology, Zurich (2001)

    Google Scholar 

  17. Knowles J.D., Corne D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)

    Article  Google Scholar 

  18. Knowles, J.D., Corne, D.W.: M-PAES: a memetic algorithm for multiobjective optimization. In: 2000 Congress on Evolutionary Computation, vol. 1, pp. 325–332. IEEE Service Center, Piscataway, NJ, July 2000

  19. Mathakari S., Gardoni P., Agarwal P., Raich A.: Reliability-based optimal design of electrical transmission towers using multi-objective genetic algorithms. Comput. Aided Civ. Inf. 22, 282–292 (2007)

    Article  Google Scholar 

  20. Su R.Y., Wang X., Gui L., Fan Z.: Multi-objective topology and sizing optimization of truss structures based on adaptive multi-island search strategy. Struct. Multidisc. Optim. 43(2), 275–286 (2010)

    Article  Google Scholar 

  21. Coello C.A.C., Van Veldhuizen D.A., Lamont G.B.: Evolutionary Algorithms for Solving Multi-objective Problems. Kluwer, New York (2002)

    MATH  Google Scholar 

  22. Kaveh A.: Structural Mechanics: Graph and Matrix Methods, 3rd edn. Research Studies Press, Somerset (2004)

    Google Scholar 

  23. Zitzler E., Deb K., Thiele L.: Comparison of multi-objective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)

    Article  Google Scholar 

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Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran

    A. Kaveh & K. Laknejadi

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  1. A. Kaveh
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  2. K. Laknejadi
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Correspondence to A. Kaveh.

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Kaveh, A., Laknejadi, K. A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures. Acta Mech 224, 343–364 (2013). https://doi.org/10.1007/s00707-012-0754-5

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  • DOI: https://doi.org/10.1007/s00707-012-0754-5

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