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Acta Mechanica Sinica

, Volume 34, Issue 2, pp 275–284 | Cite as

A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser

  • Y. Zheng
  • J. Chen
Research Paper
  • 110 Downloads

Abstract

A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multi-objective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid’s area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Pareto-optimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effectively deal with multi-objective optimizations with black-box functions.

Keywords

Multi-objective particle swarm optimization Kriging meta-model Trapezoid index Deepwater composite riser 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant 11572134).

References

  1. 1.
    Deb, K., Pratap, A., Agarwal, S., et al.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2006)CrossRefGoogle Scholar
  2. 2.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm. Computer Engineering and Networks Laboratory (TIK)-Report 103, Switerland, May (2001)Google Scholar
  3. 3.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, 1942–1948 (1995)Google Scholar
  4. 4.
    Khalili-Damghania, K., Abtahil, A.R., Tavana, M.: A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems. Reliab. Eng. Syst. Saf. 111, 58–75 (2013)CrossRefGoogle Scholar
  5. 5.
    Garg, H., Sharma, S.P.: Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput. Ind. Eng. 64, 247–255 (2013)CrossRefGoogle Scholar
  6. 6.
    Zhang, Y., Gong, D.W., Ding, Z.: A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf. Sci. 192, 213–227 (2012)CrossRefGoogle Scholar
  7. 7.
    Abido, M.A.: Two-level of nondominated solutions approach to multiobjective particle swarm optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2007), London, UK, 726–733. Assoc Computing Machinery, New York, July, 2007Google Scholar
  8. 8.
    Branke, J., Mostaghim, S.: About selecting the personal best in multi-objective particle swarm optimization. In: Proceedings of the 9th International Conference on Parallel Problem Solving from Nature (PPSNIX), Reykjavik, Iceland, 523–532. Springer, Berlin (2006)Google Scholar
  9. 9.
    Coello, C.A.C., Pulido, G.T., Lechuga, M.S.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8, 256–279 (2004)CrossRefGoogle Scholar
  10. 10.
    Zhao, S.Z., Suganthan, P.N.: Two-lbests based multi-objective particle swarm optimizer. Eng. Optim. 43, 1–17 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Mostaghim, S., Teich, J.: Strategies for Finding Good Local Guides in Multi-objective Particle Swarm Optimization. In: Swarm Intelligence Symposium 2003, Indianapolis, USA (2003)Google Scholar
  12. 12.
    Regis, R.G.: Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Trans. Evol. Comput. 18, 326–347 (2014)CrossRefGoogle Scholar
  13. 13.
    Akhtar, T., Shoemaker, C.A.: Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. J. Glob. Optim. 64, 17–32 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Isaacs, A., Ray, T., Smith, W.: Multi-objective design optimization using multiple adaptive spatially distributed surrogates. Int. J. Prod. Dev. 9, 188–217 (2009)CrossRefGoogle Scholar
  15. 15.
    Ray, T., Smith, W.: A surrogate assisted parallel multi-objective evolutionary algorithm for robust engineering design. Eng. Optim. 38, 997–1011 (2006)CrossRefGoogle Scholar
  16. 16.
    Emmerich, M.T.M., Giannakoglou, K., Naujoks, B.: Single- and multi-objective evolutionary optimization assisted by Gaussian random field meta-models. IEEE Trans. Evol. Comput. 10, 421–439 (2006)CrossRefGoogle Scholar
  17. 17.
    Singh, P., Couckuyt, I., Ferranti, F., et al.: A constrained multi-objective surrogate-based optimization algorithm. In: Proceedings of 2014 IEEE Congress on Evolutionary Computation (CEC), 3080–3087. IEEE (2014)Google Scholar
  18. 18.
    Ray, T., Liew, K.M.: A swarm metaphor for multi-objective design optimization. Eng. Optim. 34, 141–153 (2002)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina

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