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


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.


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



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


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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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