An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model

  • Xin LiuEmail author
  • Xinyu Wang
  • Lin Sun
  • Zhenhua Zhou
Research Paper


Compared with the interval model, the ellipsoidal convex model can describe the correlation of the uncertain parameters through a multidimensional ellipsoid, and whereby excludes extreme combination of uncertain parameters and avoids over-conservative designs. In this paper, we attempt to propose an efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model. Firstly, each uncertain objective function is transformed into deterministic optimization problem by using nonlinear interval number programming (NINP) method and a possibility degree of interval number is applied to deal with the uncertain constraints. The penalty function method is suggested to transform the uncertain optimization problem into deterministic non-constrained optimization problem. Secondly, the approximation model based on radial basis function (RBF) is applied to improve computational efficiency. For ensuring the accuracy of the approximation models, a local-densifying approximation technique is suggested. Then, the micro multi-objective genetic algorithm (μMOGA) is used to optimize design parameters in the outer loop and the intergeneration projection genetic algorithm (IP-GA) is used to treat uncertain vector in the inner loop. Finally, two numerical examples and an engineering example are investigated to demonstrate the effectiveness of the present method.


Uncertainty structures Multi-objective optimization Ellipsoidal convex model Local-densifying approximation technique 



The authors would also like to thank anonymous reviewers for their valuable comments.

Funding information

This work is supported by the National Natural Science Foundation of China (Grant No.51775057), the Hunan Provincial Natural Science Foundation of China (No.2017JJ3323), the Research Foundation of Education Department of Hunan Province (No.16B014), and the Science Foundation of State Key Laboratory of Mechanical Transmissions (No.SKLMT-KFKT-201609).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Safety Design and Reliability Technology for Engineering VehicleChangsha University of Science and TechnologyChangshaPeople’s Republic of China
  2. 2.The State Key Laboratory of Mechanical TransmissionsChongqing UniversityChongqingPeople’s Republic of China

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