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A method to improve computational efficiency for CSSO and BLISS


A considerable portion of the computational cost results from the solution of sensitivity information in concurrent subspace optimization and bi-level integrated system synthesis. A novel method to update sensitivity information is suggested to improve the computational efficiency in this brief note. Firstly, both the approximate insensitive terms and approximate linear terms in sensitivity information are identified, and then their values are temporarily kept constant for multiple multidisciplinary design optimization cycles. A practical engineering case study is presented to demonstrate the effectiveness of the proposed method.

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Fig. 1


i :

the i-th MDO cycle

j :

the j-th term of sensitivity information

A(j,i) :

the sensitivity value of j-th term in the i-th MDO cycle

cr(j) :

the criterion to evaluate j-th term sensitive or insensitive, if absolute value of the j-th term is below cr(j) the j-th term is insensitive.

sr (j) :

stabilization range for the j-th element in sensitivity information

to :

the total number of terms in sensitivity information

ex :

coefficient to enlarge stabilization range, ex is an integer and more than 1

re :

a coefficient to reduce stabilization range, re < 1

c (j) :

the number of MDO cycles of j-th term after sr (j) is updated

va (j,i) :

sensitivity value variation ratio of the j-th term between the (i-1)th MDO cycle and the i-th MDO cycle

p (j) :

the criterion to evaluate j-th term linear or nonlinear, if va (j,i) < p (j), the j-th term is considered as linear item

sa (j) :

update the sensitivity value of the j-th term in sensitivity information


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This work is supported by the National Science Fund for Distinguished Young Scholars under the Grant no. 10725208, Research Fund for the Doctoral Program of Higher Education of China under the Grant no. 20070532021, the national 973 program under the grant number 2010CB832705, and the National Science Foundation of China (10802028).

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Correspondence to Xu Han.

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Tao, Y.R., Han, X., Jiang, C. et al. A method to improve computational efficiency for CSSO and BLISS. Struct Multidisc Optim 44, 39–43 (2011). https://doi.org/10.1007/s00158-010-0598-3

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  • Multidisciplinary design optimization
  • Sensitivity analysis
  • Decomposition schemes
  • Computational efficiency