Efficient mechanical system optimization using two-point diagonal quadratic approximation in the nonlinear intervening variable space
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For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determinded quadratic term to match the value of aproximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.
Key WordsTwo-Point Approximation Sequential Approximate Optimization
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- Arora, J. S., 1989,Introduction to Optimum Design, McGraw-Hill, New York, pp. 489–493.Google Scholar
- Haug, E. J. and Arora, J. S., 1979,Applied optimal Design Mechanical and Structural Systems, John Wiley & Sons, New York, pp. 242–245.Google Scholar
- Reklaitis, G. V., Ravindran, A. and Ragsdell, K. M., 1983,Engineering Optimization Methods and Applications, John Wiley & Sons, New York, pp. 11–15.Google Scholar
- Xu, S. and Grandhi, R. V., 1998, “An Effective Two-Point Function Approximation for Design Optimization,”Proceedings of the AIAA/ASME/ASCE/AHS/ASC 39th Structural, Structural Dynamics, and Materials Conference, Long beach CA, April 20–23, pp. 2181–2191.Google Scholar