KSME International Journal

, Volume 15, Issue 9, pp 1257–1267

Efficient mechanical system optimization using two-point diagonal quadratic approximation in the nonlinear intervening variable space

  • Min-Soo Kim
  • Jong-Rip Kim
  • Jae-Young Jeon
  • Dong-Hoon Choi
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design

Abstract

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 Words

Two-Point Approximation Sequential Approximate Optimization 

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2001

Authors and Affiliations

  • Min-Soo Kim
    • 1
  • Jong-Rip Kim
    • 1
  • Jae-Young Jeon
    • 1
  • Dong-Hoon Choi
    • 1
  1. 1.Center of Innovative Design Optimization TechnologyHanyang UniversitySeoulKorea

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