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

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation metho ds such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shift ing level into each exponential intervening variable to avoid the lack of d efinition of the conventional exponential intervening variables due to zero - or negative-valued design variables. Then a new quadratic approximation w hose Hessian matrix has only diagonal elements of different values is propo sed in terms of these shifted exponential intervening variables. These diag onal elements are determined in a closed form that corrects the typical err or in the approximate gradient of the TANA series due to the lack of defini tion of exponential type intervening variables and their incomplete second- order terms. Also, a correction coefficient is multiplied to the pre-determ ined quadratic term to match the value of approximate 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 a pplied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed me thod gives more efficient and reliable results than TANA-3.