Comments on "Structural Optimization in the Dynamics Response Regime: A Computational Approach"
Raouf A. Ridha · AIAA Journal · 1971
I Ref. 1 the authors use the method of feasible directions in the optimization part of their paper. Although the usable feasible direction is correctly defined in their Eqs. (27) and (28), their method of obtaining the optimum feasible direction is not optimum. In order to find an optimum feasible vector the authors of Ref. 1 solve a linear programming problem in each interaction. This approach is too long and expensive for practical applications. Recently a simpler and more direct method has been developed for finding the optimum feasible direction. This method involves operations on vectors by sweeping out of the direction vector the components which lead to violation of the active constraints. Furthermore, the method presented in Ref. 2, and overlooked in Ref. 1, leads to a faster convergence towards the optimum and avoids certain local optimums. A generally steeper direction vector is used because only the effectiveactive constraints are included in the sweeping process. If the component of the direction vector along the gradient of an active constraint is positive, the movement in that direction will not lead to a violation of the active constraint. Disregarding such active constraints results in the steepest feasible direction, i.e., the direction vector closest to the gradient of the objective function. In conclusion, incorporating the approach presented in Ref. 2 for finding the optimum feasible direction will lead to an improved optimization technique, and further the contribution of Ref. 1.