Study and application of feasible direction SUMT exterior penalty method

For sequential unconstrained minimization technology (SUMT) exterior penalty method, boundaries violation of design variables may cause optimization failure. The reason for the violation of design variables is analyzed. To solve such problem, combined SUMT exterior penalty method with method of feasible directions, feasible direction SUMT (FD-SUMT) exterior penalty method is proposed. In unconstrained sub-optimizations, since the constraints of design variables are treated with feasible direction method, the search space is always limited in the feasible domain of design variables. Compared with traditional SUMT exterior penalty method, FD-SUMT exterior penalty method with better robustness and convergence performance is still easy to implement. Numerical and engineering application cases are used to validate the performance of FD-SUMT method. Optimization results demonstrate that FD-SUMT method eliminates the boundaries violation phenomenon of design variables, convergence speed and robustness performance of FD-SUMT are evidently better than SUMT, additionally, initial design point is easy to select, thus, FD-SUMT is practicable in engineering.