可行方向SUMT外点法的研究及应用

Study and application of feasible direction SUMT exterior penalty method

针对序列无约束极小化技术(sequential unconstrained minimization technology,SUMT)外点法中由于设计变量越界而导致优化失败的问题,分析了设计变量越界的原因,将SUMT外点法和可行方向法相结合,提出了一种可行方向SUMT(feasible direction SUMT,FD-SUMT)外点法。用可行方向法的思想处理设计变量的约束,将搜索空间限定在设计变量可行域内。与传统的SUMT外点法相比,该方法除实现简单外,更具有鲁棒性高、收敛快等优点。通过数值算例和工程应用实例验证了FD-SUMT外点法的性能。优化结果表明,该方法消除了设计变量越界的情况,收敛速度和鲁棒性明显高于传统的SUMT外点法,而且初值选取容易,具有工程实用性。

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.