多目标结构优化设计的中心法

METHOD OF CENTERS FOR STRUCTURAL OPTIMIZATION WITH MULTIPLE OBJECTIVES

提出一个求解多目标结构优化设计的中心法,该方法可以看作是求解单目标优化问题中心法的直接推广.它针对每个目标函数引进一个“移动靶”以形成各目标函数的水平截集,然后通过计算并跟踪这些目标函数的水平集与原约束集合形成的交集中心,来达到求解多目标优化问题的目的.这个方法在不增加额外计算量的情况下,实现了多目标优化与单目标优化的算法统一,因此非常容易在现有的结构优化设计的程序中实现.给出了几个结构优化设计问题的算例,验证了算法的有效性和可靠性.

This paper presents an efficient algorithm, named as method of centers, for solving structural optimization problems with multiple objectives. It is a natural extension of the method of centers for general nonlinear programming. The present method solves the multi-objective problem by introducing an upper bound on each objective function and consecutively calculating the center of intersection sets of the original feasible region with the level sets of objective functions. In initiation of the algorithm, all upper bounds are set to be sufficiently large such that the iteration is forced to move towards the original feasible region, and are then reduced according to certain criterion whenever the iterations become feasible. As such, the feasible region becomes smaller and smaller with iterations. This method unifies the algorithms for both single and multiple objective cases so that it greatly facilitates to adapt this algorithm to the existing FEM analysis and structural optimization programs. Some examples are provided to demonstrate the effectiveness and robustness of proposed method.