多目标结构优化设计的中心法
Method of Centers for Multi-objective Optimization of Structures
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摘要: 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.Abstract: This paper presents an efficient algorithm for multi-objective optimization of large-scale structures, which is a direct extension of the method of centers for solving general nonlinear programming. At each iteration, we define a 'moving target' for each objective function, to convert it to a level constraint and then the algorithm calculates the center of the intersection of level constraints and original constraints. Some examples are given to illustrate the proposed algorithm.