In this paper, a novel shape optimization method is proposed to improve the mechanical performance of the free-form grid structures while satisfying the architectural requirements. The height of control points are considered as the optimization variables, the structural strain energy and the comprehensive quantitative index are considered as optimization objectives. The sensitivity hybrid multi-objective evolutionary algorithm (referred to as SH-MOEA) is developed and the shape optimization of the free-form grid structures is carried out based on the developed algorithm. The optimization results are compared with those based on NGSA-II, SPEA2 and MOEA/D algorithms. The results demonstrate that the developed algorithm not only can obtain the Pareto optimal solution set with better accuracy and uniformity, but also indicates higher computational efficiency than other three algorithms. The similarity of surface, the fluence and regularity of free-form grids are effectively improved by considering the geometric comprehensive quantitative index as the optimization objective.

本文提出了一种新颖的形状优化方法，以在满足建筑要求的同时提高自由形态网格结构的力学性能。控制点的高度被认为是最优化变量，结构应变能和综合定量指标被认为是最优化目标。。提出了灵敏度混合多目标进化算法（简称SH-MOEA），并在此算法的基础上进行了自由形式网格结构的形状优化。将优化结果与基于NGSA-II，SPEA2和MOEA / D算法的优化结果进行比较。结果表明，所开发的算法不仅能够以较高的精度和均匀性获得帕累托最优解集，而且与其他三种算法相比，具有更高的计算效率。以几何综合定量指标为优化目标，有效提高了曲面的相似度，自由度网格的通量和规则性。