Abstract: To improve the efficiency of multi-objective design optimization of black-box systems,an improved multi-objective optimization algorithm was proposed based on Kriging model,expected hypervolume improvement and probability of feasibility.The feasible region identifying criterion of the algorithm that including the distances between trial points was also effective for the disconnected feasible sub-regions.A Pareto set improvement criterion was proposed which optimized the expected hypervolume improvement and the probability of feasibility simultaneously to strike a balance between improving the optimal solutions and validating the boundary of the feasible region.A convergence assessment method was proposed based on conditional simulation and random set theory,which didn't depend on the real solution set.The proposed algorithm was tested on typical benchmarks and compared with existed algorithms,and the numerical results indicated that the proposed algorithm was very efficient and useful for convergence assessment.

Key words: multi-objective design optimization, Pareto set, Kriging model, expected hypervolume improvement, probability of feasibility, conditional simulation

摘要： 为提高黑箱系统优化设计的效率,基于Kriging模型、期望超体积改进和可行性概率准则,提出一种改进的多目标代理优化算法。该算法的可行域探索准则包含考虑试验点间距离的项,对可行域非连通的优化问题也有效;Pareto解集改进准则以同时优化期望超体积和可行性概率准则为目标,在改进Pareto解集的同时兼顾了对可行域边界的刻画;最后,结合条件模拟方法和随机集理论,提出一种不依赖真实解集的算法收敛性评估方法。通过两个算例将提出的优化算法与已有算法进行对比分析,结果证实了所提算法的高效性及算法收敛性评估方法的可行性。

关键词: 多目标优化设计, Pareto解集, Kriging模型, 期望超体积改进, 可行性概率, 条件模拟