Design optimization of structural and multidisciplinary systems under uncertainty has been an active area of research due to its evident advantages over deterministic design optimization. In deterministic design optimization, the uncertainties of a structural or multidisciplinary system are taken into account by using safety factors specified in the regulations or design codes. This uncertainty treatment is a subjective and indirect way of dealing with uncertainty. On the other hand, design under uncertainty approaches provide an objective and direct way of dealing with uncertainty. This paper provides a review of the uncertainty treatment practices in design optimization of structural and multidisciplinary systems under uncertainties. To this end, the activities in uncertainty modeling are first reviewed, where theories and methods on uncertainty categorization (or classification), uncertainty handling (or management), and uncertainty characterization are discussed. Second, the tools and techniques developed and used for uncertainty modeling and propagation are discussed under the broad two classes of probabilistic and non-probabilistic approaches. Third, various design optimization methods under uncertainty which incorporate all the techniques covered in uncertainty modeling and analysis are reviewed. In addition to these in-depth reviews on uncertainty modeling, uncertainty analysis, and design optimization under uncertainty, some real-life engineering applications and benchmark test examples are provided in this paper so that readers can develop an appreciation on where and how the discussed techniques can be applied and how to compare them. Finally, concluding remarks are provided, and areas for future research are suggested.

不确定性下结构和多学科系统的设计优化一直是一个活跃的研究领域，因为它比确定性设计优化具有明显的优势。在确定性设计优化中，通过使用法规或设计规范中指定的安全系数来考虑结构或多学科系统的不确定性。这种不确定性处理是一种处理不确定性的主观和间接方式。另一方面，不确定性方法下的设计提供了一种处理不确定性的客观而直接的方法。本文综述了不确定性下结构和多学科系统设计优化中的不确定性处理实践。为此，首先回顾不确定性建模中的活动，其中讨论了不确定性分类（或分类）、不确定性处理（或管理）和不确定性表征的理论和方法。其次，在概率和非概率方法的两大类下讨论了为不确定性建模和传播而开发和使用的工具和技术。第三，回顾了不确定性下的各种设计优化方法，这些方法结合了不确定性建模和分析中涵盖的所有技术。除了这些关于不确定性建模、不确定性分析和不确定性下的设计优化的深入评论外，本文还提供了一些实际工程应用和基准测试示例，以便读者可以了解所讨论技术的位置和方式。可以应用以及如何比较它们。