The rapidly changing requirements of engineering optimization problems require unprecedented levels of compatibility to integrate diverse uncertainty information to search optimum among design region. The sophisticated optimization methods tackling uncertainty involve reliability-based design optimization and robust design optimization. In this paper, a novel alternative approach called risk-based design optimization (RiDO) has been proposed to counterpoise design results and costs under hybrid uncertainties. In this approach, the conditional value at risk (CVaR) is adopted for quantification of the hybrid uncertainties. Then, a CVaR estimation method based on Monte Carlo simulation (MCS) scenario generation approach is derived to measure the risk levels of the objective and constraint functions. The RiDO under hybrid uncertainties is established and leveraged to determine the optimal scheme which satisfies the risk requirement. Three examples with different calculation complexity are provided to verify the developed approach.

中文翻译：

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混合不确定性下基于风险的设计优化

工程优化问题的快速变化要求需要前所未有的兼容性水平，以整合各种不确定性信息以在设计区域中搜索最佳。解决不确定性的复杂优化方法包括基于可靠性的设计优化和稳健设计优化。在本文中，提出了一种称为基于风险的设计优化 (RiDO) 的新型替代方法，以平衡混合不确定性下的设计结果和成本。在这种方法中，采用风险条件值 (CVaR) 来量化混合不确定性。然后，推导出一种基于蒙特卡罗模拟（MCS）情景生成方法的CVaR估计方法，用于衡量目标函数和约束函数的风险水平。建立并利用混合不确定性下的RiDO来确定满足风险要求的最优方案。提供了三个不同计算复杂度的例子来验证所开发的方法。