In this paper, the problem of load uncertainty in compliance problems is addressed where the uncertainty is described in the form of a set of finitely many loading scenarios. Computationally more efficient methods are proposed to exactly evaluate and differentiate: 1) the mean compliance, or 2) any scalar-valued function of the individual load compliances such as the weighted sum of the mean and standard deviation. The computational time complexities of all the proposed algorithms are analyzed, compared with the naive approaches and then experimentally verified. Finally, a mean compliance minimization problem, a risk-averse compliance minimization problem and a maximum compliance constrained problem are solved to showcase the efficacy of the proposed algorithms. The maximum compliance constrained problem is solved using the augmented Lagrangian method and the method proposed for handling scalar-valued functions of the load compliances, where the scalar-valued function is the augmented Lagrangian function.

翻译：在本文件中,如果不确定性以一组有限的装货设想方案的形式加以描述,则解决了合规问题中的负载不确定性问题; 提出了比较效率更高的方法,以准确评估和区分:(1) 平均合规,或(2) 单个负载合规的任何计算价值功能,如平均和标准偏差的加权总和; 对所有拟议算法的计算时间复杂性进行了分析,与天真的方法进行比较,然后进行实验性核实; 最后,解决了一种平均合规最小化问题、风险规避合规问题最小化和最大合规受限问题,以展示拟议算法的功效; 最大合规受限问题通过扩大的拉格朗格法和拟议处理重负合规的标值功能的方法来解决,而计算值的功能是增强的拉格朗格函数。