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.

在本文中，解决了合规性问题中的负载不确定性问题，其中以一组有限多个负载场景的形式描述了不确定性。在计算上，提出了更有效的方法来准确评估和区分：(1) 平均顺应性或 (2) 单个负载顺应性的任何标量值函数，例如平均值和标准偏差的加权和。分析了所有提出的算法的计算时间复杂度，与朴素的方法进行了比较，然后进行了实验验证。最后，解决了平均合规最小化问题、风险规避合规最小化问题和最大合规约束问题，以展示所提出算法的有效性。