  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 or approximately 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 to 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 exact method proposed for
handling scalar-valued functions of the load compliances, where the
scalar-valued function is the augmented Lagrangian function.
