  Robust topology optimization (RTO) improves the robustness of designs with
respect to random sources in real-world structures, yet an accurate sensitivity
analysis requires the solution of many systems of equations at each
optimization step, leading to a high computational cost. To open up the full
potential of RTO under a variety of random sources, this paper presents a
momentum-based accelerated mirror descent stochastic approximation (AC-MDSA)
approach to efficiently solve RTO problems involving various types of load
uncertainties. The proposed framework can perform high-quality design updates
with highly noisy stochastic gradients. We reduce the sample size to two
(minimum for unbiased variance estimation) and show only two samples are
sufficient for evaluating stochastic gradients to obtain robust designs, thus
drastically reducing the computational cost. We derive the AC-MDSA update
formula based on $\ell_1$-norm with entropy function, which is tailored to the
geometry of the feasible domain. To accelerate and stabilize the algorithm, we
integrate a momentum-based acceleration scheme, which also alleviates the step
size sensitivity. Several 2D and 3D examples with various sizes are presented
to demonstrate the effectiveness and efficiency of the proposed AC-MDSA
framework to handle RTO involving various types of loading uncertainties.
