A Stochastic Method of Moving Asymptotes for Topology Optimization Under Uncertainty

Pflug L, Stingl M, Uihlein A (2025)


Publication Type: Journal article

Publication year: 2025

Journal

Book Volume: 126

Article Number: e70109

Issue: 16

DOI: 10.1002/nme.70109

Abstract

Topology optimization under uncertainty or reliability-based topology optimization is usually numerically very expensive. This is mainly due to the fact that an accurate evaluation of the probabilistic model requires the system to be simulated for a large number of varying parameters. Traditional gradient-based optimization schemes thus face the difficulty that reasonable accuracy and numerical efficiency often seem mutually exclusive. In this work, we propose a stochastic optimization technique to tackle this problem. To be precise, we combine the well-known method of moving asymptotes (MMA) with a stochastic sample-based integration strategy. By adaptively recombining gradient information from previous steps, we obtain a noisy gradient estimator that is asymptotically correct, that is, the approximation error vanishes over the course of iterations. As a consequence, the resulting stochastic method of moving asymptotes (sMMA) allows us to solve chance constraint topology optimization problems for a fraction of the cost compared to traditional approaches from literature. To demonstrate the efficiency of sMMA, we analyze structural optimization problems in two and three dimensions.

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How to cite

APA:

Pflug, L., Stingl, M., & Uihlein, A. (2025). A Stochastic Method of Moving Asymptotes for Topology Optimization Under Uncertainty. International Journal for Numerical Methods in Engineering, 126. https://doi.org/10.1002/nme.70109

MLA:

Pflug, Lukas, Michael Stingl, and Andrian Uihlein. "A Stochastic Method of Moving Asymptotes for Topology Optimization Under Uncertainty." International Journal for Numerical Methods in Engineering 126 (2025).

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