A stochastic method of moving asymptotes for topology optimization under uncertainty
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| Format: | Preprint |
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2024
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| _version_ | 1866916454329221120 |
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| author | Pflug, Lukas Stingl, Michael Uihlein, Andrian |
| author_facet | Pflug, Lukas Stingl, Michael Uihlein, Andrian |
| contents | 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, i.e., 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stochastic method of moving asymptotes for topology optimization under uncertainty Pflug, Lukas Stingl, Michael Uihlein, Andrian Optimization and Control 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, i.e., 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. |
| title | A stochastic method of moving asymptotes for topology optimization under uncertainty |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.19428 |