A stochastic method of moving asymptotes for topology optimization under uncertainty

TL;DR

This paper introduces a stochastic optimization method combining MMA with sample-based integration to efficiently solve topology optimization problems under uncertainty, significantly reducing computational costs.

Contribution

The paper presents the stochastic method of moving asymptotes (sMMA), integrating stochastic sampling with MMA for reliable and efficient topology optimization under uncertainty.

Findings

sMMA reduces computational cost compared to traditional methods.

It provides asymptotically correct gradient estimates.

Demonstrated effectiveness in 2D and 3D structural problems.

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, 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.