SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page A1555-A1582, January 2021.
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions; however, these methods can fail even in the simplest cases. In this paper, we present an algorithm to perform a systematic exploratory search for the solutions of the optimization problem via second order methods without a good initial guess. The algorithm combines the techniques of deflation, barrier methods, and primal-dual active set solvers in a novel way. We demonstrate this approach on several numerical examples, observe mesh independence in certain cases and show that multiple distinct local minima can be recovered.

中文翻译：

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计算拓扑优化问题的多个解决方案

SIAM科学计算杂志，第43卷，第3期，第A1555-A1582页，2021年1月。
由于缺乏凸度，拓扑优化问题通常支持多个局部最小值。通常，将基于梯度的技术与模型参数的连续性结合使用，以促进收敛到更优化的解决方案。但是，即使在最简单的情况下，这些方法也会失败。在本文中，我们提出了一种算法，可以通过二阶方法对优化问题的解进行系统的探索性搜索，而无需进行很好的初始猜测。该算法以新颖的方式结合了放气技术，势垒方法和原始对偶主动集求解器。我们在几个数值示例上演示了该方法，在某些情况下观察了网格无关性，并表明可以恢复多个不同的局部最小值。