Computing multiple solutions of topology optimization problems
Abstract
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.
Cite
@article{arxiv.2004.11797,
title = {Computing multiple solutions of topology optimization problems},
author = {Ioannis P. A. Papadopoulos and Patrick E. Farrell and Thomas M. Surowiec},
journal= {arXiv preprint arXiv:2004.11797},
year = {2021}
}