Computing multiple solutions of topology optimization problems

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.