Density-based topology optimization with the Null Space Optimizer: a tutorial and a comparison

Abstract

The Null Space Optimizer is a constrained optimization solver that has been developed in the context of level-set based Topology Optimization. One of its appealing aspects comes from its relative independence to the need for tuning unintuitive algorithm parameters. The first contribution of this paper is to introduce an upgrade of the Null Space Optimizer that enables to solve optimization problems featuring a large number of constraints with sparse Jacobian matrix. This allows to include in particular bound constraints, making it possible to use the Null Space Optimizer for solving density based Topology Optimization problems. The second contribution of the paper is to present three tutorials giving an educational view on how to use the open source Python implementation of the Null Space Optimizer for solving Topology Optimization problems in structural mechanics and conductive heat transfer, on structured and unstructured meshes. Elegant Python programming features are used for automating the implementation of density filters and the assembly of sparse Jacobian matrices. Numerical results are presented on three design problems and compared to those obtained with the Method of Moving Asymptotes (MMA), the Interior Point Optimizer IPOPT and the Optimality Criteria (OC) method. We found that on the situations considered, (i) the Null Space optimizer is able to compute optimized designs with performances comparable to its competitors with very little parameter tuning, (ii) the OC method or IPOPT with default parameters sometimes converge to nonoptimal designs, (iii) MMA sometimes converge to slightly better design with a faster decay than the Null Space Optimizer during the first iterations, but may also require case dependent fixes to converge to satisfactory solutions.