  The work provides an exhaustive comparison of some representative families of
topology optimization methods for 3D structural optimization, such as the Solid
Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional
Evolutionary Structural Optimization (BESO), and the Variational Topology
Optimization (VARTOP) methods. The main differences and similarities of these
approaches are then highlighted from an algorithmic standpoint. The comparison
is carried out via the study of a set of numerical benchmark cases using
industrial-like fine-discretization meshes (around 1 million finite elements),
and Matlab as the common computational platform, to ensure fair comparisons.
Then, the results obtained for every benchmark case with the different methods
are compared in terms of computational cost, topology quality, achieved minimum
value of the objective function, and robustness of the computations
(convergence in objective function and topology). Finally, some quantitative
and qualitative results are presented, from which, an attempt of qualification
of the methods, in terms of their relative performance, is done.
