A hierarchical neighbourhood search method for topology optimization
Krister Svanberg and Mats Werme
Optimization and Systems Theory, Royal Institute of
Technology (KTH), Stockholm, Sweden
ABSTRACT:
This paper presents a hierarchical neighbourhood search method for
solving topology optimization problems defined on discretized linearly
elastic continuum structures. The design of the structure is
represented by binary design variables indicating material or void in
the various finite elements. Two different designs are called
neighbours if they differ in only one single element, in which one of
them has material while the other has void. The proposed neighbourhood
search method repeatedly jumps to the "best" neighbour of the current
design until a local optimum has been found, where no further
improvement can be made. The "engine" of the method is an efficient
exploitation of the fact that if only one element is changed (from
material to void or from void to material) then the new global
stiffness matrix is just a low-rank modification of the old one. To
further speed up the process, the method is implemented in a
hierarchical way. Starting from a coarse finite element mesh, the
neighbourhood search is repeatedly applied on finer and finer meshes.
Numerical results are presented for minimum-weight problems with
constraints on respectively compliance, strain energy densities in all
non-void elements, and von Mises stresses in all non-void
elements.