A tree-based genetic algorithm for building rectilinear Steiner arborescences

A rectilinear Steiner arborescence (RSA) is a tree, whose nodes include a prescribed set of points, termed the vertices, in the first quadrant of the Cartesian plane, and whose tree edges from parent to child nodes must head either straight to the right or straight above. A minimal RSA (a MRSA) is one for which the total path length of the edges in the tree is minimal. RSAs have application in VLSI design. Curiously, although a RSA is a tree, to our knowledge, previous genetic attacks on the MRSA problem have not used tree-based approaches to representation, nor to the operations of crossover and mutation. We show why some care is needed in the choice of such genetic operators. Then we present tree-based operators for crossover and mutation, which are successful in creating true RSAs from source RSAs without the need of repair steps. We compare our results to two earlier researches, and find that our approach gives good results, but not results that are consistently better than those earlier approaches.