Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
The rectilinear Steiner arborescence problem is NP-complete
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Encoding rectilinear Steiner trees as lists of edges
Proceedings of the 2001 ACM symposium on Applied computing
Two hybrid evolutionary algorithms for the rectilinear Steiner arborescence problem
Proceedings of the 2004 ACM symposium on Applied computing
Schema disruption in tree-structured chromosomes
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
New approximations for the rectilinear Steiner arborescence problem [VLSI layout]
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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.