A parallel genetic algorithm for 3-D rectilinear Steiner tree with bounded number of bends

A rectilinear Steiner tree is one of the most important problems that are applied to the global routing in LSI and other designs. In this paper, we propose a parallel genetic algorithm in which the 3-D rectilinear Steiner tree with bounded number of bends is obtained by replacing each edge of the given Euclidean spanning tree by the segments which are parallel to the X-axis, the Y-axis, or the Z-axis. In the proposed method, the algorithm can avoid obstacles flexibly by using, at most, three bends to replace one edge of the Euclidean spanning tree. For the fitness value, a linear sum of the wire length and diameter of the rectilinear Steiner tree is used. In the experimental results, it is shown that our parallel genetic algorithm can avoid obstacles, and obtain the 3-D rectilinear Steiner tree with bounded number of bends.