A W-shaped multilevel full-chip routing framework using W-shaped optimization flow is used to find the final routing solution. The W-shaped flow consists of two sequential V-shaped optimization flows. The first V-shaped flow optimizes the global routing solution. The probabilistic congestion prediction technique is used to guide the global routing decision to find the routing solution that evenly distributes the nets. Then, the second V-shaped flow improves the quality of the routing result. Tests on a set of commonly used benchmark circuits and comparisons with other multilevel routing systems show that the routability, total wire length, total number of vias, and the runtime are all improved.
