Wire routing by Lagrangian method

Routing problems have been formulated as discrete optimization problems. The maze router has been widely used because of its ability to find a shortest path. The weakness of the maze router is that the routing quality is dependent on the ordering of the nets to be routed. We propose a new algorithm which solves the routing problem as a continuous valued constrained optimization problem. In this method, all of the continuous valued wires change their values simultaneously according to the dynamic equations of the Lagrangian method. We show that this method can solve the small switchbox routing problems with a higher completion rate as compared to the rip-up reroute maze router.