A Revisit to Floorplan Optimization by Lagrangian Relaxation

With the advent of deep sub-micron (DSM) era, floorplanning has become increasingly important in physical design process. In this paper we clarify a misunderstanding in using Lagrangian relaxation for the minimum area floorplanning problem. We show that the problem is not convex and its optimal solution cannot be obtained by solving its Lagrangian dual problem. We then propose a modified convex formulation and solve it using min-cost flow technique and trust region method. Experimental results under module aspect ratio bound [0.5, 2.0] show that the running time of our floorplanner scales well with the problem size in MCNC benchmark. Compared with the floorplanner in the work of Young et al. (2001), our floorplanner is 9.5times faster for the largest case "ami49". It also generates a floorplan with smaller deadspace for almost all test cases. In addition, since the generated floorplan has an aspect ratio closer to 1, it is more friendly to packaging. Our floorplanner is also amicable to including interconnect cost and other physical design metrics