Globally optimal floorplanning for a layout problem

In this paper, the floorplanning problem for a layout problem is formulated as a global optimization problem. The area of each building block is assumed to be fixed. However, its width and height are allowed to vary subject to aspect ratio constraints. Also, a block may be arbitrarily oriented in parallel to the xy orthogonal axes, subject to partition constraints with associated adjacency relationships. The objective is to minimize the rectangular area of the entire layout. By formulating the problem appropriately, it becomes a geometric programming problem. Its global minimum can then be found by using standard convex optimization techniques. The problem formulation and its conversion to a convex optimization problem are first illustrated through a simple example. The general procedure is then described and the effectiveness of the approach demonstrated through numerical examples.