Model and solution strategy for placement of rectangular blocks in the Euclidean plane

The authors describe a nonlinear optimization model for the placement of rectangular blocks with some wire connections among them in the Euclidean plane, so that the total wire length is minimized. Such a placement algorithm is useful as a CAD tool for VLSI and printed-circuit-board layout designs. The model ensures that the blocks will not overlap and minimizes the sum of the distances of the interconnections of the blocks with respect to their orientation as well as their position. Mechanisms are presented for solving more restrictive placement problems, including one in which there is a set of equally spaced, discrete angles to be used in the placement. The mathematical model is based on the Lennard-Jones 6-12 potential equation, on a sine-wave-shaped penalty function, and on minimizing the sum of the squares of the Euclidean distances of the block interconnections. Experimental results are presented to show that good placements are achieved with these techniques