Per-RMAP: Feasibility-Seeking and Superiorization Methods for Floorplanning with I/O Assignment.

The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be formulated as the union of convex sets. However, the convergence of conventional projection-based algorithms is not guaranteed when the constraints sets are non-convex, which is the case with unions of convex sets. In this work, we propose a resetting strategy to greatly eliminate the divergence issue of the projection-based algorithm for the feasibility-seeking formulation. Furthermore, the superiorization methodology (SM), which lies between feasibility-seeking and constrained optimization, is firstly applied to floorplanning. The SM uses perturbations to steer the iterates of a feasibility-seeking algorithm to a feasible solution with shorter total wirelength. The proposed algorithmic flow is extendable to tackle various constraints and variants of floorplanning problems, e.g., floorplanning with I/O assignment problems. We have evaluated the proposed algorithm on the MCNC benchmarks. We can obtain legal floorplans only two times slower than the branch-and-bound method in its current prototype using MATLAB, with only 3% wirelength inferior to the optimal results. We evaluate the effectiveness of the algorithmic flow by considering the constraints of I/O assignment, and our algorithm achieves 8% improvement on wirelength.