  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
as the constrain sets are non-convex. In this work, we propose a resetting
strategy to greatly eliminate the 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 feasibility-seeking algorithm to a feasible solution
with shorter total wirelength. The proposed 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 flow by considering the constraints of I/O assignment, and our algorithm
achieve 8% improvement on wirelength.
