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The feasibility-seeking approach provides a systematic scheme to manage andsolve complex constraints for continuous problems, and we explore it for thefloorplanning problems with increasingly heterogeneous constraints. The classiclegality constraints can be formulated as the union of convex sets. However,the convergence of conventional projection-based algorithms is not guaranteedas the constrain sets are non-convex. In this work, we propose a resettingstrategy to greatly eliminate the the divergence issue of the projection-basedalgorithm for the feasibility-seeking formulation. Furthermore, thesuperiorization methodology (SM), which lies between feasibility-seeking andconstrained optimization, is firstly applied to floorplanning. The SM usesperturbations to steer the feasibility-seeking algorithm to a feasible solutionwith shorter total wirelength. The proposed flow is extendable to tacklevarious constraints and variants of floorplanning problems, e.g., floorplanningwith I/O assignment problems. We have evaluated the proposed algorithm on theMCNC benchmarks. We can obtain legal floorplans only two times slower than thebranch-and-bound method in its current prototype using MATLAB, with only 3%wirelength inferior to the optimal results. We evaluate the effectiveness ofthe flow by considering the constraints of I/O assignment, and our algorithmachieve 8% improvement on wirelength.

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