  The feasibility-seeking approach offers a systematic framework for managing
and resolving intricate constraints in continuous problems, making it a
promising avenue to explore in the context of floorplanning problems with
increasingly heterogeneous constraints. The classic legality constraints can be
expressed as the union of convex sets. In implementation, we introduce a
resetting strategy aimed at effectively reducing the problem of algorithmic
divergence in the projection-based method used for the feasibility-seeking
formulation. Furthermore, we introduce the novel application of the
superiorization method (SM) to floorplanning, which bridges the gap between
feasibility-seeking and constrained optimization. The SM employs perturbations
to steer the iterations of the feasibility-seeking algorithm towards feasible
solutions with reduced (not necessarily minimal) total wirelength. To evaluate
the performance of Per-RMAP, we conduct comprehensive experiments on the MCNC
benchmarks and GSRC benchmarks. The results demonstrate that we can obtain
legal floorplanning results 166 times faster than the branch-and-bound (B&B)
method while incurring only a 5% wirelength increase compared to the optimal
results. Furthermore, we evaluate the effectiveness of the algorithmic flow
that considers the I/O assignment constraints, which achieves an 6% improvement
in wirelength. Besides, considering the soft modules with a larger feasible
solution space, we obtain 15% improved runtime compared with PeF, the
state-of-the-art analytical method. Moreover, we compared our method with
Parquet-4 and Fast-SA on GSRC benchmarks which include larger-scale instances.
The results highlight the ability of our approach to maintain a balance between
floorplanning quality and efficiency.
