Abstract
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. However, conventional projection-based algorithms for feasibility-seeking do not guarantee convergence in such situations, which are also heavily influenced by the initialization. We present a quantitative property about the choice of the initial point that helps good initialization and analyze the occurrence of the oscillation phenomena for bad initialization. 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. Notably, the proposed algorithmic flow is adaptable to handle various constraints and variations of floorplanning problems, such as those involving I/O assignment. 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× 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.