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.

翻译：可行性寻求方法为连续问题中复杂约束的管理与求解提供了系统性框架，本文将其应用于日益增多的异质约束布图规划问题。经典合法性约束可表示为凸集之并集，然而由于约束集非凸，传统投影类算法的收敛性无法保证。本文提出一种重置策略，极大消除了可行性寻求公式下投影算法的发散问题。此外，超优化方法论介于可行性寻求与约束优化之间，本文首次将其应用于布图规划。超优化通过引入扰动引导可行性寻求算法收敛至总互连线长更短的可行解。本文提出的流程具有可扩展性，能够处理布图规划问题中的各类约束及变体，例如带I/O分配的布图规划问题。基于MCNC基准测试集的评估表明：采用MATLAB的当前原型，获得合法布图仅比分支定界法慢两倍，线长仅比最优结果差3%。通过考虑I/O分配约束验证了流程有效性，本算法在线长上实现了8%的改进。