By formulating the floorplanning of VLSI as a mixed-variable optimization problem, this paper proposes to solve it by memetic algorithms, where the discrete orientation variables are addressed by the distribution evolutionary algorithm based on a population of probability model (DEA-PPM), and the continuous coordination variables are optimized by the conjugate sub-gradient algorithm (CSA). Accordingly, the fixed-outline floorplanning algorithm based on CSA and DEA-PPM (FFA-CD) and the floorplanning algorithm with golden section strategy (FA-GSS) are proposed for the floorplanning problems with and without fixed-outline constraint. %FF-CD is committed to optimizing wirelength targets within a fixed profile. FA-GSS uses the Golden Section strategy to optimize both wirelength and area targets. The CSA is used to solve the proposed non-smooth optimization model, and the DEA-PPM is used to explore the module rotation scheme to enhance the flexibility of the algorithm. Numerical experiments on GSRC test circuits show that the proposed algorithms are superior to some celebrated B*-tree based floorplanning algorithms, and are expected to be applied to large-scale floorplanning problems due to their low time complexity.

翻译：通过将VLSI布局规划问题建模为混合变量优化问题，本文提出采用模因算法进行求解：其中离散方向变量由基于概率模型种群分布进化算法（DEA-PPM）处理，连续坐标变量则通过共轭子梯度算法（CSA）优化。相应地，针对有无固定边界约束的布局规划问题，分别提出了基于CSA和DEA-PPM的固定边界布局规划算法（FFA-CD）以及结合黄金分割策略的布局规划算法（FA-GSS）。FFA-CD致力于在固定轮廓内优化线长目标，FA-GSS采用黄金分割策略同时优化线长与面积目标。CSA用于求解所提出的非光滑优化模型，DEA-PPM则用于探索模块旋转方案以增强算法灵活性。在GSRC测试电路上的数值实验表明，所提算法优于若干经典的基于B*-树的布局规划算法，且因其较低的时间复杂度，有望应用于大规模布局规划问题。