Macro placement is a crucial sub-stage of chip design that focuses on determining the locations of numerous macros while optimizing multiple metrics. In recent years, evolutionary algorithms (EAs) have emerged as a promising technique for enhancing placement performance. However, the solution space of the previous methods is often limited by two-dimensional grids due to insufficient consideration of macro orientation during placement, leading to missed opportunities for further improvement. To address this issue, we propose EA-Rotation for macro placement, which incorporates rotation into the mutation operator to perturb the placement by adjusting the orientation of macros. Utilizing this efficient operator in conjunction with a greedy algorithm, EA-Rotation achieves superior placement solutions. Additionally, EA-Rotation serves as a fine-tuning technique for optimizing both the locations and orientation of macros, significantly improving the placement solutions of existing methods. Comprehensive experiments demonstrate that EA-Rotation outperforms state-of-the-art methods and is effectively integrated with other mutation operators.

In this study, first the authors present a simplified representation of the Peng–Fan bounds on the periodic Hamming correlation of frequency‐hopping sequence (FHS) sets, which may also be used to check the optimality of an FHS set with respect to the Peng–Fan bounds. Second, they propose a recursive construction of FHS sets from the known ones using some injective functions and the Chinese remainder theorem. It generalises the previous construction of optimal FHSs and FHS sets with composite lengths employing a given function. Without the limit of the specific function, their construction can produce new optimal FHSs and FHS sets that cannot be produced by the earlier construction. By choosing appropriate injective functions and known optimal FHSs and FHS sets, infinitely many new optimal FHSs and FHS sets can be recursively obtained.