Steiner minimal tree is the best model of routing stage in modern very large-scale integration (VLSI) chips, and is often used for pre-routing, wirelength optimization, and congestion estimation. Therefore, it is of great significance to construct a high-performance Steiner minimal tree algorithm. However, with the emergence of obstacles such as IP blocks and the continuous improvement of circuit density, obstacles have become a factor that cannot be ignored in the Steiner minimal tree construction problem. Considering that in modern multi-layer routing, obstacles often only occupy the device layer and the lower metal layer. Therefore, the routing on the top of the obstacles is possible, and it can make full use of routing resources and further optimize the wirelength. Since the Steiner minimal tree construction problem is an NP-hard problem, the particle swarm optimization algorithm has a good application prospect in solving NP-hard problems. Therefore, on the basis of the particle swarm optimization algorithm, further considering the model of slew constraints that can effectively prevent signal distortion, and the X-architecture with better wirelength optimization, this paper is the first work to propose an X-architecture Steiner minimal tree algorithm with slew constraints based on hybrid discrete particle swarm optimization. Firstly, in order to avoid frequent slew calculation and judgment between routing and obstacles, an efficient preprocessing strategy is proposed. In this preprocessing strategy, the information between all possible routing of any two pins and all obstacles is calculated in advance, and a suitable lookup table is generated based on this information for subsequent queries. Secondly, in order to effectively solve the discrete problem of Steiner minimal tree construction, an effective discrete update operation formula of particle swarm optimization algorithm is redesigned, which is based on the mutation operator and the crossover operator. For discrete particle swarm optimization, a pin-pair coding method that is more suitable for this discrete particle swarm optimization and a targeted penalty mechanism that can effectively consider slew constraints are proposed. In addition, so as to speed up the search efficiency of the particle swarm optimization algorithm, the Prim method is used to construct a minimum spanning tree under a given pin set, and initialize the population. Thirdly, in order to further optimize wirelength of the routing tree, an effective local optimal refining strategy is proposed. In this step, the Steiner tree is divided into multiple subtrees with roots as pins and a depth of 2. By traversing all possible routing structures in the subtree, the routing structure with the highest degree of routing resource sharing is selected to replace the original routing structure. Thereby the goal of optimizing the wirelength is achieved. Finally, in order to make the Steiner minimal tree fully satisfy the slew constraints, a hybrid correction strategy is proposed. In this part, by estimating the cost of adjusting the routing, this paper selects the overall adjustment strategy or the adjustment strategy along the barrier to correct the routing that violates the slew constraints. Experiments show that the proposed algorithm can achieve the best routing result and fully satisfy the slew constraints. © 2021, Science Press. All right reserved.
