基于混合离散粒子群优化的Slew约束下X结构Steiner最小树算法

Hybrid Discrete Particle Swarm Optimization Algorithm for X-Architecture Steiner Minimal Tree Construction with Slew Constraints

Steiner最小树是超大规模集成电路中布线阶段的最佳模型,进一步考虑能够有效防止信号失真的电压转换速率(Slew)约束这一个更为贴近实际芯片设计模型和更具线长优化能力的X结构,首次提出基于混合离散粒子群优化的Slew约束下X结构Steiner最小树算法.首先,为了避免频繁的Slew约束计算,提出了高效的预处理策略,并且提出一种能够有效考虑Slew约束的针对性的惩罚机制.其次,为了能够有效求解该离散问题,基于遗传算子重新设计了粒子群优化算法的离散更新机制,并提出一种更适合遗传算子的引脚对编码方式.然后,为了进一步优化布线树的长度,提出一种有效的精炼策略.最终,提出一种混合修正策略以完全满足Slew约束.实验表明,所提算法可完全满足电压转换速率约束并取得同类工作中最佳的布线结果.

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 obstacles usually only occupy the device layer and the lower metal layer in modern multi-layer routing,the routing on the top of obstacles is possible,which can make full use of routing resources and further optimize the wirelength.The construction of Steiner minimal tree is an NP-hard problem,and 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,and further considering the slew constraints model which 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,an efficient preprocessing strategy is proposed to reduce frequent slew calculation and judgment between routing and obstacles.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 for subsequent queries based on the information.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.At this stage,a pin-pair coding method which is more suitable for the discrete particle swarm optimization and a target penalty mechanism which can effectively consider the 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,an effective local optimal refining strategy is proposed to further optimize the wirelength of routing tree.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,so as to achieve the goal of optimizing wirelength.Finally,a hybrid correction strategy is proposed to make the Steiner minimal tree fully satisfy the slew constraints.In this part,by estimating the cost of adjusting the routing,this paper selects the overall adjustment strategy or the adjustment strategy along obstacles 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.