Self-adapting PSO Algorithm with Efficient Hybrid Transformation Strategy for X-Architecture Steiner Minimal Tree Construction Algorithm
LIU Genggeng1,2, CHEN Zhisheng1, GUO Wenzhong1,2,3, CHEN Guolong1
1.College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116
2.Fujian Provincial Key Laboratory of Networking Computing and Intelligent Information Processing, Fuzhou University, Fuzhou 350116
3.Key Laboratory of Spatial Data Mining and Information Sharing, Ministry of Education, Fuzhou University， Fuzhou
X-architecture Steiner minimal tree (XSMT) problem is an NP-hard problem, and it is the best connection model for a multi-terminal net in non-Manhattan global routing problem. An XSMT construction algorithm based on hybrid transformation strategy and self-adapting particle swarm optimization(PSO) is proposed. Firstly, an effective hybrid transformation strategy is designed to enlarge the search space and enhance the convergence of the algorithm. Secondly, the crossover and mutation operators based on union-find sets and a self-adapting strategy to adjust the learning factors are proposed to satisfy the robustness of particle coding and further speed up the convergence of algorithm. The experimental results show that the proposed algorithm efficiently produces a better solution than others. Moreover, it obtains a series of XSMTs with different topology but same length. Thus, it provides a variety of options for global routing and opportunities to reduce congestion.
[1] 徐 宁,洪先龙.超大规模集成电路物理设计理论与算法.北京:清华大学出版社, 2009.
(XU N, HONG X L. Very Large Scale Integration Physical Design Theory and Method. Beijing, China: Tsinghua University Press, 2009.)
[2] SIDDIQI U F, SAIT S M. A Game Theory Based Post-Processing Method to Enhance VLSI Global Routers. IEEE Access, 2017, 5: 1328-1339.
[3] HELD S, M LLER D, ROTTER D, et al . Global Routing with Timing Constraints. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2018, 37(2): 406-419.
[4] SCHEIFELE R. RC-Aware Global Routing//Proc of the 35th IEEE/ACM International Conference on Computer-Aided Design. Washington, USA: IEEE, 2016. DOI: 10.1145/2966986.2967067.
[5] SCHEIFELE R. Steiner Trees with Bounded RC-Delay//Proc of the International Workshop on Approximation and Online Algorithms. Berlin, Germany: Springer, 2014: 224-235.
[6] COULSTON C S. Constructing Exact Octagonal Steiner Minimal Tree//Proc of the 13th ACM Great Lakes Symposium on VLSI. New York, USA: ACM, 2003: 1-6.
[7] THURBER A P, XUE G L. Computing Hexagonal Steiner Trees Using PCX for VLS//Proc of the 6th IEEE International Conference on Electronics, Circuits and Systems. Washington, USA: IEEE, 1999, I： 381-384.
[8] SAMANTA T, GHOSAL P, RAHAMAN H, et al. A Heuristic Method for Constructing Hexagonal Steiner Minimal Trees for Routing in VLS//Proc of the International Symposium on Circuits and Systems. Washington, USA: IEEE, 2006: 1788-1791.
[9] ZHU Q, ZHOU H, JING T, et al . Spanning Graph-Based Nonrectilinear Steiner Tree Algorithms. IEEE Transactions on Computer-Ai-ded Design of Integrated Circuits and Systems, 2005, 24(7): 1066-1075.
[10] YAN J T. Timing-Driven Octilinear Steiner Tree Construction Ba sed on Steiner-Point Reassignment and Path Reconstruction. ACM Transactions on Design Automation of Electronic Systems, 2008, 13(2): 26:1-26:18.
[11] SAMANTA T, RAHAMAN H, DASGUPTA P. Near-Optimal Y-Routed Delay Trees in Nanometric Interconnect Design. IET Computers & Digital Techniques, 2011, 5(1): 36-48.
[12] GAREY M R, JOHNSON D S. The Rectilinear Steiner Tree Pro blem Is NP-Complete. SIAM Journal on Applied Mathematics, 1977, 32(4): 826-834.
[13] BHATTACHARYA P, KHAN A, SARKAR S K. A Global Routing Optimization Scheme Based on ABC Algorithm//KUNDU M K, MOHAPATRA D P, KONAR A, et al. , eds. Advanced Computing, Networking and Informatics. Berlin，German: Springer, 2014, II: 189-197.
[14] KHAN A, LAHA S, SARKAR S K. A Novel Particle Swarm Optimization Approach for VLSI Routing//Proc of the 3rd IEEE International Advance Computing Conference. Washington, USA: IEEE, 2013： 258-262.
[15] LIU G G, CHEN G L, GUO W Z, et al . DPSO-Based Rectilinear Steiner Minimal Tree Construction Considering Bend Reduction//Proc of the 7th International Conference on Natural Computation. Washington, USA: IEEE, 2011. DOI: 10.1109/ICNC.2011.6022221.
[16] LIU G G, CHEN G L, GUO W Z. DPSO Based Octagonal Steiner Tree Algorithm for VLSI Routing//Proc of the 5th IEEE International Conference on Advanced Computational Intelligence. Wa shington , USA: IEEE, 2012. DOI: 10.1109/ICACI.2012.6463191.
[17] LIU G G, HUANG X, GUO W Z, et al . Multilayer Obstacle-Avoiding X-Architecture Steiner Minimal Tree Construction Based on Particle Swarm Optimization. IEEE Transactions on Cybernetics, 2015, 45(5): 989-1002.
[18] EBERHART R, KENNEDY J. A New Optimizer Using Particles Swarm Theory//Proc of the 6th International Symposium on Micro Machine and Human Science. Washington, USA: IEEE, 1995: 39-43.
[19] HUANG X, GUO W Z, LIU G G, et al . FH-OAOS: A Fast Four-Step Heuristic for Obstacle-Avoiding Octilinear Steiner Tree Construction. ACM Transactions on Design Automation of Electronic Systems, 2016. DOI: 10.1145/2856033.
[20] HUANG X, GUO W Z, LIU G G, et al . MLXR: Multi-layer Obstacle-Avoiding X-Architecture Steiner Tree Construction for VLSI Routing. Science China Information Sciences, 2017, 60(1): 19102:1-19102:3.
[21] LIU G G, GUO W Z, LI R R, et al . XGRouter: High-Quality Global Router in X-Architecture with Particle Swarm Optimization. Frontiers of Computer Science, 2015, 9(4): 576-594.
[22] 马 军,杨 波,马绍汉.近乎最佳的Manhattan型Steiner树近似算法.软件学报, 2000, 11(2): 260-264.
(MA J, YANG B, MA S H. A Near-Optimal Approximation -Algorithm for Manhattan Steiner Tree. Journal of Software, 2000, 11(2): 260-264.)
[23] RUDOLPH G. Convergence Analysis of Canonical Genetic Algorithms. IEEE Transactions on Neural Networks, 1994, 5(1): 96-101.
[24] WARME D, WINTER P, ZACHARIASEN M. GeoSteiner Home-page [DB/OL].[2017-11-30]. http://geosteiner.net.
[25] RATNAWEERA A, HALGAMUGE S K, WATSON H C. Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255.
2018, Vol. 31 
