Skip to main content

Advertisement

SpringerLink
Log in

A unified algorithm based on HTS and self-adapting PSO for the construction of octagonal and rectilinear SMT

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The Steiner minimal tree (SMT) problem is an NP-hard problem, which is the best connection model for a multi-terminal net in global routing problem. This paper presents a unified algorithm for octagonal and rectilinear SMT construction based on hybrid transformation strategy (HTS) and self-adapting particle swarm optimization. Firstly, an effective HTS is proposed to enlarge the search space and improve the convergence speed. Secondly, the proposed HTS in the evolutionary process may produce an ineffective solution, and consequently the crossover and mutation operators of genetic algorithm (GA) based on union-find sets is proposed. Thirdly, a self-adapting strategy that can adjust the acceleration coefficients is proposed to further improve the convergence and the quality of the proposed algorithm. Finally, the hybrid transformation can be applied to GA and the proposed algorithm can be applied to rectilinear architecture. To our best knowledge, the proposed algorithm is the first unified algorithm to solve the SMT construction under both octagonal and rectilinear architecture. The experimental results show that the proposed algorithm can efficiently provide a better solution for SMT problem both in octagonal and rectilinear architectures than others. Moreover, the algorithm can obtain several topologies of SMT, which is beneficial for optimizing congestion in VLSI global routing stage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Agrawal S, Silakari S (2014) FRPSO: Fletcher-Reeves based particle swarm optimization for multimodal function optimization. Soft Comput 18(11):2227–2243

    Article  Google Scholar 

  • Alpert CJ (1998) The ISPD98 circuit benchmark suite. In: Proceedings of the 1998 international symposium on Physical design, pp 80–85

  • Arora T, Mose ME (2009) Ant colony optimization for power efficient routing in manhattan and non-manhattan VLSI architectures. In: Proceedings of the Swarm intelligence symposium, pp 137–144

  • Bhattacharya P, Khan A, Sarkar, SK (2014) A global routing optimization scheme based on ABC algorithm. In: Proceedings of the 2nd international conference on advanced computing, networking and informatics, pp 189–197

    Chapter  Google Scholar 

  • Chang YJ, Lee YT, Gao JR, Wu PC, Wang TC (2010) NTHU-Route. 20: a robust global router for modern designs. IEEE Trans Comput Aid Des 29(12):1931–1944

    Article  Google Scholar 

  • Chen G, Guo W, Chen Y (2010) A PSO-based intelligent decision algorithm for VLSI floorplanning. Soft Comput 14(12):1329–1337

    Article  Google Scholar 

  • Chiang C, Chiang CS (2002) Octilinear steiner tree construction. In: Proceedings of the 45th midwest symposium on circuits and systems, pp 603–606

  • Costas V, Konstantinos E, Isaac E (2012) Particle swarm optimization with deliberate loss of information. Soft Comput 16(8):1373–1392

    Article  Google Scholar 

  • Coulston CS (2003) Constructing exact octagonal steiner minimal trees. In: Proceedings of the 13th ACM Great Lakes symposium on VLSI, pp 1–6

  • Dai KR, Liu WH, Li YL (2009) Efficient simulated evolution based rerouting and congestion-relaxed layer assignment on 3-D global routing. In: Proceedings of Asia and South Pacific Design Automation Conference, pp 570V575

  • Dai KR, Liu WH, Li YL (2012) NCTU-GR: Efficient simulated evolution-based rerouting and congestion-relaxed layer assignment on 3-D global routing. IEEE Trans VLSI Syst 20(3):459–472

    Article  Google Scholar 

  • Eberhar RC, Kennedy J (1995) A new optimizer using particles swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39–43

  • Garey M, Johnson D (1977) The rectilinear steiner tree problem is NP-complete. SIAM J Appl Math 32:826–834

    Article  MathSciNet  MATH  Google Scholar 

  • Gottlieb J, Julstrom BA, Raidl GR, Rothlauf F (2001) Prufer Numbers: a poor representation of spanning trees for evolutionary search. In: Proceedings of the genetic and evolutionary computation conference, pp 343–350

  • Guo WZ, Liu GG, Chen GL, Peng SJ (2014) A hybrid multi- objective PSO algorithm with local search strategy for VLSI partitioning. Front Comput Sci 8(2):203–216

    Article  MathSciNet  Google Scholar 

  • Han Y, Ancajas DM, Chakraborty K, Roy S (2014) Exploring high-throughput computing paradigm for global routing. IEEE Trans VLSI Syst 22(1):155–167

    Article  Google Scholar 

  • Held S, Muller D, Rotter D, Scheifele R, Traub V, Vygen J (2017) Global routing with timing constraints. IEEE Trans Comput Aid Des 1–17

  • Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, Cambridge

    Book  Google Scholar 

  • Huang X, Guo W, Liu G, Chen G (2016) FH-OAOS: a fast four-step heuristic for obstacle-avoiding octilinear steiner tree construction. ACM Trans Des Automat Elec 21(3):1–31

    Google Scholar 

  • Huang X, Guo W, Liu G, Chen G (2017) MLXR: multi- layer obstacle-avoiding X-architecture steiner tree construction for VLSI routing. Sci China Inform Sci 60(1):1–3

    Article  Google Scholar 

  • Khan A, Laha S, Sarkar SK (2013) A novel particle swarm optimization approach for VLSI routing. In: Proceedings of advance computing conference, pp 258–262

  • Koh CK, Madden PH (2000) Manhattan or non-manhattan? a study of alternative VLSI routing architectures. In: Proceedings of Great Lake symposium on VLSI, pp 47–52

  • Kundu S, Roy S, Mukherjee S (2016) SAT based rectilinear steiner tree construction. In: Proceedings of Appl. Theor Comput Commun Tech, pp 623–627

  • Kundu S, Roy S, Mukherjee S (2017) K-nearest neighbour (KNN) approach using SAT based technique for rectilinear steiner tree construction. In: Proceedings of embedded computer systems design, pp 1–5

  • Liu G, Chen G, Guo W, Chen Z (2011) DPSO-based rectilinear steiner minimal tree construction considering bend reduction. In: Proceedings of the 7th international conference on natural computation, pp 1161–1165

  • Liu G, Chen G, Guo W (2012) DPSO based octagonal steiner tree algorithm for VLSI routing. In: Proceedings of the 5th international conference on advanced computational intellligence, pp 383–387

  • Liu G, Guo W, Li R, Niu Y, Chen G (2015) XGRouter: high-quality global router in X-architecture with particle swarm optimization. Front Comput Sci 9(4):576–594

    Article  Google Scholar 

  • Liu G, Guo W, Niu Y, Chen G, Huang X (2015) A PSO-based timing-driven Octilinear Steiner tree algorithm for VLSI routing considering bend reduction. Soft Comput 19(5):1153–1169

    Article  MATH  Google Scholar 

  • Liu G, Huang X, Guo W, Niu Y, Chen G (2015) Multilayer obstacle-avoiding X-architecture steiner minimal tree construction based on particle swarm optimization. IEEE Trans Cybern 45(5):989–1002

    Google Scholar 

  • Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10(2):629–640

    Article  Google Scholar 

  • Liu W, Kao W, Li Y, Chao K (2013) NCTU-GR 2.0: multithreaded collision-aware global routing with bounded-length maze routing. IEEE Trans Comput Aid Des 32(5):709–722

    Article  Google Scholar 

  • Lv H, Zheng J, Zhou C, Zhou, C, Li K (2009) The convergence analysis of genetic algorithm based on space mating. In: Proceeding of the 5th international conference on natural computation, pp 557–562

  • Ma J, Yang B, Ma SH (2000) A near-optimal approximation algorithm for Manhattan Steiner Tree. J Soft 11(2):260–264 (in Chinese)

    Google Scholar 

  • Manna S, Chakrabarti T, Sharma U, Sarkar SK (2015) Efficient VLSI routing optimization employing discrete differential evolution technique. In: Proceedings of Recent Trends in Information Systems, pp 461–464

  • Moscato P (1989) On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. Caltech Concurr Comput Progr C3P Rep 826: 1989

  • Numaoka C (1996) Bacterial evolution algorithm for rapid adaptation. In: Proceedings of European workshop on modelling autonomous agents in a multi-agent world, pp 139–148

    Google Scholar 

  • Rada-Vilela J, Zhang M, Seah W (2013) A performance study on synchronicity and neighborhood size in particle swarm optimization. Soft Comput 17(6):1019–1030

    Article  Google Scholar 

  • Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255

    Article  Google Scholar 

  • Rudolph G (1994) Convergence analysis of canonical genetic algorithms. IEEE Trans Neural Network 5(1):96–101

    Article  MathSciNet  Google Scholar 

  • Ruiz-Cruz R, Sanchez EN, Ornelas-Tellez F, Loukianov AG, Harley RG (2013) Particle swarm optimization for discrete-time inverse optimal control of a doubly fed induction generator. IEEE Trans Cybern 43(6):1698–1709

    Article  Google Scholar 

  • Samanta T, Ghosal P, Rahaman H, Dasgupta PS (2006) A heuristic methiod for constructing hexagonal steiner minimal trees for routing in VLSI. In: IEEE international symposium on circuits and systems, pp 1788–1791

  • Samanta T, Rahaman H, Dasgupta PS (2011) Near-optimal Y-routed delay trees in nanometric interconnect design. IET Comput Digit Tec 5(1):36–48

    Article  Google Scholar 

  • Scheifele R (2016) RC-aware global routing. In: IEEE/ACM international conference on computer-aided design, pp 1–8

  • Scheifele R (2017) Steiner trees with bounded RC-delay. Alogithmica 78(1):86–109

    Article  MathSciNet  MATH  Google Scholar 

  • Shi YH, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference of evolutionary computation, pp 69–73

  • Siddiqi UF, Sait SM (2017) A game theory based post-processing method to enhance VLSI global routers. IEEE Access 5:1328–1339

    Article  Google Scholar 

  • Thurber A, Xue G (1999) Computing hexagonal steiner trees using PCx for VLS. In: Proceedings of the 6th IEEE international conference on electronic, circuits, and system, pp 381–384

  • Wang D, Tan D, Liu L (2017) Particle swarm optimization algorithm: an overview. Soft Comput 1–22

  • Xu N, Hong XL (2009) Very large scale integration physical design theory and method. Tsinghua University Press, Tsinghua (in Chinese)

    Google Scholar 

  • Xu X, Rong H, Trovati M, Liptrott M, Bessis N (2016) CS-PSO: chaotic particle swarm optimization algorithm for solving combinatorial optimization problems. Soft Comput 1–13

  • Xue B, Zhang MJ, Browne MN (2013) Particle swarm optimization for feature selection in classification: a multi-objective approach. IEEE Trans Cybern 43(6):1656–1671

    Article  Google Scholar 

  • Yan JT (2008) Timing-driven octilinear steiner tree construction based on steiner-point reassignment and path reconstruction. ACM Trans Des Automat El 13(2):26

    MathSciNet  Google Scholar 

  • Zachariasen M (2003) GeoSteiner Homepage. Available: http://www.diku.dk/geosteiner

  • Zhu Q, Zhou H, Jing T, Hong XL, Yang Y (2005) Spanning graph-based nonrectilinear Steiner tree allgorithms. IEEE Trans Comput Aid Des 24(7):1066–1075

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the reviewers for their valuable comments/suggestions which helped to improve the quality of this paper significantly. This work was supported in part by the National Natural Science Foundation of China under Grants No. 61877010 and No.11501114, the National Basic Research Program of China No. 2011CB808000, and the Fujian Natural Science Funds under Grant No. 2019J01243, the project of Technology Innovation Platform of Fujian Province (Grant No. 2014H2005 and No. 2009J1007), and the Fujian Collaborative Innovation Center for Big Data Applications in Governments.

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, China

    Genggeng Liu, Zhisheng Chen, Zhen Zhuang, Wenzhong Guo & Guolong Chen

  2. Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, 350116, China

    Genggeng Liu & Wenzhong Guo

  3. Key Laboratory of Spatial Data Mining and Information Sharing, Ministry of Education, Fuzhou, 350116, China

    Genggeng Liu & Wenzhong Guo

Authors
  1. Genggeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhisheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhen Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenzhong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Guolong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guolong Chen.

Ethics declarations

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, G., Chen, Z., Zhuang, Z. et al. A unified algorithm based on HTS and self-adapting PSO for the construction of octagonal and rectilinear SMT. Soft Comput 24, 3943–3961 (2020). https://doi.org/10.1007/s00500-019-04165-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-04165-2

Keywords

Search

Navigation