skip to main content
article

Annealing placement by thermodynamic combinatorial optimization

Published: 01 July 2004 Publication History

Abstract

Placement is key issue of integrated circuit physical design. There exist some techniques inspired in thermodynamics coping with this problem as Simulated Annealing. In this article, we present a combinatorial optimization method directly derived from both Thermodynamics and Information Theory. In TCO (Thermodynamic Combinatorial Optimization), two kinds of processes are considered: microstate and macrostate transformations. Applying the Shannon's definition of entropy to reversible microstate transformations, a probability of acceptance based on Fermi--Dirac statistics is derived. On the other hand, applying thermodynamic laws to macrostate transformations, an efficient annealing schedule is provided. TCO has been compared with a custom Simulated Annealing (SA) tool on a set of benchmark circuits for the FPGA (Field Programmable Gate Arrays) placement problem. TCO has provided the high-quality results of SA, while inheriting the adaptive properties of Natural Optimization (NO).

References

[1]
Aarts E. and Korst J. 1989. Simulated Annealing and Boltzmann Machines, A Stochastic Approach to Combinatorial Optimization and Neural Computing. Wiley, New York.
[2]
Betz, V. and Rose, J., Eds. 1997. VPR: A new packing, placement and routing tools for FPGA research. In Proceedings of the 7th International Workshop on Field-Programmable Logic and Applications (FPL) (Oxford, UK. Sept). Springer-Verlag, New York, 213--222.
[3]
Betz, V. and Rose, J. 1998. Effect of the prefabricated routing track distribution on FPGA area-efficiency. IEEE Trans. VLSI 6, 445--456.
[4]
Breuer, M. A. 1977. A class of min-cut placement algorithms. In Proceedings of the ACM/IEEE DAC, 284--290.
[5]
Callen, H. B. 1960. Thermodynamics. Willey, New York.
[6]
Cheng, C. E. 1994. RISA: Accurate and efficient placement routability modeling. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (San Jose, Calif., Nov.). ACM, New York, 690--695.
[7]
Cohoon, J. P. and Paris, W. 1986. Genetic Placement. Proc. IEEE ICCAD. Washington, DC, United States, 422--425.
[8]
de Vicente, J., Lanchares, J., and Hermida R. 1998. RSR: A new rectilinear steiner minimum tree approximation for FPGA placement and global routing. In Proceedings of the 24th Euromicro Conference (Västeras, Sweden). 192--195.
[9]
de Vicente, J., Lanchares, J., and Hermida R. 1999. Placement optimization based on global routing updating for system partitioning onto multi-FPGA mesh topologies. In Proceedings of the International Workshop on Field Programmable Logic and Applications (FPL), (Glasgow). Lecture Notes in Computer Science, vol. 1673. Springer-Verlag, New York, 91--100.
[10]
de Vicente, J., Lanchares, J., and Hermida R. 2000. Adaptive placement by natural optimization. In Proceedings of the 11th IEEE International Workshop on Rapid System Prototyping. IEEE Computer Society Press, Los Alamitos, Calif., 188--193.
[11]
Geman S. and Geman, D. 1984. Stochastic relaxation, Gibbs distribution and the Bayesian restoration in images. IEEE Trans. Patt. Anal. Mac. Int. 6, 6, 721--741.
[12]
Hajec B. 1988. Cooling schedules for optimal annealing. Math. Oper. Res. 13, 311--329.
[13]
Ingber, L. 1989. Very fast simulated re-annealing. Math. Comput. Model. 12, 967--973.
[14]
Ingber, L. 1996. Adaptive simulated annealing (ASA): Lesson learned. Control Cybernet. 25, 33--54.
[15]
Johnson, M. E., Bohachevsky, I. O., and Stein, M. L. 1986. Generalized simulated annealing for function optimization. Technometrics 28, 3, 209--217.
[16]
Kirkpatric, S., Gelatt, C. D., and Vecchi, M. P. 1983. Optimization by simulated annealing. Science 220, 671--680.
[17]
Kleinhans, J. M., Sigl, G., and Johannes, F. M., and Antreich, K. J.1991. GORDIAN: VLSI placement by quadratic programming and slicing optimization. IEEE Trans. CAD Integ. Circ. Syst. 10, 356--365.
[18]
Otten, R. H. J. M. and van Ginneken L. P. P. P. 1989. The Annealing Algorithm. Kluwer.
[19]
Quinn, N. R. and Breuer, M. A. 1979. A force directed component placement procedure for printed circuit boards. IEEE Trans. Circ. Syst. CAS-26, 377--388.
[20]
Rose, J., Klebsch, W., and Wolf, J. 1990. Temperature measurement and equilibrium dynamics of simulated annealing placement. IEEE Trans. CAD 9, 253--259.
[21]
Rose, J., el Gamal, A., and Sangiovanni-Vincentelli, A. 1993. Architecture of FPGAs. In Proceedings of IEEE, 1013--1029.
[22]
Sechen, C. and Sangiovanni-Vincentelli, A. 1984. The TimberWolf placement and routing package. In Proceedings of the Custom Integrated Circuit Conference (Rochester, N.Y.). 522--527.
[23]
Shannon, C. E. 1948. A mathematical theory of communication. I & II. Bell Syst. Tech. J., 27, 379--423, 623--656.
[24]
Sherwani, N. A. 1999. Algorithms for VLSI Physical Design Automation. Kluwer Academic Publishers.
[25]
Siarry, P., Bergonzi, L., and Dreyfus G. 1987. Thermodynamic optimization of block placement. IEEE Trans. CAD 6, 211--221.
[26]
Szu H. and Hartley, R. 1987. Fast simulated annealing. Phys. Lett. A 122, 157--162.
[27]
Wong, D. F., Leong, H. W., and Liu, C. L. 1988. Simulated Annealing for VLSI Desing. Kluwer.
[28]
Wong, D. F. and Liu, C. L. 1986. A new algorithm for floorplan design. In Proceedings of the 23rd ACM/IEEE Design Automation Conference (Las Vegas, Nev.). ACM, New York, 101--107. (RSP), (Paris, France). IEEE Computer Society, Press, Los Alamitos, Calif., 188--193.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Design Automation of Electronic Systems
ACM Transactions on Design Automation of Electronic Systems  Volume 9, Issue 3
July 2004
112 pages
ISSN:1084-4309
EISSN:1557-7309
DOI:10.1145/1013948
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

Publication History

Published: 01 July 2004
Published in TODAES Volume 9, Issue 3

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Recofigurable
  2. combinatorial optimization
  3. entropy
  4. information theory
  5. programmable logic
  6. thermodynamics

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)9
  • Downloads (Last 6 weeks)0
Reflects downloads up to 14 Sep 2024

Other Metrics

Citations

Cited By

View all

View Options

Get Access

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media