skip to main content
10.1145/3240765.3240806guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
research-article

Enhancing the Solution Quality of Hardware Ising-Model Solver via Parallel Tempering

Authors Info & Claims
Published:05 November 2018Publication History

ABSTRACT

We propose an efficient Ising processor with approximated parallel tempering (IPAPT) implemented on an FPGA. Hardware-friendly approximations of the components of parallel tempering (PT) are proposed to enhance solution quality with low hardware overhead. Multiple replicas of Ising states having different temperatures run in parallel by sharing a single network structure, and the replicas are exchanged based on the approximated energy evaluation. The application of PT substantially improves the quality of optimization solutions. The experimental results on the various max-cut problems have shown that utilization of PT significantly increases the probability of obtaining optimal solutions, and IPAPT obtains optimal solutions two orders magnitude faster than a software solver.

References

  1. [1].D-Wave. http://www.dwavesys.com/Google ScholarGoogle Scholar
  2. [2].G-Set. http://web.stanford.edu/-yyye/yyye/Gset/Google ScholarGoogle Scholar
  3. [3].Geyer C.J. 1991. Markov chain Monte Carlo maximum likelihood. In Computing science and statistics: Proceedings of 23rd Symposium on the Interface Interface Foundation. 156163.Google ScholarGoogle Scholar
  4. [4].Vasil S Denchev, Sergio Boixo, Sergei V Isakov, Ding Nan, Babbush Ryan, Smelyanskiy Vadim, Martinis John, and Neven Hartmut. 2016. What is the computational value of finite-range tunneling? Physical Review X 6, 3, 031015. https://doi.org/10.1103/PhysRevX.6.031015Google ScholarGoogle Scholar
  5. [5].Dorigo Marco and Gambardella Luca Maria. 1997. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on evolutionary computation 1, 1, 5366. https://doi.org/10.1109/4235.585892Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. [6].Earl David J. and Deem Michael W.. 2005. Parallel tempering: Theory, applications, and new perspectives. Physical Chemistry Chemical Physics 7, 23, 39103916. https://doi.org/10.1039/B509983HGoogle ScholarGoogle ScholarCross RefCross Ref
  7. [7].Farhi Edward, Goldstone Jeffrey, Gutmann Sam, Lapan Joshua, Lundgren Andrew, and Preda Daniel. 2001. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 5516, 472475. https://doi.org/10.1126/science.1057726Google ScholarGoogle ScholarCross RefCross Ref
  8. [8].Grippo Luigi, Palagi Laura, Piacentini Mauro, Piccialli Veronica, and Rinaldi Giovanni. 2012. SpeeDP: an algorithm to compute SDP bounds for very large Max-Cut instances. Mathematical programming 136, 2, 353373. https://doi.org/10.1007/s10107-012-0593-0Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. [9].Gyoten Hidenori, Hiromoto Masayuki, and Sato Takashi. 2018. Area efficient annealing processor for Ising model without random number generator. IEICE Transactions on Information and Systems E101-D, 2, 314323. https://doi.org/10.1587/transinf.2017RCP0015Google ScholarGoogle Scholar
  10. [10].Helmberg Christoph and Rendl Franz. 2000. A spectral bundle method for semidefinite programming. SIAM Journal on Optimization 10, 3, 673696. https://doi.org/10.1137/s1052623497328987Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. [11].Hukushima Koji and Nemoto Koji. 1996. Exchange Monte Carlo method and application to spin glass simulations. Journal of the Physical Society of Japan 65, 6, 16041608. https://doi.org/10.1143/JPSJ.65.1604Google ScholarGoogle ScholarCross RefCross Ref
  12. [12].IBM. IBM ILOG CPLEX Optimization Studio V12.6.2 documentation.Google ScholarGoogle Scholar
  13. [13].Kadowaki Tadashi and Nishimori Hidetoshi. 1998. Quantum annealing in the transverse Ising model. Physical Review E 58, 5, 53555363. https://doi.org/10.1103/PhysRevE.58.5355Google ScholarGoogle ScholarCross RefCross Ref
  14. [14].Kahruman Sera, Kolotoglu Elif, Butenko Sergiy, and Hicks Illya V. 2007. On greedy construction heuristics for the MAX-CUT problem. International Journal of Computational Science and Engineering 3, 3, 211218. https://doi.org/10.1504/ijcse.2007.017827Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. [15].Kochenberger Gary A, Hao Jin-Kao, Lü Zhipeng, Wang Haibo, and Glover Fred. 2013. Solving large scale max cut problems via tabu search. Journal of Heuristics 19, 4, 565571. https://doi.org/10.1007/s10732-011-9189-8Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. [16].Lucas Andrew. 2014. Ising formulations of many NP problems. Frontiers in Physics 2, 5, 115. https://doi.org/10.3389/fphy.2014.00005Google ScholarGoogle Scholar
  17. [17].Matsubara Satoshi, Tamura Hirotaka, Takatsu Motomu, Yoo Danny, Vatankhahghadim Behraz, Yamasaki Hironobu, Miyazawa Toshiyuki, Tsukamoto Sanroku, Watanabe Yasuhiro, Takemoto Kazuya, et al. 2017. Ising-Model Optimizer with Parallel-Trial Bit-Sieve Engine. In Conference on Complex, Intelligent, and Software Intensive Systems. Springer, 432438. https://doi.org/10.1007/978-3-319-61566-0_39Google ScholarGoogle Scholar
  18. [18].McMahon Peter L, Marandi Alireza, Haribara Yoshitaka, Hamerly Ryan, Langrock Carsten, Tamate Shuhei, Inagaki Takahiro, Takesue Hiroki, Utsunomiya Shoko, Aihara Kazuyuki, et al. 2016. A fully programmable 100-spin coherent Ising machine with all-to-all connections. Science 354, 6312, 614617. https://doi.org/10.1126/science.aah5178Google ScholarGoogle ScholarCross RefCross Ref
  19. [19].Metropolis Nicholas, Rosenbluth Arianna W., Rosenbluth Marshall N., Teller Augusta H., and Teller Edward. 1953. Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics 21, 6, 10871092. https://doi.org/10.1063/1.1699114Google ScholarGoogle ScholarCross RefCross Ref
  20. [20].Nishimori Hidetoshi. 2001. Statistical physics of spin glasses and information processing. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198509417.001.0001Google ScholarGoogle ScholarCross RefCross Ref
  21. [21].Someya Kenta, Ono Ryoto, and Kawahara Takayuki. 2016. Novel Ising model using dimension-control for high-speed solver for Ising machines. In New Circuits and Systems Conference (NEWCAS), 2016 14th IEEE International. IEEE, 14. https://doi.org/10.1109/NEWCAS.2016.7604797Google ScholarGoogle Scholar
  22. [22].Swendsen Robert H. and Wang Jian-Sheng. 1986. Replica Monte Carlo Simulation of Spin-Glasses. Physical Review Letters 57, 21, 26072609. https://doi.org/10.1103/PhysRevLett.57.2607Google ScholarGoogle ScholarCross RefCross Ref
  23. [23].Tovey Craig A. 1984. A simplified NP-complete satisfiability problem. Discrete applied mathematics 8, 1, 8589. https://doi.org/10.1016/0166-218X_84_90081-7Google ScholarGoogle ScholarCross RefCross Ref
  24. [24].Wang Xingfu, Li Pengcheng, Wang Lin, and Wang Lei. 2017. A novel genetic algorithm based on circles for larger-scale traveling salesman problem. In 2017 International Conference on Robotics and Automation Sciences (ICRAS). IEEE, 189194. https://doi.org/10.1109/ICRAS.2017.8071942Google ScholarGoogle Scholar
  25. [25].Yamaoka Masanao, Yoshimura Chihiro, Hayashi Masato, Okuyama Takuya, Aoki Hidetaka, and Mizuno Hiroyuki. 2016. A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing. IEEE Journal of Solid-State Circuits 51, 1, 303309. https://doi.org/10.1109/JSSC.2015.2498601Google ScholarGoogle ScholarCross RefCross Ref
  26. [26].Yoshimura Chihiro, Hayashi Masato, Okuyama Takuya, and Yamaoka Masanao. 2017. Implementation and Evaluation of FPGA-based Annealing Processor for Ising Model by use of Resource Sharing. International Journal of Networking and Computing 7, 2, 154172. https://doi.org/10.15803/ijnc.7.2_154Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Enhancing the Solution Quality of Hardware Ising-Model Solver via Parallel Tempering
        Index terms have been assigned to the content through auto-classification.

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in
        • Published in

          cover image Guide Proceedings
          2018 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)
          Nov 2018
          939 pages

          Copyright © 2018

          Publisher

          IEEE Press

          Publication History

          • Published: 5 November 2018

          Permissions

          Request permissions about this article.

          Request Permissions

          Qualifiers

          • research-article