research-article

Adaptive Bulk Search: Solving Quadratic Unconstrained Binary Optimization Problems on Multiple GPUs

Authors:

Masaru Tatekawa,

Takashi Yazane,

Yoko InabaAuthors Info & Claims

ICPP '20: Proceedings of the 49th International Conference on Parallel Processing

Article No.: 62, Pages 1 - 11

https://doi.org/10.1145/3404397.3404423

Published: 17 August 2020 Publication History

Abstract

The quadratic unconstrained binary optimization (QUBO) is recently gathering attention in conjunction with quantum annealing (QA), since it is equivalent to finding the ground state of an Ising model. Due to the limitation of current QA systems, classical computers may outperform them. Researchers have thus been proposed to solve QUBO on FPGAs, GPUs, and special purpose processors. In this paper, we propose an adaptive bulk search (ABS), a framework for solving QUBO that can perform many searches in parallel on multiple GPUs. It supports fully-connected Ising models with up to 32k spins and 16-bit weights. In our ABS, a CPU host performs genetic algorithm (GA) while GPUs asynchronously perform local searches. A bottleneck for solving QUBO exists in the evaluation of the energy function, which requires computational cost for each solution. We show this can be reduced to in our ABS. The experimental results show that, with four NVIDIA GeForce RTX 2080 Ti GPUs, our framework can search up to 1.24 × 1012 solutions per second. We also show that our system quickly solves maximum cut and traveling salesman problems.

References

[1]

Mohammad H Amin. 2015. Searching for quantum speedup in quasistatic quantum annealers. Physical Review A 92, 5 (2015), 1–5.

[2]

Frank Arute 2019. Quantum supremacy using a programmable superconducting processor. Nature 574, 7779 (2019), 505–510.

[3]

Demian A Battaglia, Giuseppe E Santoro, and Erio Tosatti. 2005. Optimization by quantum annealing: Lessons from hard satisfiability problems. Physical Review E 71, 6 (2005), 066707.

[4]

Paul Benioff. 1980. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. Journal of statistical physics 22, 5 (1980), 563–591.

[5]

Jun Cai, William G Macready, and Aidan Roy. 2014. A practical heuristic for finding graph minors. arXiv preprint arXiv:1406.2741(2014).

[6]

NVIDIA Corporation. 2019. CUDA C++ programming guide (version 10.2).

[7]

NVIDIA Corporation. 2020. NVIDIA Turing GPU architecture. https://www.nvidia.com/content/dam/en-zz/Solutions/design-visualization/technologies/turing-architecture/NVIDIA-Turing-Architecture-Whitepaper.pdf.

[8]

Daniel Crawford, Anna Levit, Navid Ghadermarzy, Jaspreet S Oberoi, and Pooya Ronagh. 2016. Reinforcement learning using quantum Boltzmann machines. arXiv preprint arXiv:1612.05695(2016).

[9]

Vincent Dumoulin, Ian J Goodfellow, Aaron Courville, and Yoshua Bengio. 2014. On the challenges of physical implementations of RBMs. In Twenty-Eighth AAAI Conference on Artificial Intelligence.

Digital Library

[10]

David J Earl and Michael W Deem. 2005. Parallel tempering: Theory, applications, and new perspectives. Physical Chemistry Chemical Physics 7, 23 (2005), 3910–3916.

[11]

Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser. 2000. Quantum computation by adiabatic evolution. arXiv preprint quant-ph/0001106(2000).

[12]

Hayato Goto, Kosuke Tatsumura, and Alexander R. Dixon. 2019. Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems. Science advances 5, 4 (2019).

[13]

Laszlo Gyongyosi and Sandor Imre. 2019. A survey on quantum computing technology. Computer Science Review 31 (2019), 51–71.

Digital Library

[14]

Takahiro Inagaki, Yoshitaka Haribara, Koji Igarashi, Tomohiro Sonobe, Shuhei Tamate, Toshimori Honjo, Alireza Marandi, Peter L. McMahon, Takeshi Umeki, Koji Enbutsu, Osamu Tadanaga, Hirokazu Takenouchi, Kazuyuki Aihara, Ken ichi Kawarabayashi, Kyo Inoue, Shoko Utsunomiya, and Hiroki Takesue. 2016. A coherent Ising machine for 2000-node optimization problems. Science 354, 6312 (2016), 603–606.

[15]

M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose. 2011. Quantum annealing with manufactured spins. Nature 473, 7346 (2011), 194–198.

[16]

Tadashi Kadowaki and Hidetoshi Nishimori. 1998. Quantum annealing in the transverse Ising model. Physical Review E 58, 5 (1998), 5355.

[17]

Scott Kirkpatrick, C Daniel Gelatt, and Mario P Vecchi. 1983. Optimization by simulated annealing. Science 220, 4598 (1983), 671–680.

[18]

Gary Kochenberger, Jin-Kao Hao, Fred Glover, Mark Lewis, Zhipeng Lü, Haibo Wang, and Yang Wang. 2014. The unconstrained binary quadratic programming problem: a survey. Journal of Combinatorial Optimization 28, 1 (2014), 58–81.

Digital Library

[19]

Duan Li, X. L. Sun, and C. L. Liu. 2012. An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach. Journal of Global Optimization 52, 4 (2012), 797–829.

Digital Library

[20]

Bas Lodewijks. 2019. Mapping NP-hard and NP-complete optimisation problems to Quadratic Unconstrained Binary Optimisation problems. arXiv preprint arXiv:1911.08043(2019).

[21]

Andrew Lucas. 2014. Ising formulations of many NP problems. Frontiers in Physics 2(2014), 5.

[22]

Satoshi Matsubara, Hirotaka Tamura, Motomu Takatsu, Danny Yoo, Behraz Vatankhahghadim, Hironobu Yamasaki, Toshiyuki Miyazawa, Sanroku Tsukamoto, Yasuhiro Watanabe, Kazuya Takemoto, and Ali Sheikholeslami. 2017. Ising-model optimizer with parallel-trial bit-sieve engine. In Proc. of the International Conference on Complex, Intelligent, and Software Intensive Systems. 432–438.

[23]

Florian Neukart, Gabriele Compostella, Christian Seidel, David Von Dollen, Sheir Yarkoni, and Bob Parney. 2017. Traffic flow optimization using a quantum annealer. Frontiers in ICT 4(2017), 29.

[24]

Ruprecht Karl University of Heidelberg. 2020. TSPLIB. http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/.

[25]

Takuya Okuyama, Tomohiro Sonobe, Ken’ichi Kawarabayashi, and Masanao Yamaoka. 2019. Binary optimization by momentum annealing. Physical Review E 100, 1 (2019).

[26]

Panos M Pardalos and Somesh Jha. 1992. Complexity of Uniqueness and Local Search in Quadratic 0-1 Programming. Oper. Res. Lett. 11, 2 (1992), 119–123.

Digital Library

[27]

Gerhard Reinelt. 1991. TSPLIB: A traveling salesman problem library. ORSA journal on computing 3, 4 (1991), 376–384.

[28]

Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, and Marcos López De Prado. 2016. Solving the optimal trading trajectory problem using a quantum annealer. IEEE Journal of Selected Topics in Signal Processing 10, 6(2016), 1053–1060.

[29]

Kosuke Tatsumura, Alexander R. Dixon, and Hayato Goto. 2019. FPGA-Based Simulated Bifurcation Machine. In International Conference on Field Programmable Logic and Applications (FPL). 59–66.

[30]

Masanao Yamaoka, Chihiro Yoshimura, Masato Hayashi, Takuya Okuyama, Hidetaka Aoki, and Hiroyuki Mizuno. 2015. 20k-spin Ising chip for combinational optimization problem with CMOS annealing. In IEEE International Solid-State Circuits Conference (ISSCC). 1–3.

[31]

Yinyu Ye. 2020. G-set. https://web.stanford.edu/~yyye/yyye/Gset/.

Cited By

Chen YHua HNien CLin S(2024)VLSI Implementation of an Annealing Accelerator for Solving Combinatorial Optimization ProblemsIEEE Nanotechnology Magazine10.1109/MNANO.2024.337848318:3(23-30)Online publication date: Jun-2024
https://doi.org/10.1109/MNANO.2024.3378483
Huang KNien CZhang YLee CWang Y(2024)GPU-based Ising Machine for Solving Combinatorial Optimization Problems with Enhanced Parallel Tempering Techniques2024 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)10.1109/APCCAS62602.2024.10808341(636-640)Online publication date: 7-Nov-2024
https://doi.org/10.1109/APCCAS62602.2024.10808341
Li XNakano KTsukiyama SIto YKato TKawamata Y(2024)Generating hard quadratic unconstrained binary optimization instances via the method of combining bit reduction and duplication techniqueInternational Journal of Parallel, Emergent and Distributed Systems10.1080/17445760.2024.237692839:5(589-608)Online publication date: 9-Jul-2024
https://doi.org/10.1080/17445760.2024.2376928
Show More Cited By

Recommendations

GPU-accelerated scalable solver with bit permutated cyclic-min algorithm for quadratic unconstrained binary optimization
Highlights
- The adaptive bulk search is a QUBO solver alternative to quantum annealing.
- The ...
Abstract
A wide range of combinatorial optimization problems can be reduced to the Ising model, and equivalently the quadratic unconstrained binary optimization (QUBO) problem. Thus, in recent years, researchers have proposed to solve QUBO on ...
Compressed quadratization of higher order binary optimization problems
CF '20: Proceedings of the 17th ACM International Conference on Computing Frontiers

Recent hardware advances in quantum and quantum-inspired annealers promise substantial speedup for solving NP-hard combinatorial optimization problems compared to general-purpose computers. These special-purpose hardware are built for solving hard ...
Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization
Computational Science – ICCS 2023
Abstract
We introduce a novel approach to translate arbitrary 3-sat instances to Quadratic Unconstrained Binary Optimization (qubo) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach requires ...

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences

ICPP '20: Proceedings of the 49th International Conference on Parallel Processing

August 2020

844 pages

ISBN:9781450388160

DOI:10.1145/3404397

Copyright © 2020 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 August 2020

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed limited

Conference

ICPP '20

ICPP '20: 49th International Conference on Parallel Processing

August 17 - 20, 2020

AB, Edmonton, Canada

Acceptance Rates

Overall Acceptance Rate 91 of 313 submissions, 29%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

11
Total Citations
View Citations
368
Total Downloads

Downloads (Last 12 months)36
Downloads (Last 6 weeks)3

Reflects downloads up to 03 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Chen YHua HNien CLin S(2024)VLSI Implementation of an Annealing Accelerator for Solving Combinatorial Optimization ProblemsIEEE Nanotechnology Magazine10.1109/MNANO.2024.337848318:3(23-30)Online publication date: Jun-2024
https://doi.org/10.1109/MNANO.2024.3378483
Huang KNien CZhang YLee CWang Y(2024)GPU-based Ising Machine for Solving Combinatorial Optimization Problems with Enhanced Parallel Tempering Techniques2024 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)10.1109/APCCAS62602.2024.10808341(636-640)Online publication date: 7-Nov-2024
https://doi.org/10.1109/APCCAS62602.2024.10808341
Li XNakano KTsukiyama SIto YKato TKawamata Y(2024)Generating hard quadratic unconstrained binary optimization instances via the method of combining bit reduction and duplication techniqueInternational Journal of Parallel, Emergent and Distributed Systems10.1080/17445760.2024.237692839:5(589-608)Online publication date: 9-Jul-2024
https://doi.org/10.1080/17445760.2024.2376928
Pauckert JDebevere PParizy MAyodele MSilva SPaquete L(2023)Comparing Solution Combination Techniques in Scatter Search for Quadratic Unconstrained Binary OptimizationProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3596319(2241-2249)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583133.3596319
Yasudo R(2023)Bandit-based Variable Fixing for Binary Optimization on GPU Parallel Computing2023 31st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP)10.1109/PDP59025.2023.00031(154-158)Online publication date: Mar-2023
https://doi.org/10.1109/PDP59025.2023.00031
Li XNakano KIto YTakafuji DYazane TYano JKato TOzaki SMori RKatsuki R(2023)Bit duplication technique to generate hard quadratic unconstrained binary optimization problems with adjustable sizesConcurrency and Computation: Practice and Experience10.1002/cpe.796736:10Online publication date: 20-Nov-2023
https://doi.org/10.1002/cpe.7967
Li XNakano KIto YTakafuji DYazane TYano JOzaki SKatsuki RMori R(2022)Bit duplication technique to generate hard QUBO problems2022 Tenth International Symposium on Computing and Networking Workshops (CANDARW)10.1109/CANDARW57323.2022.00029(180-184)Online publication date: Nov-2022
https://doi.org/10.1109/CANDARW57323.2022.00029
Imanaga TNakano KYasudo RIto YKawamata YKatsuki ROzaki SYazane THamano K(2021)Solving the sparse QUBO on multiple GPUs for Simulating a Quantum Annealer2021 Ninth International Symposium on Computing and Networking (CANDAR)10.1109/CANDAR53791.2021.00011(19-28)Online publication date: Nov-2021
https://doi.org/10.1109/CANDAR53791.2021.00011
Kagawa HIto YNakano KYasudo RKawamata YKatsuki RTabata YYazane THamano K(2021)High‐throughput FPGA implementation for quadratic unconstrained binary optimizationConcurrency and Computation: Practice and Experience10.1002/cpe.656535:14Online publication date: 19-Aug-2021
https://doi.org/10.1002/cpe.6565
Kagawa HIto YNakano KYasudo RKawamata YKatsuki RTabata YYazane THamano K(2020)Fully-Pipelined Architecture for Simulated Annealing-based QUBO Solver on the FPGA2020 Eighth International Symposium on Computing and Networking (CANDAR)10.1109/CANDAR51075.2020.00013(39-48)Online publication date: Nov-2020
https://doi.org/10.1109/CANDAR51075.2020.00013
Show More Cited By

View Options

Login options

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

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Figures

Tables

Media

View Table of Conten