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.
- [1].D-Wave. http://www.dwavesys.com/Google Scholar
- [2].G-Set. http://web.stanford.edu/-yyye/yyye/Gset/Google Scholar
- [3]. 1991. Markov chain Monte Carlo maximum likelihood. In Computing science and statistics: Proceedings of 23rd Symposium on the Interface Interface Foundation. 156–163.Google Scholar
- [4]. . 2016. What is the computational value of finite-range tunneling? Physical Review X 6, 3, 031015. https://doi.org/10.1103/PhysRevX.6.031015Google Scholar
- [5]. . 1997. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on evolutionary computation 1, 1, 53–66. https://doi.org/10.1109/4235.585892Google ScholarDigital Library
- [6]. . 2005. Parallel tempering: Theory, applications, and new perspectives. Physical Chemistry Chemical Physics 7, 23, 3910–3916. https://doi.org/10.1039/B509983HGoogle ScholarCross Ref
- [7]. . 2001. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 5516, 472–475. https://doi.org/10.1126/science.1057726Google ScholarCross Ref
- [8]. . 2012. SpeeDP: an algorithm to compute SDP bounds for very large Max-Cut instances. Mathematical programming 136, 2, 353–373. https://doi.org/10.1007/s10107-012-0593-0Google ScholarDigital Library
- [9]. . 2018. Area efficient annealing processor for Ising model without random number generator. IEICE Transactions on Information and Systems E101-D, 2, 314–323. https://doi.org/10.1587/transinf.2017RCP0015Google Scholar
- [10]. . 2000. A spectral bundle method for semidefinite programming. SIAM Journal on Optimization 10, 3, 673–696. https://doi.org/10.1137/s1052623497328987Google ScholarDigital Library
- [11]. . 1996. Exchange Monte Carlo method and application to spin glass simulations. Journal of the Physical Society of Japan 65, 6, 1604–1608. https://doi.org/10.1143/JPSJ.65.1604Google ScholarCross Ref
- [12].IBM. IBM ILOG CPLEX Optimization Studio V12.6.2 documentation.Google Scholar
- [13]. . 1998. Quantum annealing in the transverse Ising model. Physical Review E 58, 5, 5355–5363. https://doi.org/10.1103/PhysRevE.58.5355Google ScholarCross Ref
- [14]. . 2007. On greedy construction heuristics for the MAX-CUT problem. International Journal of Computational Science and Engineering 3, 3, 211–218. https://doi.org/10.1504/ijcse.2007.017827Google ScholarDigital Library
- [15]. . 2013. Solving large scale max cut problems via tabu search. Journal of Heuristics 19, 4, 565–571. https://doi.org/10.1007/s10732-011-9189-8Google ScholarDigital Library
- [16]. . 2014. Ising formulations of many NP problems. Frontiers in Physics 2, 5, 1–15. https://doi.org/10.3389/fphy.2014.00005Google Scholar
- [17]. 2017. Ising-Model Optimizer with Parallel-Trial Bit-Sieve Engine. In Conference on Complex, Intelligent, and Software Intensive Systems. Springer, 432–438. https://doi.org/10.1007/978-3-319-61566-0_39Google Scholar
- [18]. 2016. A fully programmable 100-spin coherent Ising machine with all-to-all connections. Science 354, 6312, 614–617. https://doi.org/10.1126/science.aah5178Google ScholarCross Ref
- [19]. . 1953. Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics 21, 6, 1087–1092. https://doi.org/10.1063/1.1699114Google ScholarCross Ref
- [20]. . 2001. Statistical physics of spin glasses and information processing. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198509417.001.0001Google ScholarCross Ref
- [21]. . 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, 1–4. https://doi.org/10.1109/NEWCAS.2016.7604797Google Scholar
- [22]. . 1986. Replica Monte Carlo Simulation of Spin-Glasses. Physical Review Letters 57, 21, 2607–2609. https://doi.org/10.1103/PhysRevLett.57.2607Google ScholarCross Ref
- [23]. . 1984. A simplified NP-complete satisfiability problem. Discrete applied mathematics 8, 1, 85–89. https://doi.org/10.1016/0166-218X_84_90081-7Google ScholarCross Ref
- [24]. . 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, 189–194. https://doi.org/10.1109/ICRAS.2017.8071942Google Scholar
- [25]. . 2016. A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing. IEEE Journal of Solid-State Circuits 51, 1, 303–309. https://doi.org/10.1109/JSSC.2015.2498601Google ScholarCross Ref
- [26]. . 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, 154–172. https://doi.org/10.15803/ijnc.7.2_154Google ScholarCross Ref
Index Terms
- Enhancing the Solution Quality of Hardware Ising-Model Solver via Parallel Tempering
Recommendations
Reconfigurable hardware solution to parallel prefix computation
This paper presents the design and implementation of an efficient reconfigurable parallel prefix computation hardware on field-programmable gate arrays (FPGAs). The design is based on a pipelined dataflow algorithm, and control logic is added to ...
A decentralized parallel implementation for parallel tempering algorithm
Parallel tempering (PT), also known as replica exchange, is a powerful Markov Chain Monte Carlo sampling approach, which aims at reducing the relaxation time in simulations of physical systems. In this paper, we present a novel decentralized parallel ...
Comments