Efficient Ising Model Mapping to Solving Slot Placement Problem

Kanamaru, Sho; Oku, Daisuke; Tawada, Masashi; Tanaka, Shu; Hayashi, Masato; Yamaoka, Masanao; Yanagisawa, Masao; Togawa, Nozomu

doi:10.1109/icce.2019.8661947

Cited by 12 publications

(6 citation statements)

References 7 publications

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“…The objective function of the slotplacement problem is to minimize the total weighted wiring length (TWWL). The slot-placement problem plays an important role such as in logic-block placement in Field-Probrammable Gate Array (FPGA) design [16]- [18]. In practice, several item pairs must be placed within a given distance when severe timing constraints are imposed on them in FPGA design.…”

Section: Constrained Slot Placement Problemmentioning

confidence: 99%

“…In addition, the performance of quantum annealing for quadratic assignment problems was investigated [25]. Recently an Ising model mapping of slot-placement problem was proposed [18]. In this paper, based on the previous study [18], Ising machines are applied to the constrained slot-placement problem.…”

Section: Constrained Slot Placement Problemmentioning

confidence: 99%

“…Recently an Ising model mapping of slot-placement problem was proposed [18]. In this paper, based on the previous study [18], Ising machines are applied to the constrained slot-placement problem.…”

Section: Constrained Slot Placement Problemmentioning

confidence: 99%

See 2 more Smart Citations

Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

Kanamaru

Kawamura

Tanaka

et al. 2021

IEICE Trans. Inf. & Syst.

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Ising machines have attracted attention, which is expected to obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slotplacement problem is one of the combinatorial optimization problems, regarded as a quadratic assignment problem, which relates to the optimal logic-block placement in a digital circuit as well as optimal delivery planning. Here, we propose a mapping to the Ising model for solving a slotplacement problem with additional constraints, called a constrained slotplacement problem, where several item pairs must be placed within a given distance. Since the behavior of Ising machines is stochastic and we map the problem to the Ising model which uses the penalty method, the obtained solution does not always satisfy the slot-placement constraint, which is different from the conventional methods such as the conventional simulated annealing. To resolve the problem, we propose an interpretation method in which a feasible solution is generated by post-processing procedures. We measured the execution time of an Ising machine and compared the execution time of the simulated annealing in which solutions with almost the same accuracy are obtained. As a result, we found that the Ising machine is faster than the simulated annealing that we implemented.

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Section: Constrained Slot Placement Problemmentioning

confidence: 99%

Section: Constrained Slot Placement Problemmentioning

confidence: 99%

See 1 more Smart Citation

Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

Kanamaru

Kawamura

Tanaka

et al. 2021

IEICE Trans. Inf. & Syst.

Self Cite

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“…CBMs are equivalent to Ising models; therefore, CBMs are also adaptable to combinatorial optimization problems. Many studies were related to Ising models [25], [26] and their hardware implementations [27]- [29] in recent years FIGURE 20: Efficiency of the calculation time because many problems in our society can be expressed as combinatorial optimization problems. Table 10 compares the results of our implementation and related studies.…”

Section: Related Workmentioning

confidence: 99%

FPGA Implementation of Hardware-Oriented Chaotic Boltzmann Machines

2020

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“…Substituting eqs. (19) and (22) into (21) gives (16). The guiding principle of ME design to achieve a high performance in Ising machines is that the intra-ring-coupling strength must be tuned according to eq.…”

Section: Types Of Minor-embeddingmentioning

confidence: 99%

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

2020

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We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

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Efficient Ising Model Mapping to Solving Slot Placement Problem

Cited by 12 publications

References 7 publications

Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

FPGA Implementation of Hardware-Oriented Chaotic Boltzmann Machines

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

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