Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Tamura, Kensuke; Shirai, Tatsuhiko; Katsura, Hosho; Tanaka, Shu; Togawa, Nozomu

doi:10.1109/access.2021.3081685

Cited by 32 publications

(22 citation statements)

References 42 publications

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“…It is known that some combinatorial optimization problems can be transformed into QUBO 13 . In addition, other transformation techniques for QUBO formulation have also been proposed, such as encoding techniques to a binary variable 14 , 15 and converting methods from higher-order polynomial to a quadratic model 16 . And, furthermore, many applications have been reported as the success cases of the QUBO formulation, including vehicle path generation 12 , 17 , traffic signal control 18 , portfolio optimization 19 , quantum chemistry 20 , and machine learning 21 .…”

Section: Introductionmentioning

confidence: 99%

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Matsumori

Taki

Kadowaki

2022

Sci Rep

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Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We propose a BBO method based on factorization machine to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. For the efficient approximation around the optimum solution, in the proposed method, we probabilistically generate the neighbors of the optimized solution of the current model and update the model. We demonstrated that the proposed method can find the optimum mounting point positions in shorter calculation time and higher success probability of finding the optimal solution than a conventional BBO method. Our results can open up QUBO solvers’ potential for other applications in structural designs.

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Section: Introductionmentioning

confidence: 99%

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Matsumori

Taki

Kadowaki

2022

Sci Rep

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show abstract

“…It is known that some combinatorial optimization problems can be transformed into QUBO 11 . In addition, other transformation techniques for QUBO formulation have also been proposed, such as encoding techniques to a binary variable 12,13 and converting methods from higher-order polynomial to a quadratic model 14 . And, furthermore, many applications have been reported as the success cases of the QUBO formulation, including vehicle path generation 10,15 , traffic signal control 16 , portfolio optimization 17 , quantum chemistry 18 , and machine learning 19 .…”

Section: Introductionmentioning

confidence: 99%

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Matsumori,

Taki,

Kadowaki

2022

Preprint

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Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We employed the BBO methods to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. We demonstrated that BBO using a factorization machine shows good performance in both the calculation time and the success probability of finding the optimal solution. Our results can open up QUBO solvers' potential for other applications in structural designs.

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“…On the other hand, it is known that the quality of solutions obtained from solid-state annealers greatly depends on the formulation method [18]. Therefore, if multiple formulation methods can exist for a COP, it is quite important to clarify their strengths and weaknesses.…”

Section: Introductionmentioning

confidence: 99%

“…While we need some integer encoding method in formulating the QKP as QUBO, two typical methods exist: binary encoding (BE) and unary encoding (UE). In the previous study [18], these two methods were compared based on the experimental results obtained from a solid-state annealer. However, it is still unclear why a method is superior (or inferior) to the other because the annealing process is unobservable in the previous annealers.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Integer Encoding Method for Obtaining High-Quality Solutions of Quadratic Knapsack Problems on Solid-State Annealers

Jimbo

Okonogi

Ando

et al. 2022

IEICE Trans. Inf. & Syst.

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For formulating Quadratic Knapsack Problems (QKPs) into the form of Quadratic Unconstrained Binary Optimization (QUBO), it is necessary to introduce an integer variable, which converts and incorporates the knapsack capacity constraint into the overall energy function. In QUBO, this integer variable is encoded with auxiliary binary variables, and the encoding method used for it affects the behavior of Simulated Annealing (SA) significantly. For improving the efficiency of SA for QKP instances, this paper first visualized and analyzed their annealing processes encoded by conventional binary and unary encoding methods. Based on this analysis, we proposed a novel hybrid encoding (HE), getting the best of both worlds. The proposed HE obtained feasible solutions in the evaluation, outperforming the others in small-and medium-scale models.

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Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Cited by 32 publications

References 42 publications

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

A Hybrid Integer Encoding Method for Obtaining High-Quality Solutions of Quadratic Knapsack Problems on Solid-State Annealers

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