TY - JOUR

T1 - Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

AU - Tamura, Kensuke

AU - Shirai, Tatsuhiko

AU - Katsura, Hosho

AU - Tanaka, Shu

AU - Togawa, Nozomu

N1 - Funding Information:
This article is based on the results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO). The work of Shu Tanaka was supported in part by the Japan Society for the Promotion of Science (JSPS) KAKENHI under Grant 19H01553. Kensuke Tamura and Hosho Katsura acknowledge Yutaka Akagi for fruitful discussions.
Publisher Copyright:
© 2013 IEEE.

PY - 2021

Y1 - 2021

N2 - The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binary-integer encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

AB - The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binary-integer encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

KW - Ising machine

KW - Ising model

KW - binary-integer encoding

KW - combinatorial optimization problem

KW - quadratic knapsack problem

KW - quadratic unconstrained binary optimization

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U2 - 10.1109/ACCESS.2021.3081685

DO - 10.1109/ACCESS.2021.3081685

M3 - Article

AN - SCOPUS:85107233033

VL - 9

SP - 81032

EP - 81039

JO - IEEE Access

JF - IEEE Access

SN - 2169-3536

M1 - 9435359

ER -