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

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

doi:10.1109/access.2021.3081685

Kensuke Tamura, Shu Tanaka + Show 3 more

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https://doi.org/10.1109/access.2021.3081685

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Abstract

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.

Highlights

IntroductionA. MOTIVATION Combinatorial optimization problems find the combination of decision variables that minimize or maximize an objective function under given constraints
We investigate the performance of common types of binary-integer encoding: one-hot encoding, binary encoding, and unary encoding
The feasible solutions (FSs) rate is obtained by calculating Hconstraint since the inequality constraint is satisfied if and only if Hconstraint = 0

Summary

Introduction

A. MOTIVATION Combinatorial optimization problems find the combination of decision variables that minimize or maximize an objective function under given constraints. Most problems are known as NP-hard or NP-complete [1], and the number of solution candidates exponentially increases with the number of decision variables. Because combinatorial optimization problems are ubiquitous in social life and industry [2]–[12], there is a growing interest in developing technologies that can efficiently and accurately find optimal or quasi-optimal solutions. Ising machines have recently attracted attention as efficient solvers that achieve faster computations than conventional digital computers with the von Neumann architecture [13]–[25]. Many underlying algorithms for Ising machines have been proposed [26]–[28]. Proposals have been made for efficient input formats to Ising machines based on the operation

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