Translating Constraints into QUBOs for the Quadratic Knapsack Problem

Tariq H. Bontekoe; W. van der Schoot; Frank Phillipson

doi:10.1007/978-3-031-36030-5_8

Translating Constraints into QUBOs for the Quadratic Knapsack Problem

Tariq H. Bontekoe, W. van der Schoot, Frank Phillipson

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

One of the first fields where quantum computing will likely show its use is optimisation. Many optimisation problems naturally arise in a quadratic manner, such as the quadratic knapsack problem. The current state of quantum computers requires these problems to be formulated as a quadratic unconstrained binary optimisation problem, or QUBO. Constrained quadratic binary optimisation can be translated into QUBOs by translating the constraint. However, this translation can be made in several ways, which can have a large impact on the performance when solving the QUBO. We show six different formulations for the quadratic knapsack problem and compare their performance using simulated annealing. The best performance is obtained by a formulation that uses no auxiliary variables for modelling the inequality constraint.

Original language	English
Title of host publication	Computational Science - ICCS 2023
Subtitle of host publication	23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V
Editors	Jiri Mikyska, Clélia de Mulatier, Maciej Paszynski, Valeria V. Krzhizhanovskaya, Jack J. Dongorra, Peter M.A. Sloot
Publisher	Springer, Cham
Pages	90-107
ISBN (Electronic)	978-3-031-36030-5
ISBN (Print)	978-3-031-36029-9
DOIs	https://doi.org/10.1007/978-3-031-36030-5_8
Publication status	Published - 2023

Publication series

Series	Lecture Notes in Computer Science
Volume	14077
ISSN	0302-9743

Keywords

quadratic knapsack problem
quadratic unconstrained binary optimisation problem
quantum computing
simulated annealing

Access to Document

10.1007/978-3-031-36030-5_8

Cite this

Bontekoe, T. H., van der Schoot, W., & Phillipson, F. (2023). Translating Constraints into QUBOs for the Quadratic Knapsack Problem. In J. Mikyska, C. de Mulatier, M. Paszynski, V. V. Krzhizhanovskaya, J. J. Dongorra, & P. M. A. Sloot (Eds.), Computational Science - ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V (pp. 90-107). Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_8

Bontekoe, Tariq H. ; van der Schoot, W. ; Phillipson, Frank. / Translating Constraints into QUBOs for the Quadratic Knapsack Problem. Computational Science - ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. editor / Jiri Mikyska ; Clélia de Mulatier ; Maciej Paszynski ; Valeria V. Krzhizhanovskaya ; Jack J. Dongorra ; Peter M.A. Sloot. Springer, Cham, 2023. pp. 90-107 (Lecture Notes in Computer Science, Vol. 14077).

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abstract = "One of the first fields where quantum computing will likely show its use is optimisation. Many optimisation problems naturally arise in a quadratic manner, such as the quadratic knapsack problem. The current state of quantum computers requires these problems to be formulated as a quadratic unconstrained binary optimisation problem, or QUBO. Constrained quadratic binary optimisation can be translated into QUBOs by translating the constraint. However, this translation can be made in several ways, which can have a large impact on the performance when solving the QUBO. We show six different formulations for the quadratic knapsack problem and compare their performance using simulated annealing. The best performance is obtained by a formulation that uses no auxiliary variables for modelling the inequality constraint.",

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author = "Bontekoe, {Tariq H.} and {van der Schoot}, W. and Frank Phillipson",

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Bontekoe, TH, van der Schoot, W & Phillipson, F 2023, Translating Constraints into QUBOs for the Quadratic Knapsack Problem. in J Mikyska, C de Mulatier, M Paszynski, VV Krzhizhanovskaya, JJ Dongorra & PMA Sloot (eds), Computational Science - ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. Springer, Cham, Lecture Notes in Computer Science, vol. 14077, pp. 90-107. https://doi.org/10.1007/978-3-031-36030-5_8

Translating Constraints into QUBOs for the Quadratic Knapsack Problem. / Bontekoe, Tariq H.; van der Schoot, W.; Phillipson, Frank.
Computational Science - ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. ed. / Jiri Mikyska; Clélia de Mulatier; Maciej Paszynski; Valeria V. Krzhizhanovskaya; Jack J. Dongorra; Peter M.A. Sloot. Springer, Cham, 2023. p. 90-107 (Lecture Notes in Computer Science, Vol. 14077).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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Bontekoe TH, van der Schoot W, Phillipson F. Translating Constraints into QUBOs for the Quadratic Knapsack Problem. In Mikyska J, de Mulatier C, Paszynski M, Krzhizhanovskaya VV, Dongorra JJ, Sloot PMA, editors, Computational Science - ICCS 2023: 23rd International Conference Prague, Czech Republic, July 3-5, 2023 Proceedings, Part V. Springer, Cham. 2023. p. 90-107. (Lecture Notes in Computer Science, Vol. 14077). doi: 10.1007/978-3-031-36030-5_8