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Title: Application of Quantum Annealing to Nurse Scheduling Problem

Abstract

Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is potentially achievable for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine returned results by using the annealing process a second time. We compare the performance of NSP using both forward and reverse annealing methods and describe how this approach might be used in practice.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Osaka Univ. (Japan)
  2. Univ. of Tennessee, Knoxville, TN (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1560436
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Volume: 9; Journal Issue: 1; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Ikeda, Kazuki, Nakamura, Yuma, and Humble, Travis S. Application of Quantum Annealing to Nurse Scheduling Problem. United States: N. p., 2019. Web. doi:10.1038/s41598-019-49172-3.
Ikeda, Kazuki, Nakamura, Yuma, & Humble, Travis S. Application of Quantum Annealing to Nurse Scheduling Problem. United States. doi:10.1038/s41598-019-49172-3.
Ikeda, Kazuki, Nakamura, Yuma, and Humble, Travis S. Fri . "Application of Quantum Annealing to Nurse Scheduling Problem". United States. doi:10.1038/s41598-019-49172-3. https://www.osti.gov/servlets/purl/1560436.
@article{osti_1560436,
title = {Application of Quantum Annealing to Nurse Scheduling Problem},
author = {Ikeda, Kazuki and Nakamura, Yuma and Humble, Travis S.},
abstractNote = {Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is potentially achievable for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine returned results by using the annealing process a second time. We compare the performance of NSP using both forward and reverse annealing methods and describe how this approach might be used in practice.},
doi = {10.1038/s41598-019-49172-3},
journal = {Scientific Reports},
number = 1,
volume = 9,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
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Cited by: 1 work
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Figures / Tables:

Figure 1 Figure 1: Graphical examples of the computed shift schedules for the case of $N$ = 3 nurses for $D$ = 4 days. A black square indicates that a nurse is scheduled to work. The horizontal axes labels the days and the vertical axes labels the nurses. Te left figure representsmore » a schedule that satisfies all the constraints, while the right figure represents a schedule that fails to satisfy the soft nurse constraint of every nurse being assigned some days of work.« less

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