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Roster evaluation based on classifiers for the nurse rostering problem

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Abstract

The personnel scheduling problem is a well-known NP-hard combinatorial problem. Due to the complexity of this problem and the size of the real-world instances, it is not possible to use exact methods, and thus heuristics, meta-heuristics, or hyper-heuristics must be employed. The majority of heuristic approaches are based on iterative search, where the quality of intermediate solutions must be calculated. Unfortunately, this is computationally highly expensive because these problems have many constraints and some are very complex. In this study, we propose a machine learning technique as a tool to accelerate the evaluation phase in heuristic approaches. The solution is based on a simple classifier, which is able to determine whether the changed solution (more precisely, the changed part of the solution) is better than the original or not. This decision is made much faster than a standard cost-oriented evaluation process. However, the classification process cannot guarantee 100 % correctness. Therefore, our approach, which is illustrated using a tabu search algorithm in this study, includes a filtering mechanism, where the classifier rejects the majority of the potentially bad solutions and the remaining solutions are then evaluated in a standard manner. We also show how the boosting algorithms can improve the quality of the final solution compared with a simple classifier. We verified our proposed approach and premises, based on standard and real-world benchmark instances, to demonstrate the significant speedup obtained with comparable solution quality.

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Notes

  1. In this study, we do not count the input layer as a layer.

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Acknowledgments

This work was supported by ARTEMIS FP7 EU and by the Ministry of Education of the Czech Republic under the project DEMANES 295372 and by the Grant Agency of the Czech Republic under the Project GACR FOREST P103-16-23509S.

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Authors and Affiliations

  1. Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo náměstí 13, 121 35, Prague 2, Czech Republic

    Roman Václavík, Přemysl Šůcha & Zdeněk Hanzálek

  2. Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University in Prague, Zikova Street 1903/4, 166 36 , Prague 6, Czech Republic

    Zdeněk Hanzálek

Authors
  1. Roman Václavík
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  2. Přemysl Šůcha
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  3. Zdeněk Hanzálek
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Corresponding author

Correspondence to Roman Václavík.

Appendix I: Progress of the tabu search algorithm on the benchmark instances

Appendix I: Progress of the tabu search algorithm on the benchmark instances

See Figs. 8, 9, 10, 11, 12, 13, 14, 15 and 16.

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Millar’s problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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Millar-s’s problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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Gpost problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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Ortec problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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bp01 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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bp02 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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bp03 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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pb04 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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pb05 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers

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Václavík, R., Šůcha, P. & Hanzálek, Z. Roster evaluation based on classifiers for the nurse rostering problem. J Heuristics 22, 667–697 (2016). https://doi.org/10.1007/s10732-016-9314-9

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  • DOI: https://doi.org/10.1007/s10732-016-9314-9

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