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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In this study, we do not count the input layer as a layer.
References
Aickelin, U., Dowsland, K.: Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem. J. Sched. 3(3), 139–153 (2000)
Bäumelt, Z., Šůcha, P., Hanzálek, Z.: A multistage approach for an employee timetabling problem with a high diversity of shifts as a solution for a strongly varying workforce demand. Comput. Oper. Res. 49, 117–129 (2014)
Beddoe, G., Petrovic, S., Li, J.: A hybrid metaheuristic case-based reasoning system for nurse rostering. J. Sched. 12(2), 99–119 (2009)
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, New York (1995)
Bühlmann, P., Hothorn, T.: Boosting algorithms: regularization, prediction and model fitting. Stat. Sci. 22(4), 477–505 (2007)
Burke, E.K., De Causmaecker, P., Petrovic, S., Berghe, G.: Fitness evaluation for nurse scheduling problems. In: Proceedings of the 2001 Congress on Evolutionary Computation, 2001, vol. 2, pp. 1139–1146 (2001)
Burke, E.K., De Causmaecker, P., Vanden Berghe, G., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7(6), 441–499 (2004)
Carter, M., Laporte, G.: Recent developments in practical examination timetabling. In: Practice and Theory of Automated Timetabling. Lecture Notes in Computer Science, vol. 1153, pp. 373–383. Springer, Berlin (1996)
Chen, C.: Handbook of Pattern Recognition and Computer Vision, 4th edn. World Scientific Publishing, Singapore (2010)
Curtois, T.: Employee scheduling benchmark data sets (2013) . http://www.cs.nott.ac.uk/~tec/NRP/. Accessed 11 Sept 2013
Dowsland, K.A.: Nurse scheduling with tabu search and strategic oscillation. Eur. J. Oper. Res. 106(2–3), 393–407 (1998)
Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci. 55(1), 119–139 (1997)
Glover, F., Laguna, M.: Tabu Search. Springer, New York (1997)
Karp, R.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Li, J., Burke, E.K., Qu, R.: Integrating neural networks and logistic regression to underpin hyper-heuristic search. Knowl.-Based Syst. 24(2), 322–330 (2011)
Li, J., Burke, E.K., Qu, R.: A pattern recognition based intelligent search method and two assignment problem case studies. Appl. Intell. 36(2), 442–453 (2012)
Ripley, B.: Pattern Recognition and Neural Networks. Cambridge University Press, New York (2007)
Ross, P., Corne, D., Fang, H.-L.: Improving evolutionary timetabling with delta evaluation and directed mutation. In: Davidor, Y., Schwefel, H.-P., Manner, R. (eds.) Parallel Problem Solving from Nature PPSN III. Lecture Notes in Computer Science, vol. 866, pp. 556–565. Springer, Berlin (1994)
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Rumelhart, D.E., McClelland, J.L., PDP Research Group, C. (eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. 1, pp. 318–362. MIT Press, Cambridge (1986)
Sochman, J., Matas, J.: Waldboost-learning for time constrained sequential detection. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, vol. 2, pp. 150–156 (2005)
Staff Roster Solutions: Tool Roster Booster (2013) . http://www.staffrostersolutions.com/downloads.php. Accessed 11 Sept 2013
Staff Roster Solutions: Autoroster Problem Data Format (2015) . http://www.staffrostersolutions.com/support/autoroster-problem-data.php. Accessed 30 June 2015
Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat. 16(2), 117–186 (1945)
Yegnanarayana, B.: Artificial Neural Networks. PHI Learning, New Delhi (2009)
Zhang, W., Dietterich, T.G.: Solving combinatorial optimization tasks by reinforcement learning: a general methodology applied to resource-constrained scheduling. J. Artif. Intell. Res. 1, 1–38 (2000)
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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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.
Millar’s problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
Millar-s’s problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
Gpost problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
Ortec problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
bp01 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
bp02 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
bp03 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
pb04 problem instance—progress of the objective value over time for the cost-oriented evaluation and the evaluations using the classifiers
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