Abstract
This paper considers the Rotating Workforce Scheduling Problem, and shows how the strengths and weaknesses of various solution methods can be understood by the in-depth evaluation offered by a recently developed methodology known as Instance Space Analysis. We first present a set of features aiming to describe hardness of test instances. We create a new, more diverse set of instances based on an initial instance space analysis that reveals gaps in the instance space, and offers the opportunity to generate additional instances to add diversity to the test suite. The results of three algorithms on our extended instance set reveal insights based on this visual methodology. We observe different regions of strength and weakness in the instance space for each algorithm, as well as a phase transition from feasible to infeasible instances with more challenging instances at the phase transition boundary. This rigorous and insightful approach to analyzing algorithm performance highlights the critical role played by the choice of test instances, and the importance of ensuring diversity and unbiasedness of test instances to support valid conclusions.
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References
Baker, K.R.: Workforce allocation in cyclical scheduling problems: a survey. J. Oper. Res. Soc. 27(1), 155–167 (1976)
Balakrishnan, N., Wong, R.T.: A network model for the rotating workforce scheduling problem. Networks 20(1), 25–42 (1990)
Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)
Chuin Lau, H.: On the complexity of manpower shift scheduling. Comput. Oper. Res. 23(1), 93–102 (1996)
Erkinger, C., Musliu, N.: Personnel scheduling as satisfiability modulo theories. In: International Joint Conference on Artificial Intelligence – IJCAI 2017, Melbourne, Australia, August 19-25, 2017. https://doi.org/10.24963/ijcai.2017/86, pp 614–621 (2017)
Falcón, R., Barrena, E., Canca, D., Laporte, G.: Counting and enumerating feasible rotating schedules by means of gröbner bases. Math. Comput. Simul. 125, 139–151 (2016)
Kang, Y., Hyndman, R., Smith-Miles, K.: Visualising forecasting algorithm performance using time series instance spaces. Int. J. Forecast 33(2), 345–358 (2017). https://doi.org/10.1016/j.ijforecast.2016.09.004
Kletzander, L., Musliu, N., Gärtner, J., Krennwallner, T., Schafhauser, W.: Exact methods for extended rotating workforce scheduling problems. In: Proceedings of the Twenty-Ninth International Conference on Automated Planning and Scheduling, vol. 29, pp. 519–527. American Association for Artificial Intelligence (AAAI) (2019)
Laporte, G.: The art and science of designing rotating schedules. J. Oper. Res. Soc. 50, 1011–1017 (1999)
Laporte, G., Nobert, Y., Biron, J.: Rotating schedules. Eur. J. Oper. Res. 4(1), 24–30 (1980)
Laporte, G., Pesant, G.: A general multi-shift scheduling system. J. Oper. Res. Soc. 55(11), 1208–1217 (2004)
Muñoz, M., Smith-Miles, K.: Performance analysis of continuous black-box optimization algorithms via footprints in instance space. Evol. Comput. 25(4), 529–554 (2017). https://doi.org/10.1162/EVCO_a_00194
Muñoz, M.A., Villanova, L., Baatar, D., Smith-Miles, K.: Instance spaces for machine learning classification. Mach. Learn. 107(1), 109–147 (2018)
Musliu, N.: Combination of local search strategies for rotating workforce scheduling problem. In: International Joint Conference on Artificial Intelligence – IJCAI 2005, Edinburgh, Scotland, UK, July 30 - August 5, 2005, pp. 1529–1530. http://ijcai.org/Proceedings/05/Papers/post-0448.pdf (2005)
Musliu, N.: Heuristic methods for automatic rotating workforce scheduling. Int. J. Comput. Intell. Res. 2(4), 309–326 (2006)
Musliu, N., Gärtner, J., Slany, W.: Efficient generation of rotating workforce schedules. Discret. Appl. Math. 118(1-2), 85–98 (2002)
Musliu, N., Schutt, A., Stuckey, P.J.: Solver independent rotating workforce scheduling. In: International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pp 429–445. Springer (2018)
Oliveira, C., Aleti, A., Grunske, L., Smith-Miles, K.: Mapping the effectiveness of automated test suite generation techniques. IEEE Trans. Reliab. 67(3), 771–785 (2018)
Restrepo, M.I., Gendron, B., Rousseau, L.M.: Branch-and-price for personalized multiactivity tour scheduling. INFORMS J. Comput. 28(2), 334–350 (2016)
Rice, J.: The algorithm selection problem. In: Advances in Computers. https://doi.org/10.1016/S0065-2458(08)60520-3, vol. 15, pp 65–118. Elsevier (1976)
Smith-Miles, K., Baatar, D., Wreford, B., Lewis, R.: Towards objective measures of algorithm performance across instance space. Comput. Oper. Res. 45, 12–24 (2014). https://doi.org/10.1016/j.cor.2013.11.015
Smith-Miles, K., Bowly, S.: Generating new test instances by evolving in instance space. Comput. Oper. Res. 63, 102–113 (2015). 10.1016/j.cor.2015.04.022
Smith-Miles, K., Lopes, L.: Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)
Smith-Miles, K.A.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Computing Surveys (CSUR) 41(1), 6 (2009)
Triska, M., Musliu, N.: A constraint programming application for rotating workforce scheduling. In: Developing Concepts in Applied Intelligence, Studies in Computational Intelligence, vol. 363 , pp 83–88. Springer, Berlin (2011)
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Open access funding provided by TU Wien (TUW). The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development, and the Australian Research Council under grant FL140100012, is gratefully acknowledged.
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Kletzander, L., Musliu, N. & Smith-Miles, K. Instance space analysis for a personnel scheduling problem. Ann Math Artif Intell 89, 617–637 (2021). https://doi.org/10.1007/s10472-020-09695-2
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DOI: https://doi.org/10.1007/s10472-020-09695-2