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Quantifying the Effects of Increasing User Choice in MAP-Elites Applied to a Workforce Scheduling and Routing Problem

  • Neil UrquhartEmail author
  • Emma Hart
  • William Hutcheson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11454)

Abstract

Quality-diversity algorithms such as MAP-Elites provide a means of supporting the users when finding and choosing solutions to a problem by returning a set of solutions which are diverse according to set of user-defined features. The number of solutions that can potentially be returned by MAP-Elites is controlled by a parameter that discretises the user-defined features into ‘bins’. For a fixed evaluation budget, increasing the number of bins increases user-choice, but at the same time, can lead to a reduction in overall quality of solutions. Vice-versa, decreasing the number of bins can lead to higher-quality solutions but at the expense of reducing choice. The goal of this paper it to explicitly quantify this trade-off, through a study of the application of Map-Elites to a Workforce Scheduling and Routing problem, using a large set of realistic instances based in London. We note that for the problems under consideration 30 bins or above maximises coverage (and therefore choice to the end user), whilst reducing the bins to the minimal size of 5 can lead to improvements in fitness between 23 and 38% in comparison to the maximum setting of 50.

Keywords

MAP-Elites Transportation Illumination WSRP 

References

  1. 1.
    Pugh, J.K., Soros, L.B., Stanley, K.O.: Quality diversity: a new frontier for evolutionary computation. Front. Robot. AI 3, 40 (2016)CrossRefGoogle Scholar
  2. 2.
    Urquhart, N., Hart, E.: Optimisation and illumination of a real-world workforce scheduling and routing application (WSRP) via Map-Elites. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11101, pp. 488–499. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-99253-2_39CrossRefGoogle Scholar
  3. 3.
    Castillo-Salazar, J.A., Landa-Silva, D., Qu, R.: A survey on workforce scheduling and routing problems. In: Proceedings of the 9th International Conference on the Practice and Theory of Automated Timetabling, pp. 283–302 (2012)Google Scholar
  4. 4.
    Castillo-Salazar, J.A., Landa-Silva, D., Qu, R.: Workforce scheduling and routing problems: literature survey and computational study. Ann. Oper. Res. 239(1), 39–67 (2016).  https://doi.org/10.1007/s10479-014-1687-2MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Braekers, K., Hartl, R.F., Parragh, S.N., Tricoire, F.: A bi-objective home care scheduling problem: analyzing the trade-off between costs and client inconvenience. Eur. J. Oper. Res. 248(2), 428–443 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hiermann, G., Prandtstetter, M., Rendl, A., Puchinger, J., Raidl, G.R.: Metaheuristics for solving a multimodal home-healthcare scheduling problem. Cent. Eur. J. Oper. Res. 23(1), 89–113 (2015).  https://doi.org/10.1007/s10100-013-0305-8MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Rasmussen, M., Justesen, T., Dohn, A., Larsen, J.: The home care crew scheduling problem: preference-based visit clustering and temporal dependencies. DTU Management (2010)Google Scholar
  8. 8.
    Misir, M., Smet, P., Verbeeck, K., Berghe, G.V.: Security personnel routing and rostering: a hyper-heuristic approach. In: Proceedings of the 3rd International Conference on Applied Operational Research, ICAOR11 (2011)Google Scholar
  9. 9.
    Günther, M., Nissen, V.: Application of particle swarm optimization to the British telecom workforce scheduling problem. In: Proceedings of the 9th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012), Son, Norway (2012)Google Scholar
  10. 10.
    Lehman, J., Stanley, K.O.: Evolving a diversity of virtual creatures through novelty search and local competition. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, pp. 211–218. ACM (2011)Google Scholar
  11. 11.
    Mouret, J., Clune, J.: Illuminating search spaces by mapping elites. CoRR (2015)Google Scholar
  12. 12.
    Vassiliades, V., Chatzilygeroudis, K., Mouret, J.B.: Using centroidal voronoi tessellations to scale up the multi-dimensional archive of phenotypic elites algorithm, pp. 1–1 (2017)Google Scholar
  13. 13.
    Gaier, A., Asteroth, A., Mouret, J.B.: Data-efficient design exploration through surrogate-assisted illumination. Evol. Comput. 26(3), 381–410 (2018)CrossRefGoogle Scholar
  14. 14.
    Hagg, A., Asteroth, A., Bäck, T.: Prototype discovery using quality-diversity. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11101, pp. 500–511. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-99253-2_40CrossRefGoogle Scholar
  15. 15.
    Urquhart, N.B., Hart, E., Judson, A.: Multi-modal employee routing with time windows in an urban environment. In: Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 1503–1504. ACM (2015)Google Scholar
  16. 16.
    TFL: Travel in London: key trends and developments. Techical report, Transport for London (2009)Google Scholar
  17. 17.
    Urquhart, N.B., Hart, E., Judson, A.: Multi-modal employee routing with time windows in an urban environment. In: Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 1503–1504. GECCO Companion 2015. ACM, New York (2015).  https://doi.org/10.1145/2739482.2764649

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ComputingEdinburgh Napier UniversityEdinburghUK

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