Edinburgh Napier University

  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 while vice-versa, decreasing the number of bins can lead to higher-quality solutions 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 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 fewer bins maximises performance.