Abstract
Researchers in the multicriteria analysis community have recently started to study the application of clustering techniques. Different methods have been proposed leading to complete or partial multicriteria partitions. Recently, a method based on the exploitation of the ordinal properties of a valued preference relation has been developed in order to obtain a totally ordered clustering. The underlying idea is to find a partition that minimizes the inconsistencies between the obtained ordered clusters and the input preference matrix. The exact algorithm gives the guarantee to achieve this goal based on a lexicographic order. In this contribution, we propose to further extend their approach to the case where minimum and maximum capacities are imposed on the cluster sizes. This leads to add a constraint satisfaction test (that is based on the levels and the ranks of the graph built during the procedure). The algorithm is evaluated regarding its execution time and illustrated on the academic ranking of world universities.
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Rosenfeld, J., Van Assche, D., De Smet, Y. (2021). Lexicographic Constrained Multicriteria Ordered Clustering. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_36
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