A Genetic Approach to Solve the MultiCriteria Anti-Clustering Problem

We consider decision problems involving the simultaneous optimization of conflicting criteria. In this context, we introduce the notion of anti-clustering. One looks to a partition of objects characterized by a high level of intra-group heterogeneity and a high level of inter-group homogeneity. This goal is in opposition with traditional clustering methods. In addition, it is related to the notion of fairness in clustering. We propose a first implementation based on a genetic algorithm and compare it to random algorithms on illustrative data sets such as the academic ranking of world universities. Tests are performed to fine-tune the algorithm's parameters.