  In this paper, we deal with semi-supervised Minimum Sum-of-Squares Clustering
(MSSC) problems where background knowledge is given in the form of
instance-level constraints. In particular, we take into account "must-link" and
"cannot-link" constraints, each of which indicates if two dataset points should
be associated to the same or to a different cluster. The presence of such
constraints makes the problem at least as hard as its unsupervised version: it
is no more true that each point is associated to its nearest cluster center,
thus requiring some modifications in crucial operations, such as the assignment
step. In this scenario, we propose a novel memetic strategy based on the
Differential Evolution paradigm, directly extending a state-of-the-art
framework recently proposed in the unsupervised clustering literature. As far
as we know, our contribution represents the first attempt to define a memetic
methodology designed to generate a (hopefully) optimal feasible solution for
the semi-supervised MSSC problem. The proposal is compared with some
state-of-the-art algorithms from the literature on a set of well-known
datasets, highlighting its effectiveness and efficiency in finding good quality
clustering solutions.
