A memetic algorithm for the balanced minimum sum-of-squares clustering problem

The balanced minimum sum-of-squares clustering problem (BMSSC) is an important combinatorial optimization problem with many applications. The goal of this problem is to divide N data points in Euclidean space into K clusters such that the sizes of clusters differ at most by one. In this paper, we propose a memetic algorithm (denoted by MABMSSC) for the BMSSC problem. The algorithm employs an iterated variable neighborhood search algorithm (IVNS) as its local optimization method and a crossover operator to generate the offspring solutions. The experimental results on a number of benchmark instances show that the proposed algorithm is very efficient in terms of solution-quality. In particular, the proposed algorithm obtains a better solution compared with the best performing algorithm in the literature for many instances tested.