A memetic algorithm based on reformulation local search for minimum sum-of-squares clustering in networks

Abstract

The edge minimum sum-of-squares clustering problem (E-MSSC) aims at finding p prototypes such that the sum of squares of distances from a set of vertices to their closest prototype is minimized, where a prototype is either a vertex or an interior point of an edge. This paper proposes a highly effective memetic algorithm for E-MSSC that combines a dedicated crossover operator for solution generation with a reformulation local search for solution improvement. Reformulation local search is a recent algorithmic framework for continuous location problems that is based on an alternation between original (continuous) and discrete formulations of a given problem. Furthermore, the proposed algorithm uses a simple strategy for population updating, and a mutation operator to prevent from premature convergence. The computational results obtained on three sets of 132 benchmark instances show that the proposed algorithm competes very favorably with the existing state-of-the-art algorithms in terms of both solution quality and computational efficiency. We also analyze several essential components of the proposed algorithm to understand their contribution to the algorithm’s performance.