SOLVING NET-CONSTRAINED CLUSTERING PROBLEM

In this paper, we consider a planar clustering problem with location constraints for cluster centers. A simple adaptation of the k-means algorithm solving the presented problem to local optimality is outlined. We further show that our problem can be stated as a MIQCP (mixed-integer-quadratically-constrained-programming) problem, and some results to solve the formulated problem to global optimality with a popular solver are presented. We also present a specialized enumeration algorithm which can be used to find the global optima of the problem and our numerical experiments indicate that this approach is a better choice in comparison to solving the formulated MIQCP problem with a general solver.