A branch-and-price procedure for clustering data that are graph connected

This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. problem, introduced Benati, Puerto, Rodríguez-Chía (2017) under name of Connected Partitioning Problem, shows that combination two data types improves quality comparison with other methodologies. Nevertheless, resulting problem is difficult to solve; only small-sized instances can be solved exactly, large-sized require application heuristic algorithms. In this we improve exact algorithms previously proposed. Here, provide new Integer Linear Programming (ILP) formulation, solves larger instances, but at cost using an exponential number variables. order limit variables necessary calculate optimum, ILP formulation implementing branch-and-price (B&P) algorithm. The pricing itself combinatorial model: Maximum-weighted Single-Clique (MGCSC), solve testing various Mixed (MILP) formulations proposing fast “random shrink” heuristic. way, able previous algorithms: B&P method outperforms computational times MILP random shrink heuristic, when applied GCCP, faster more accurate than methods. Moreover, column generation MILP-relaxed matheuristic large too. Its main advantage all local optima combined together restricted MILP, consisting solving heuristically problem.