Integer programming techniques for modeling clique relaxations and key players in networks

Modern optimization software packages (Gurobi, Fico Xpress, CPLEX, etc.) have been demonstrating significant performance enhancements over the last decade. These improvements allow finding solutions for many combinatorial problems on real-life networks within a reasonable time via modeling efficient mixed integer programming (MIP) formulations. In this talk we will discuss various integer programming techniques for modeling so-called clique relaxations (subgraphs with a ‘relaxed’ clique defining property) and ‘key’ players in networks that we have developed. Many potential applications, effectiveness and flexibility of the proposed MIP formulations will also be demonstrated.