Theoretical Karush-Kuhn-Tucker (KKT) optimality conditions are singular properties valid only at the optimal and KKT points. Their violation is not monotonic in the vicinity of optimal solutions. We have suggested a KKT proximity measure (KKTPM) which brings back the monotonicity property in the context of single-objective optimization problems in 2011. At COIN, we have extended the concept for multi-objective optimization problems and suggested a KKTPM that provides a smaller value for solutions closer to Pareto-optimal solutions. KKTPM offers a number of neat ways to have a confident application, as a guaranteed convergence is now possible and the metric can also be used in many other ways to improve the performance of an algorithm. Moreover, at COIN Lab, we are making other theoretical contributions, such as suggesting a faster non-dominated sorting procedure for multi and many-objective optimization.