Introducing pareto minimal correction subsets

Abstract

A Minimal Correction Subset (MCS) of an unsatisfiable constraint set is a minimal subset of constraints that, if removed, makes the constraint set satisfiable. MCSs enjoy a wide range of applications, one of them being approximate solutions to constrained optimization problems. However, existing work on applying MCS enumeration to optimization problems focuses on the single-objective case. In this work, a first definition of Pareto Minimal Correction Subsets (Pareto-MCSs) is proposed with the goal of approximating the Pareto-optimal solution set of multi-objective constrained optimization problems. We formalize and prove an equivalence relationship between Pareto-optimal solutions and Pareto-MCSs. Moreover, Pareto-MCSs and MCSs can be connected in such a way that existing state-of-the-art MCS enumeration algorithms can be used to enumerate Pareto-MCSs. An experimental evaluation considers the multi-objective virtual machine consolidation problem. Results show that the proposed Pareto-MCS approach outperforms the state-of-the-art approaches.