{"type":"ScholarlyArticle","title":"Multi-Objective Optimization Through Pareto Minimal Correction Subsets","authors":[{"name":"Miguel Terra-Neves","slug":"miguel-terra-neves","given":"Miguel","family":"Terra-Neves","affiliation":"INESC-ID / Instituto Superior Técnico , Universidade de Lisboa , Portugal"},{"name":"Inês Lynce","slug":"ines-lynce","given":"Inês","family":"Lynce","affiliation":"INESC-ID / Instituto Superior Técnico , Universidade de Lisboa , Portugal"},{"name":"Vasco Manquinho","slug":"vasco-manquinho","given":"Vasco","family":"Manquinho","affiliation":"INESC-ID / Instituto Superior Técnico , Universidade de Lisboa , Portugal"}],"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, such as finding approximate solutions to constrained optimization problems. However, existing work on applying MCS enumeration to optimization problems focuses on the single-objective case.\r\nIn this work, Pareto Minimal Correction Subsets (Pareto-MCSs) are proposed for 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. Finally, experimental results on the multi-objective virtual machine consolidation problem show that the Pareto-MCS approach is competitive with state-of-the-art algorithms.","doi":"10.24963/ijcai.2018/757","url":"https://ijcai.org/proceedings/2018/757","pdf":"https://ijcai.org/proceedings/2018/0757.pdf","markdown":"https://ijcai.org/proceedings/2018/757.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/757","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":757,"pages":{"first":5379,"last":5383},"keywords":["Constraints and SAT: Constraint Optimisation","Constraints and SAT: SAT: Solvers and Tools"],"videos":[],"references":[{"position":1,"raw":"[Bacchus et al., 2014] Fahiem Bacchus, Jessica Davies, Maria Tsimpoukelli, and George Katsirelos. 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