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Introducing Pareto Minimal Correction Subsets

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Theory and Applications of Satisfiability Testing – SAT 2017 (SAT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

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.

The authors would like to thank Salvador Abreu and Pedro Salgueiro from Universidade de Évora for granting the authors permission to use their cluster. This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with references UID/CEC/50021/2013 and SFRH/BD/111471/2015.

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Notes

  1. 1.

    http://moeaframework.org/.

  2. 2.

    http://code.google.com/p/googleclusterdata/.

  3. 3.

    http://sat.inesc-id.pt/dome.

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Authors and Affiliations

  1. INESC-ID/Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Miguel Terra-Neves, Inês Lynce & Vasco Manquinho

Authors
  1. Miguel Terra-Neves
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  2. Inês Lynce
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  3. Vasco Manquinho
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Correspondence to Miguel Terra-Neves .

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Editors and Affiliations

  1. UNSW Sydney, Sydney, New South Wales, Australia

    Serge Gaspers

  2. University of New South Wales , Sydney, New South Wales, Australia

    Toby Walsh

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Terra-Neves, M., Lynce, I., Manquinho, V. (2017). Introducing Pareto Minimal Correction Subsets. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-66263-3_13

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  • Online ISBN: 978-3-319-66263-3

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