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Optimization Problems in Graph Theory pp 107–122Cite as

Dominance Certificates for Combinatorial Optimization Problems

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 139))

Abstract

Heuristic algorithms, such as simulated annealing, are widely used in practice to solve combinatorial optimization problems. However, they offer no guarantees regarding the quality of the provided solution. An f(I) combinatorial dominance guarantee is a certificate that a solution is not worse than at least f(I) solutions for a particular problem instance I. In this paper, we introduce simple but general techniques for awarding combinatorial dominance certificates to arbitrary solutions of various optimization problems. We demonstrate these techniques by applying them to the Traveling Salesman and Maximum Satisfiability problems, and briefly experiment their usability.

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Acknowledgements

The authors would like to thank Gregory Gutin and the referees for their helpful comments on this paper.

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Authors and Affiliations

  1. Department of Mathematics and of Computer Science, Ben-Gurion University, Beer Sheva, Israel

    Daniel Berend

  2. Department of Mathematics, Rice University, Houston, TX, USA

    Daniel Berend

  3. Department of Computer Science, Stony Brook University, Stony Brook, NY, USA

    Steven S. Skiena

  4. Department of Computer Science, Ben-Gurion University, Beer Sheva, Israel

    Yochai Twitto

Authors
  1. Daniel Berend
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  2. Steven S. Skiena
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  3. Yochai Twitto
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Correspondence to Daniel Berend .

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Editors and Affiliations

  1. Department of Information Systems and Decision Science, Merrick School of Business, University of Baltimore, Baltimore, MD, USA

    Boris Goldengorin

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Berend, D., Skiena, S.S., Twitto, Y. (2018). Dominance Certificates for Combinatorial Optimization Problems. In: Goldengorin, B. (eds) Optimization Problems in Graph Theory. Springer Optimization and Its Applications, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-319-94830-0_6

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