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Mathematical Programming Computation

, Volume 5, Issue 1, pp 75–112 | Cite as

Branch-and-cut for separable piecewise linear optimization and intersection with semi-continuous constraints

  • I. R. de FariasJr.Email author
  • E. Kozyreff
  • R. Gupta
  • M. Zhao
Full Length Paper

Abstract

We report and analyze the results of our computational testing of branch-and-cut for piecewise linear optimization using the cutting planes given recently by Zhao and de Farias. Besides evaluating the performance of the cuts, we evaluate the effect of formulation on the performance of branch-and-cut. Finally, we report and analyze results on piecewise linear optimization problems with semi-continuous constraints.

Keywords

Piecewise linear optimization Mixed-integer programming  Knapsack problem Special ordered set Semi-continuous variable  Polyhedral method Branch-and-cut 

Mathematics Subject Classification

90 

Notes

Acknowledgments

This research was partially supported by the Office of Naval Research and the National Science Foundation through grants N000140910332 and CMMI-0620755, respectively. Their support is gratefully acknowledged. We are grateful to George Nemhauser and Juan-Pablo Vielma for making available to us the instances of their paper [30]. We are also grateful to Zhonghao Gu and Ed Rothberg for enlightening discussions. Finally, we are grateful to the anonymous referees and the editors, for several valuable suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2012

Authors and Affiliations

  • I. R. de FariasJr.
    • 1
    Email author
  • E. Kozyreff
    • 1
  • R. Gupta
    • 1
  • M. Zhao
    • 2
  1. 1.Department of Industrial EngineeringTexas Tech UniversityLubbockUSA
  2. 2.SASCaryUSA

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