Journal of Heuristics

, Volume 13, Issue 5, pp 471–503 | Cite as

Pivot, Cut, and Dive: a heuristic for 0-1 mixed integer programming

  • Jonathan Eckstein
  • Mikhail Nediak


This paper describes a heuristic for 0-1 mixed-integer linear programming problems, focusing on “stand-alone” implementation. Our approach is built around concave “merit functions” measuring solution integrality, and consists of four layers: gradient-based pivoting, probing pivoting, convexity/intersection cutting, and diving on blocks of variables. The concavity of the merit function plays an important role in the first and third layers, as well as in connecting the four layers. We present both the mathematical and software details of a test implementation, along with computational results for several variants.


Integer programming Simplex pivot Convexity cut 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Business School and RUTCORRutgers UniversityPiscatawayUSA
  2. 2.Queen’s School of BusinessQueen’s UniversityKingstonCanada

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