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Octane: A New Heuristic for Pure 0--1 Programs

Author

Listed:
  • Egon Balas

    (GSIA, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Sebastián Ceria

    (Graduate School of Business, Columbia University, New York 10027 and Axioma, New York)

  • Milind Dawande

    (University of Texas at Dallas, PO Box 830688, Richardson, Texas 78083)

  • Francois Margot

    (University of Kentucky, Lexington, Kentucky)

  • Gábor Pataki

    (Department of Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599)

Abstract

We propose a new heuristic for pure 0--1 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and we explain how our heuristic can be embedded in a branch-and-cut framework. Finally, we present computational results on a set of pure 0--1 programs taken from MIPLIB and other sources.

Suggested Citation

  • Egon Balas & Sebastián Ceria & Milind Dawande & Francois Margot & Gábor Pataki, 2001. "Octane: A New Heuristic for Pure 0--1 Programs," Operations Research, INFORMS, vol. 49(2), pages 207-225, April.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:2:p:207-225
    DOI: 10.1287/opre.49.2.207.13535
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    References listed on IDEAS

    as
    1. Egon Balas & Clarence H. Martin, 1980. "Pivot and Complement--A Heuristic for 0-1 Programming," Management Science, INFORMS, vol. 26(1), pages 86-96, January.
    2. Egon Balas & V. Joseph Bowman & Fred Glover & David Sommer, 1971. "An Intersection Cut from the Dual of the Unit Hypercube," Operations Research, INFORMS, vol. 19(1), pages 40-44, February.
    3. Bruce H. Faaland & Frederick S. Hillier, 1979. "Interior Path Methods for Heuristic Integer Programming Procedures," Operations Research, INFORMS, vol. 27(6), pages 1069-1087, December.
    4. Egon Balas, 1971. "Intersection Cuts—A New Type of Cutting Planes for Integer Programming," Operations Research, INFORMS, vol. 19(1), pages 19-39, February.
    5. Fred Glover, 1968. "A Note on Linear Programming and Integer Feasibility," Operations Research, INFORMS, vol. 16(6), pages 1212-1216, December.
    6. Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
    7. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2013. "A new class of functions for measuring solution integrality in the Feasibility Pump approach: Complete Results," DIAG Technical Reports 2013-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "Feasibility Pump-Like Heuristics for Mixed Integer Problems," DIS Technical Reports 2010-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    3. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "New concave penalty functions for improving the Feasibility Pump," DIS Technical Reports 2010-10, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Guastaroba, G. & Savelsbergh, M. & Speranza, M.G., 2017. "Adaptive Kernel Search: A heuristic for solving Mixed Integer linear Programs," European Journal of Operational Research, Elsevier, vol. 263(3), pages 789-804.
    5. Saïd Hanafi & Raca Todosijević, 2017. "Mathematical programming based heuristics for the 0–1 MIP: a survey," Journal of Heuristics, Springer, vol. 23(4), pages 165-206, August.
    6. Lluís-Miquel Munguía & Shabbir Ahmed & David A. Bader & George L. Nemhauser & Yufen Shao, 2018. "Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs," Computational Optimization and Applications, Springer, vol. 69(1), pages 1-24, January.
    7. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2011. "A new class of functions for measuring solution integrality in the Feasibility Pump approach," DIS Technical Reports 2011-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    8. Weili Zhang & Charles D. Nicholson, 2020. "Objective scaling ensemble approach for integer linear programming," Journal of Heuristics, Springer, vol. 26(1), pages 1-19, February.

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