IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v23y2017i4d10.1007_s10732-017-9336-y.html
   My bibliography  Save this article

Mathematical programming based heuristics for the 0–1 MIP: a survey

Author

Listed:
  • Saïd Hanafi

    (LAMIH UMR CNRS 8201 - Université de Valenciennes)

  • Raca Todosijević

    (LAMIH UMR CNRS 8201 - Université de Valenciennes)

Abstract

The 0–1 mixed integer programming problem is used for modeling many combinatorial problems, ranging from logical design to scheduling and routing as well as encompassing graph theory models for resource allocation and financial planning. This paper provides a survey of heuristics based on mathematical programming for solving 0–1 mixed integer programs (MIP). More precisely, we focus on the stand-alone heuristics for 0–1 MIP as well as those heuristics that use linear programming techniques or solve a series of linear programming models or reduced problems, deduced from the initial one, in order to produce a high quality solution of a considered problem. Our emphasis will be on how mathematical programming techniques can be used for approximate problem solving, rather than on comparing performances of heuristics.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joheur:v:23:y:2017:i:4:d:10.1007_s10732-017-9336-y
    DOI: 10.1007/s10732-017-9336-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-017-9336-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-017-9336-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Imai, Akio & Nishimura, Etsuko & Current, John, 2007. "A Lagrangian relaxation-based heuristic for the vehicle routing with full container load," European Journal of Operational Research, Elsevier, vol. 176(1), pages 87-105, January.
    2. Robert M. Saltzman & Frederick S. Hillier, 1992. "A Heuristic Ceiling Point Algorithm for General Integer Linear Programming," Management Science, INFORMS, vol. 38(2), pages 263-283, February.
    3. 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.
    4. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    5. Wilbaut, Christophe & Hanafi, Said, 2009. "New convergent heuristics for 0-1 mixed integer programming," European Journal of Operational Research, Elsevier, vol. 195(1), pages 62-74, May.
    6. Ronny Aboudi & Kurt Jörnsten, 1994. "Tabu Search for General Zero-One Integer Programs Using the Pivot and Complement Heuristic," INFORMS Journal on Computing, INFORMS, vol. 6(1), pages 82-93, February.
    7. 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.
    8. Kaj Holmberg & Di Yuan, 2000. "A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem," Operations Research, INFORMS, vol. 48(3), pages 461-481, June.
    9. Fred Glover, 1968. "A Note on Linear Programming and Integer Feasibility," Operations Research, INFORMS, vol. 16(6), pages 1212-1216, December.
    10. Wilbaut, Christophe & Salhi, Saïd & Hanafi, Saïd, 2009. "An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(2), pages 339-348, December.
    11. Soyster, A. L. & Lev, B. & Slivka, W., 1978. "Zero-one programming with many variables and few constraints," European Journal of Operational Research, Elsevier, vol. 2(3), pages 195-201, May.
    12. Saïd Hanafi & Christophe Wilbaut, 2011. "Improved convergent heuristics for the 0-1 multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 183(1), pages 125-142, March.
    13. Stadtler, Hartmut, 2003. "Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20204, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    14. Rego, César & Gamboa, Dorabela & Glover, Fred & Osterman, Colin, 2011. "Traveling salesman problem heuristics: Leading methods, implementations and latest advances," European Journal of Operational Research, Elsevier, vol. 211(3), pages 427-441, June.
    15. Lokketangen, Arne & Glover, Fred, 1998. "Solving zero-one mixed integer programming problems using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 624-658, April.
    16. A. Victor Cabot & Arthur P. Hurter, 1968. "An Approach to Zero-One Integer Programming," Operations Research, INFORMS, vol. 16(6), pages 1206-1211, December.
    17. Hartmut Stadtler, 2003. "Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows," Operations Research, INFORMS, vol. 51(3), pages 487-502, June.
    18. Glover, Fred, 1978. "Parametric branch and bound," Omega, Elsevier, vol. 6(2), pages 145-152.
    19. Hassan Hijazi & Pierre Bonami & Gérard Cornuéjols & Adam Ouorou, 2012. "Mixed-integer nonlinear programs featuring “on/off” constraints," Computational Optimization and Applications, Springer, vol. 52(2), pages 537-558, June.
    20. Fred Glover, 1995. "Tabu Thresholding: Improved Search by Nonmonotonic Trajectories," INFORMS Journal on Computing, INFORMS, vol. 7(4), pages 426-442, November.
    21. Toledo, Franklina Maria Bragion & Armentano, Vinicius Amaral, 2006. "A Lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1070-1083, December.
    22. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 383-399, March.
    23. Pierre Bonami & João Gonçalves, 2012. "Heuristics for convex mixed integer nonlinear programs," Computational Optimization and Applications, Springer, vol. 51(2), pages 729-747, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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".
    2. 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".
    3. 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".
    4. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    5. 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".
    6. Gendron, Bernard & Hanafi, Saïd & Todosijević, Raca, 2018. "Matheuristics based on iterative linear programming and slope scaling for multicommodity capacitated fixed charge network design," European Journal of Operational Research, Elsevier, vol. 268(1), pages 70-81.
    7. Tao Wu & Zhe Liang & Canrong Zhang, 2018. "Analytics Branching and Selection for the Capacitated Multi-Item Lot Sizing Problem with Nonidentical Machines," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 236-258, May.
    8. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    9. Silvio Alexandre de Araujo & Bert De Reyck & Zeger Degraeve & Ioannis Fragkos & Raf Jans, 2015. "Period Decompositions for the Capacitated Lot Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 431-448, August.
    10. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    11. Al-Shihabi, Sameh, 2021. "A Novel Core-Based Optimization Framework for Binary Integer Programs- the Multidemand Multidimesional Knapsack Problem as a Test Problem," Operations Research Perspectives, Elsevier, vol. 8(C).
    12. Diego Fiorotto & Silvio Araujo, 2014. "Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines," Annals of Operations Research, Springer, vol. 217(1), pages 213-231, June.
    13. Lokketangen, Arne & Glover, Fred, 1998. "Solving zero-one mixed integer programming problems using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 624-658, April.
    14. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    15. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    16. Chunyi Wang & Fengzhang Luo & Zheng Jiao & Xiaolei Zhang & Zhipeng Lu & Yanshuo Wang & Ren Zhao & Yang Yang, 2022. "An Enhanced Second-Order Cone Programming-Based Evaluation Method on Maximum Hosting Capacity of Solar Energy in Distribution Systems with Integrated Energy," Energies, MDPI, vol. 15(23), pages 1-19, November.
    17. Tao Wu & Leyuan Shi & Joseph Geunes & Kerem Akartunalı, 2012. "On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times," Journal of Global Optimization, Springer, vol. 53(4), pages 615-639, August.
    18. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    19. Lang, Jan Christian & Shen, Zuo-Jun Max, 2011. "Fix-and-optimize heuristics for capacitated lot-sizing with sequence-dependent setups and substitutions," European Journal of Operational Research, Elsevier, vol. 214(3), pages 595-605, November.
    20. Renata Mansini & M. Grazia Speranza, 2012. "CORAL: An Exact Algorithm for the Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 399-415, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joheur:v:23:y:2017:i:4:d:10.1007_s10732-017-9336-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.