IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v41y1994i3p455-463.html
   My bibliography  Save this article

A penalty for concave minimization derived from the tuy cutting plane

Author

Listed:
  • Kurt M. Bretthauer

Abstract

A wide variety of optimization problems have been approached with branch‐and‐bound methodology, most notably integer programming and continuous nonconvex programming. Penalty calculations provide a means to reduce the number of subproblems solved during the branch‐and‐bound search. We develop a new penalty based on the Tuy cutting plane for the nonconvex problem of globally minimizing a concave function over linear constraints and continuous variables. Computational testing with a branch‐and‐bound algorithm for concave minimization indicates that, for the problems solved, the penalty reduces solution time by a factor ranging from 1.2 to 7.2. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:3:p:455-463
    DOI: 10.1002/1520-6750(199404)41:33.0.CO;2-Q
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199404)41:33.0.CO;2-Q
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199404)41:33.0.CO;2-Q?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
    ---><---

    References listed on IDEAS

    as
    1. Norman J. Driebeek, 1966. "An Algorithm for the Solution of Mixed Integer Programming Problems," Management Science, INFORMS, vol. 12(7), pages 576-587, March.
    2. Matteo Fischetti & Paolo Toth, 1989. "An Additive Bounding Procedure for Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 37(2), pages 319-328, April.
    3. A. Victor Cabot, 1974. "Variations on a cutting plane method for solving concave minimization problems with linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(2), pages 265-274, June.
    4. R. L. Rardin & V. E. Unger, 1976. "Solving fixed charge network problems with group theory‐based penalties," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 67-84, March.
    5. A. Victor Cabot & S. Selcuk Erenguc, 1984. "Some branch‐and‐bound procedures for fixed‐cost transportation problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 145-154, March.
    6. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.
    7. Lin, Edward Y. H. & Bricker, Dennis L., 1991. "On the calculation of true and pseudo penalties in multiple choice integer programming," European Journal of Operational Research, Elsevier, vol. 55(2), pages 228-236, November.
    8. Harold P. Benson, 1985. "A finite algorithm for concave minimization over a polyhedron," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(1), pages 165-177, February.
    9. A. Victor Cabot & S. Selcuk Erenguc, 1986. "Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation," Management Science, INFORMS, vol. 32(7), pages 856-869, July.
    10. Harold P. Benson & S. Selcuk Erenguc, 1990. "An algorithm for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 515-525, August.
    11. Gallo, Giorgio & Sandi, Claudio & Sodini, Claudio, 1980. "An algorithm for the min concave cost flow problem," European Journal of Operational Research, Elsevier, vol. 4(4), pages 248-255, April.
    12. J. A. Tomlin, 1971. "Technical Note—An Improved Branch-and-Bound Method for Integer Programming," Operations Research, INFORMS, vol. 19(4), pages 1070-1075, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marcus Porembski, 2008. "On the hierarchy of γ‐valid cuts in global optimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 1-15, February.
    2. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    3. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.

    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. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    2. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    3. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.
    6. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    7. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    8. Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
    9. Roberto Roberti & Enrico Bartolini & Aristide Mingozzi, 2015. "The Fixed Charge Transportation Problem: An Exact Algorithm Based on a New Integer Programming Formulation," Management Science, INFORMS, vol. 61(6), pages 1275-1291, June.
    10. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    11. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
    12. Vincenzo Bonifaci & Tobias Harks & Guido Schäfer, 2010. "Stackelberg Routing in Arbitrary Networks," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 330-346, May.
    13. Bożena Staruch & Bogdan Staruch, 2021. "Competence-based assignment of tasks to workers in factories with demand-driven manufacturing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 553-565, June.
    14. Alejandro Marcos Alvarez & Quentin Louveaux & Louis Wehenkel, 2017. "A Machine Learning-Based Approximation of Strong Branching," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 185-195, February.
    15. Klein, Robert & Scholl, Armin, 1999. "Computing lower bounds by destructive improvement: An application to resource-constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 112(2), pages 322-346, January.
    16. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    17. Shangyao Yan & Yu-Lin Shih & Wang-Tsang Lee, 2011. "A particle swarm optimization-based hybrid algorithm for minimum concave cost network flow problems," Journal of Global Optimization, Springer, vol. 49(4), pages 539-559, April.
    18. Harold P. Benson & S. Selcuk Erenguc, 1990. "An algorithm for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 515-525, August.
    19. Lai, Minghui & Cai, Xiaoqiang & Li, Xiang, 2017. "Mechanism design for collaborative production-distribution planning with shipment consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 137-159.
    20. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2020. "An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 263-278, April.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:41:y:1994:i:3:p:455-463. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.