IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v223y2012i2p360-371.html
   My bibliography  Save this article

Stabilized dynamic constraint aggregation for solving set partitioning problems

Author

Listed:
  • Benchimol, Pascal
  • Desaulniers, Guy
  • Desrosiers, Jacques

Abstract

Dynamic constraint aggregation (DCA) and dual variable stabilization (DVS) are two methods that can reduce the negative impact of degeneracy when solving linear programs. The first uses a projection to reduce the primal space whereas the second acts in the dual space. In this paper, we develop a new method, called stabilized dynamic constraint aggregation (SDCA), that combines DCA and DVS for solving set partitioning problems. It allows to fight degeneracy from both primal and dual perspectives simultaneously. To assess the effectiveness of SDCA, we report computational results obtained for highly degenerate multi-depot vehicle scheduling problem instances solved by column generation. These results indicate that SDCA can reduce the average computational time of the master problem by a factor of up to 7 with respect to the best of the two combined methods. Furthermore, they show that its performance is robust with regard to increasing levels of degeneracy in test problems.

Suggested Citation

  • Benchimol, Pascal & Desaulniers, Guy & Desrosiers, Jacques, 2012. "Stabilized dynamic constraint aggregation for solving set partitioning problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 360-371.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:360-371
    DOI: 10.1016/j.ejor.2012.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712005255
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.07.004?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. Ahmed Hadjar & Odile Marcotte & François Soumis, 2006. "A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 54(1), pages 130-149, February.
    2. Kliewer, Natalia & Mellouli, Taieb & Suhl, Leena, 2006. "A time-space network based exact optimization model for multi-depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1616-1627, December.
    3. Celso C. Ribeiro & François Soumis, 1994. "A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 42(1), pages 41-52, February.
    4. Andreas Löbel, 1998. "Vehicle Scheduling in Public Transit and Lagrangean Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1637-1649, December.
    5. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    6. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    7. Carraresi, P. & Gallo, G., 1984. "Network models for vehicle and crew scheduling," European Journal of Operational Research, Elsevier, vol. 16(2), pages 139-151, May.
    8. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, 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. Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
    2. Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
    3. Desrosiers, Jacques & Gauthier, Jean Bertrand & Lübbecke, Marco E., 2014. "Row-reduced column generation for degenerate master problems," European Journal of Operational Research, Elsevier, vol. 236(2), pages 453-460.
    4. Sebastian Ruther & Natashia Boland & Faramroze G. Engineer & Ian Evans, 2017. "Integrated Aircraft Routing, Crew Pairing, and Tail Assignment: Branch-and-Price with Many Pricing Problems," Transportation Science, INFORMS, vol. 51(1), pages 177-195, February.
    5. Liu, Haichao & Wang, Yang & Hao, Jin-Kao, 2024. "Solving the patient admission scheduling problem using constraint aggregation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 85-99.
    6. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.
    7. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.

    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. Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
    2. Perumal, Shyam S.G. & Lusby, Richard M. & Larsen, Jesper, 2022. "Electric bus planning & scheduling: A review of related problems and methodologies," European Journal of Operational Research, Elsevier, vol. 301(2), pages 395-413.
    3. Perumal, S.S.G. & Dollevoet, T.A.B. & Huisman, D. & Lusby, R.M. & Larsen, J. & Riis, M., 2020. "Solution Approaches for Vehicle and Crew Scheduling with Electric Buses," Econometric Institute Research Papers EI-2020-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Stefan Irnich & Guy Desaulniers & Jacques Desrosiers & Ahmed Hadjar, 2010. "Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 297-313, May.
    5. Jing-Quan Li, 2014. "Transit Bus Scheduling with Limited Energy," Transportation Science, INFORMS, vol. 48(4), pages 521-539, November.
    6. Ricard, Léa & Desaulniers, Guy & Lodi, Andrea & Rousseau, Louis-Martin, 2024. "Increasing schedule reliability in the multiple depot vehicle scheduling problem with stochastic travel time," Omega, Elsevier, vol. 127(C).
    7. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    8. Shyam S. G. Perumal & Jesper Larsen & Richard M. Lusby & Morten Riis & Tue R. L. Christensen, 2022. "A column generation approach for the driver scheduling problem with staff cars," Public Transport, Springer, vol. 14(3), pages 705-738, October.
    9. Uçar, Ezgi & İlker Birbil, Ş. & Muter, İbrahim, 2017. "Managing disruptions in the multi-depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 249-269.
    10. Kim, Byung-In & Kim, Seongbae & Park, Junhyuk, 2012. "A school bus scheduling problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 577-585.
    11. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    12. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    13. Peng, Yiyang & Li, Guoyuan & Xu, Min & Chen, Anthony, 2024. "Mixed-fleet operation of battery electric bus and hydrogen bus: Considering limited depot size with flexible refueling processes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 188(C).
    14. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2018. "Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 52(5), pages 1174-1190, October.
    15. Timo Gschwind & Stefan Irnich, 2012. "Effective Handling of Dynamic Time Windows and Synchronization with Precedences for Exact Vehicle Routing," Working Papers 1211, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    16. Timo Gschwind & Stefan Irnich & Simon Emde & Christian Tilk, 2018. "Branch-Cut-and-Price for the Scheduling Deliveries with Time Windows in a Direct Shipping Network," Working Papers 1805, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    17. Guy Desaulniers & Diego Pecin & Claudio Contardo, 2019. "Selective pricing in branch-price-and-cut algorithms for vehicle routing," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 147-168, June.
    18. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
    19. Li, Jiliu & Qin, Hu & Baldacci, Roberto & Zhu, Wenbin, 2020. "Branch-and-price-and-cut for the synchronized vehicle routing problem with split delivery, proportional service time and multiple time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    20. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2015. "Branch-and-Price for the Active-Passive Vehicle-Routing Problem," Working Papers 1513, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    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:eee:ejores:v:223:y:2012:i:2:p:360-371. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.