IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v156y2007i1p83-9710.1007-s10479-007-0230-0.html
   My bibliography  Save this article

On local optima in multiobjective combinatorial optimization problems

Author

Listed:
  • Luis Paquete
  • Tommaso Schiavinotto
  • Thomas Stützle

Abstract

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Luis Paquete & Tommaso Schiavinotto & Thomas Stützle, 2007. "On local optima in multiobjective combinatorial optimization problems," Annals of Operations Research, Springer, vol. 156(1), pages 83-97, December.
    • Handle: RePEc:spr:annopr:v:156:y:2007:i:1:p:83-97:10.1007/s10479-007-0230-0
    DOI: 10.1007/s10479-007-0230-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0230-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0230-0?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. Thomas Erlebach & Hans Kellerer & Ulrich Pferschy, 2002. "Approximating Multiobjective Knapsack Problems," Management Science, INFORMS, vol. 48(12), pages 1603-1612, December.
    2. Paquete, Luis & Stutzle, Thomas, 2006. "A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices," European Journal of Operational Research, Elsevier, vol. 169(3), pages 943-959, March.
    3. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    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. Diaz, Juan Esteban & López-Ibáñez, Manuel, 2021. "Incorporating decision-maker’s preferences into the automatic configuration of bi-objective optimisation algorithms," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1209-1222.
    2. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    3. Jaszkiewicz, Andrzej, 2018. "Many-Objective Pareto Local Search," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1001-1013.
    4. Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    5. Mădălina M. Drugan, 2018. "Scaling-up many-objective combinatorial optimization with Cartesian products of scalarization functions," Journal of Heuristics, Springer, vol. 24(2), pages 135-172, April.
    6. Justus Bonz, 2021. "Application of a multi-objective multi traveling salesperson problem with time windows," Public Transport, Springer, vol. 13(1), pages 35-57, March.

    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. Dubois-Lacoste, Jérémie & López-Ibáñez, Manuel & Stützle, Thomas, 2015. "Anytime Pareto local search," European Journal of Operational Research, Elsevier, vol. 243(2), pages 369-385.
    2. Arne Herzel & Stefan Ruzika & Clemens Thielen, 2021. "Approximation Methods for Multiobjective Optimization Problems: A Survey," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1284-1299, October.
    3. Verel, Sébastien & Liefooghe, Arnaud & Jourdan, Laetitia & Dhaenens, Clarisse, 2013. "On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives," European Journal of Operational Research, Elsevier, vol. 227(2), pages 331-342.
    4. T. Gómez & M. Hernández & J. Molina & M. León & E. Aldana & R. Caballero, 2011. "A multiobjective model for forest planning with adjacency constraints," Annals of Operations Research, Springer, vol. 190(1), pages 75-92, October.
    5. Tobias Kuhn & Stefan Ruzika, 2017. "A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions," Journal of Global Optimization, Springer, vol. 67(3), pages 581-600, March.
    6. Delorme, Xavier & Gandibleux, Xavier & Degoutin, Fabien, 2010. "Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 206-217, July.
    7. Mancini, Simona & Triki, Chefi & Piya, Sujan, 2022. "Optimal selection of touristic packages based on user preferences during sports mega-events," European Journal of Operational Research, Elsevier, vol. 302(3), pages 819-830.
    8. Herbert Dawid & Reinhold Decker & Thomas Hermann & Hermann Jahnke & Wilhelm Klat & Rolf König & Christian Stummer, 2017. "Management science in the era of smart consumer products: challenges and research perspectives," 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. 25(1), pages 203-230, March.
    9. Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    10. Liesio, Juuso & Mild, Pekka & Salo, Ahti, 2007. "Preference programming for robust portfolio modeling and project selection," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1488-1505, September.
    11. Hanne, Thomas, 2007. "A multiobjective evolutionary algorithm for approximating the efficient set," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1723-1734, February.
    12. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    13. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F. & Sainz-Pardo, José L., 2020. "Multi-objective evolutionary algorithms for a reliability location problem," European Journal of Operational Research, Elsevier, vol. 283(1), pages 83-93.
    14. Braekers, Kris & Hartl, Richard F. & Parragh, Sophie N. & Tricoire, Fabien, 2016. "A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience," European Journal of Operational Research, Elsevier, vol. 248(2), pages 428-443.
    15. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, June.
    16. Doerner, K.F. & Gutjahr, W.J. & Hartl, R.F. & Strauss, C. & Stummer, C., 2008. "Nature-inspired metaheuristics for multiobjective activity crashing," Omega, Elsevier, vol. 36(6), pages 1019-1037, December.
    17. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
    18. Fündeling, C.-U. & Trautmann, N., 2010. "A priority-rule method for project scheduling with work-content constraints," European Journal of Operational Research, Elsevier, vol. 203(3), pages 568-574, June.
    19. Shah, Ruchit & Reed, Patrick, 2011. "Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 211(3), pages 466-479, June.
    20. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.

    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:annopr:v:156:y:2007:i:1:p:83-97:10.1007/s10479-007-0230-0. 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.