IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v24y2018i1d10.1007_s10732-017-9356-7.html
   My bibliography  Save this article

Hybrid multi-objective Bayesian estimation of distribution algorithm: a comparative analysis for the multi-objective knapsack problem

Author

Listed:
  • Marcella S. R. Martins

    (Federal University of Technology - Paraná (UTFPR))

  • Myriam R. B. S. Delgado

    (Federal University of Technology - Paraná (UTFPR))

  • Ricardo Lüders

    (Federal University of Technology - Paraná (UTFPR))

  • Roberto Santana

    (University of the Basque Country (UPV/EHU))

  • Richard A. Gonçalves

    (Midwest State University of Parana (UNICENTRO))

  • Carolina P. Almeida

    (Midwest State University of Parana (UNICENTRO))

Abstract

Nowadays, a number of metaheuristics have been developed for efficiently solving multi-objective optimization problems. Estimation of distribution algorithms are a special class of metaheuristic that intensively apply probabilistic modeling and, as well as local search methods, are widely used to make the search more efficient. In this paper, we apply a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm (HMOBEDA) in multi and many objective scenarios by modeling the joint probability of decision variables, objectives, and the configuration parameters of an embedded local search (LS). We analyze the benefits of the online configuration of LS parameters by comparing the proposed approach with LS off-line versions using instances of the multi-objective knapsack problem with two to five and eight objectives. HMOBEDA is also compared with five advanced evolutionary methods using the same instances. Results show that HMOBEDA outperforms the other approaches including those with off-line configuration. HMOBEDA not only provides the best value for hypervolume indicator and IGD metric in most of the cases, but it also computes a very diverse solutions set close to the estimated Pareto front.

Suggested Citation

  • Marcella S. R. Martins & Myriam R. B. S. Delgado & Ricardo Lüders & Roberto Santana & Richard A. Gonçalves & Carolina P. Almeida, 2018. "Hybrid multi-objective Bayesian estimation of distribution algorithm: a comparative analysis for the multi-objective knapsack problem," Journal of Heuristics, Springer, vol. 24(1), pages 25-47, February.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:1:d:10.1007_s10732-017-9356-7
    DOI: 10.1007/s10732-017-9356-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-017-9356-7
    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/s10732-017-9356-7?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. 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.
    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. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
    2. Probst, Malte & Rothlauf, Franz & Grahl, Jörn, 2017. "Scalability of using Restricted Boltzmann Machines for combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 256(2), pages 368-383.
    3. Madjid Tavana & Kaveh Khalili-Damghani & Amir-Reza Abtahi, 2013. "A fuzzy multidimensional multiple-choice knapsack model for project portfolio selection using an evolutionary algorithm," Annals of Operations Research, Springer, vol. 206(1), pages 449-483, July.
    4. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    5. Alexandros Nikas & Angelos Fountoulakis & Aikaterini Forouli & Haris Doukas, 2022. "A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems," Operational Research, Springer, vol. 22(2), pages 1291-1332, April.
    6. Marcella S. R. Martins & Mohamed El Yafrani & Myriam Delgado & Ricardo Lüders & Roberto Santana & Hugo V. Siqueira & Huseyin G. Akcay & Belaïd Ahiod, 2021. "Analysis of Bayesian Network Learning Techniques for a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm: a case study on MNK Landscape," Journal of Heuristics, Springer, vol. 27(4), pages 549-573, 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:24:y:2018:i:1:d:10.1007_s10732-017-9356-7. 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.