Document Open Access Logo

Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem

Authors Satya Tamby , Daniel Vanderpooten



PDF
Thumbnail PDF

File

LIPIcs.SEA.2023.9.pdf
  • Filesize: 0.75 MB
  • 13 pages

Document Identifiers

Author Details

Satya Tamby
  • Université Paris Dauphine, PSL Research University, LAMSADE, France
Daniel Vanderpooten
  • Université Paris Dauphine, PSL Research University, LAMSADE, France

Cite AsGet BibTex

Satya Tamby and Daniel Vanderpooten. Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 9:1-9:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SEA.2023.9

Abstract

Optimizing over the efficient set of a discrete multi-objective problem is a challenging issue. The main reason is that, unlike when optimizing over the feasible set, the efficient set is implicitly characterized. Therefore, methods designed for this purpose iteratively generate efficient solutions by solving appropriate single-objective problems. However, the number of efficient solutions can be quite large and the problems to be solved can be difficult practically. Thus, the challenge is both to minimize the number of iterations and to reduce the difficulty of the problems to be solved at each iteration. In this paper, a new enumeration scheme is proposed. By introducing some constraints and optimizing over projections of the search region, potentially large parts of the search space can be discarded, drastically reducing the number of iterations. Moreover, the single-objective programs to be solved can be guaranteed to be feasible, and a starting solution can be provided allowing warm start resolutions. This results in a fast algorithm that is simple to implement. Experimental computations on two standard multi-objective instance families show that our approach seems to perform significantly faster than the state of the art algorithm.

Subject Classification

ACM Subject Classification
  • Applied computing → Multi-criterion optimization and decision-making
  • Theory of computation → Integer programming
Keywords
  • discrete optimization
  • multi-objective optimization
  • non-dominated set
  • efficient set

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Natashia Boland, Hadi Charkhgard, and Martin Savelsbergh. A new method for optimizing a linear function over the efficient set of a multiobjective integer program. European Journal of Operational Research, 260(3):904-919, 2017. Google Scholar
  2. Natashia Boland, Hadi Charkhgard, and Martin W. P. Savelsbergh. The L-shape search method for triobjective integer programming. Mathematical Programming Computation, 8(2):217-251, 2016. Google Scholar
  3. Djamal Chaabane and Marc Pirlot. A method for optimizing over the integer efficient set. Journal of Industrial and Management Optimization, 6(4):811-823, 2010. Google Scholar
  4. Kerstin Dächert, Kathrin Klamroth, Renaud Lacour, and Daniel Vanderpooten. Efficient computation of the search region in multi-objective optimization. European Journal of Operational Research, 260(3):841-855, 2017. Google Scholar
  5. Jesus Jorge. An algorithm for optimizing a linear function over an integer efficient set. European Journal of Operational Research, 195(3):98-103, 2009. Google Scholar
  6. Gokhan Kirlik and Serpil Sayin. A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems. European Journal of Operational Research, 232(3):479-488, 2014. Google Scholar
  7. Gokhan Kirlik and Serpil Sayin. Computing the nadir point for multiobjective discrete optimization problems. Journal of Global Optimization, 62(1):79-99, 2015. Google Scholar
  8. Kathrin Klamroth, Renaud Lacour, and Daniel Vanderpooten. On the representation of the search region in multi-objective optimization. European Journal of Operational Research, 245(3):767-778, 2015. Google Scholar
  9. Dieter Klein and Edward L. Hannan. An algorithm for the multiple objective integer linear programming problem. European Journal of Operational Research, 9(4):378-385, 1982. Google Scholar
  10. Murat Köksalan and Banu Lokman. Finding nadir points in multi-objective integer programs. Journal of Global Optimization, 62(1):55-77, 2015. Google Scholar
  11. Banu Lokman. Optimizing a linear function over the nondominated set of multiobjective integer programs. International Transactions in Operational Research, 28(4):2248-2267, 2021. Google Scholar
  12. Banu Lokman and Murat Köksalan. Finding all nondominated points of multi-objective integer programs. Journal of Global Optimization, 57(2):347-365, 2013. Google Scholar
  13. John Sylva and Alejandro Crema. A method for finding the set of non-dominated vectors for multiple objective integer linear programs. European Journal of Operational Research, 158(1):46-55, 2004. Google Scholar
  14. Satya Tamby and Daniel Vanderpooten. Enumeration of the nondominated set of multiobjective discrete optimization problems. INFORMS Journal on Computing, 33(1):72-85, 2021. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail