Pareto Solutions in Multicriteria Optimization Under Uncertainty

Devon Sigler, Alexander Engau

Research output: Contribution to journalArticlepeer-review

25 Scopus Citations

Abstract

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions.

Original languageAmerican English
Pages (from-to)357-368
Number of pages12
JournalEuropean Journal of Operational Research
Volume281
Issue number2
DOIs
StatePublished - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.

NREL Publication Number

  • NREL/JA-2C00-75199

Keywords

  • Efficient set hierarchy
  • Multiple objective programming
  • Optimization under uncertainty
  • Pareto solutions
  • Scalarization methods

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