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Multiobjective Bilevel Programming: Concepts and Perspectives of Development

  • Maria João AlvesEmail author
  • Carlos Henggeler Antunes
  • João Paulo Costa
Chapter
Part of the Multiple Criteria Decision Making book series (MCDM)

Abstract

Bilevel programs model hierarchical non-cooperative decision processes with two decision makers, the leader and the follower, who control different sets of variables and have their own objective functions with interdependent constraints. Bilevel programs are very difficult to solve and even the linear case is NP-hard. In this chapter, a novel view on the main concepts in multiobjective and semivectorial bilevel problems is offered, including new types of solutions that are relevant for decision support. Optimistic and pessimistic leader’s perspectives are explored; the extreme optimistic/deceiving and pessimistic/rewarding solutions in semivectorial problems and the optimistic Pareto fronts in multiobjective problems are defined and illustrated. Traditional and emerging application fields are reviewed. Potential difficulties and pitfalls associated with computing solutions to bilevel models with multiple objectives are outlined, shaping possible research avenues.

Keywords

Multiobjective optimization Bilevel programming Semivectorial bilevel Optimistic versus pessimistic approaches Optimistic Deceiving Pessimistic Rewarding solutions 

Notes

Acknowledgements

This work was supported by projects UID/MULTI/00308/2019, ESGRIDS (POCI-01-0145-FEDER-016434) and MAnAGER (POCI-01-0145-FEDER-028040).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maria João Alves
    • 1
    • 3
    Email author
  • Carlos Henggeler Antunes
    • 2
    • 3
  • João Paulo Costa
    • 1
    • 3
  1. 1.CeBER and Faculty of EconomicsUniversity of CoimbraCoimbraPortugal
  2. 2.DEEC, University of CoimbraCoimbraPortugal
  3. 3.INESC CoimbraCoimbraPortugal

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