Approximated set-valued mapping approach for handling multiobjective bilevel problems

Ankur Sinha*, Pekka Malo, Kalyanmoy Deb

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)


A significant amount of research has been done on bilevel optimization problems both in the realm of classical and evolutionary optimization. However, the multiobjective extensions of bilevel programming have received relatively little attention from researchers in both the domains. The existing algorithms are mostly brute-force nested strategies, and therefore computationally demanding. In this paper, we develop insights into multiobjective bilevel optimization through theoretical progress made in the direction of parametric multiobjective programming. We introduce an approximated set-valued mapping procedure that would be helpful in the development of efficient evolutionary approaches for solving these problems. The utility of the procedure has been emphasized by incorporating it in a hierarchical evolutionary framework and assessing the improvements. Test problems with varying levels of complexity have been used in the experiments.

Original languageEnglish
Pages (from-to)194-209
Number of pages16
JournalComputers and Operations Research
Publication statusPublished - 1 Jan 2017
MoE publication typeA1 Journal article-refereed


  • Bilevel optimization
  • Evolutionary algorithm
  • Multiobjective optimization


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