Solving Bilevel Multicriterion Optimization Problems with Lower Level Decision Uncertainty

Ankur Sinha, Pekka Malo, Kalyanmoy Deb, Pekka Korhonen, Jyrki Wallenius

Research output: Contribution to journalArticleScientificpeer-review

32 Citations (Scopus)


Bilevel optimization problems are characterized by a hierarchical leader-follower structure, in which the leader desires to optimize her own strategy taking the response of the follower into account. These problems are referred to as Stackelberg problems in the domain of game theory, and as bilevel problems in the domain of mathematical programming. In a number of practical scenarios, a bilevel problem is solved by a leader who needs to take multiple objectives into account and simultaneously deal with the decision uncertainty involved in modeling the follower's behavior. Such problems are often encountered in strategic product design, homeland security applications, and taxation policy. However, the hierarchical nature makes the problem difficult to solve and they are commonly simplified by assuming a deterministic setup with smooth objective functions. In this paper, we focus our attention on the development of a flexible evolutionary algorithm for solving multicriterion bilevel problems with lower level (follower) decision uncertainty. The performance of the algorithm is evaluated in a comparative study on a number of test problems. In addition to the numerical experiments, we consider two real-world examples from the field of environmental economics and management to illustrate how the framework can be used to obtain optimal strategies.

Original languageEnglish
Article number7120105
Pages (from-to)199-217
Number of pages19
JournalIEEE Transactions on Evolutionary Computation
Issue number2
Publication statusPublished - 1 Apr 2016
MoE publication typeA1 Journal article-refereed


  • Bilevel optimization
  • Decision Uncertainty
  • Evolutionary algorithms
  • Stackelberg Programming


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