EURO 2024 Copenhagen
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2119. What is the meaning of pessimistic Pareto front in multiobjective bilevel problems?

Invited abstract in session WC-37: Theory of Multiobjective Optimization, stream Multiobjective Optimization.

Wednesday, 12:30-14:00
Room: 33 (building: 306)

Authors (first author is the speaker)

1. Carlos Henggeler Antunes
INESC Coimbra, Department of Electrical and Computer Engineering, University of Coimbra
2. Maria João Alves
Faculty of Economics of University of Coimbra / INESC - Coimbra

Abstract

Bilevel optimization deals with decision problems in which two decision-makers, the leader and the follower, control different sets of variables and have their own objective functions subject to interdependent constraints. A lower-level optimization problem is embedded in an upper-level problem. When the lower-level problem has multiple objective functions, the leader should cope with the uncertainty related to the follower’s reaction. The leader can adopt a more optimistic or more pessimistic stance regarding the follower’s choice within his efficient region, which is restricted by the leader’s choices. The leader may also have multiple objective functions.
The concepts of optimism and pessimism are well established when the leader has a single objective function. However, this is not the case when there are multiple objective functions at both levels. Most approaches aim to calculate the optimistic Pareto frontier (efficient solutions for the leader, considering that the follower's choices are always the best for the leader). However, this approach is seldom realistic, and the definition of the pessimistic Pareto frontier may not be consensual.
We propose a definition of pessimistic Pareto front for bilevel optimization problems with multiple objective functions at both levels, which is compared with the optimistic Pareto front. These new concepts are illustrated using examples, emphasizing the difficulties associated with the computation of those solutions.

Keywords

Status: accepted

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