FCN E.ON Energy Research Center Teaching Visits | Single and Multi-Objective Bilevel Optimization


Bilevel optimization problems model hierarchical non-cooperative decision processes with two decision
makers (the leader and the follower), who control different sets of variables, have their own objective functions
subject to interdependent constraints, and make decisions sequentially. The follower’s optimization problem is
embedded in the constraints of the leader’s problem.

This course has aimed to present the main concepts in single and multi-objective bilevel optimization using
illustrative graphical examples, as well as applications in real-world problems, particularly in the energy sector.
A particular application in the electricity retail market was presented, which studies the interaction between
electricity retailers and consumers engaging in demand response.

Topics covered:

  • Formulations and main concepts of single-objective bilevel optimization
  • Optimistic vs. pessimistic solutions
  • Algorithmic approaches to solve bilevel optimization models
  • Models and applications of single-objective bilevel optimization
  • Application in the energy sector: optimization of time-of-use electricity pricing considering demand response
  • Formulations and main concepts of multi-objective bilevel optimization
  • The semivectorial bilevel problem (SVBP)
  • Different types of solutions to the SVBP: optimistic, pessimistic, deceiving and rewarding solutions
  • Optimistic and pessimistic Pareto fronts of bilevel problems with multiple objective functions at both levels
  • Models and applications of multi-objective bilevel optimization
  • A SVBP approach to optimize electricity dynamic retail pricing.


Prof. Henggeler Antunes and Prof. Maria João Alves visit RWTH Aachen University on invitation by the Chair of Energy Economics and Management (Prof. Reinhard Madlener)

Institute for Future Energy Consumer Needs and Behavior (FCN)
E.ON Energy Research Center
School of Business and Economics
Mathieustraße 10
52074 Aachen, Germany

Tel.: +49 241 80 49820 / 49822