2550155 – Multiobjective Optimization

Lecturer: Prof. Dr. Oliver Stein, Institute for Operations Research

Time and place: Tuesday, 9:45 - 11:15, 10.91-Mittlerer Hörsaal

Start: Tuesday, October 27, 2026.

Format: In-person lecture.

Assessment: Successful participation in mandatory prerequisite (30% of the exercise points) and a written exam.

Contents:

Multiobjective optimization deals with optimization problems with multiple objective functions. In practice, the minimization or maximization of several objectives often conflict with each other, such as weight and stability of mechanical components, return and risk of stock portfolios, or cost and duration of transports. Various scalarization approaches allow one to formulate single-objective problems that can be solved using nonlinear or global optimization techniques, and whose optimal points have a reasonable interpretation for the underlying multicriteria problem.

However, some seemingly obvious scalarization approaches suffer from various drawbacks, so that regardless of scalarization approaches, it is necessary to clarify what is meant by the solution of a multiobjective optimization problem in the first place. For such efficient (aka Pareto-optimal) points, optimality conditions and solution procedures based on them can be formulated. From the usually non-unique efficient set, decision makers finally choose an alternative based on their subjective preferences.

The lecture gives a mathematically sound introduction to multiobjective optimization and is structured as follows:

• Introductory examples and terminology
• Solution concepts
• Methods for the determination of the efficient set
• Selection of efficient points under subjective preferences

Additional Information:
To acquire a solid foundation of knowledge, it is strongly recommended to take at least one of the following courses before attending this special lecture: Nonlinear Optimization I and II and Global Optimization I and II.

Exercises (Instructor: Felix Neussel):
Thursday, 11:30 - 13:00 (biweekly), 10.11-Seminarraum Hauptgebäude.
Start: November 5, 2026.

Literature:
M. Ehrgott, Multicriteria Optimization, Second Edition, Springer, Berlin, 2005.
J. Jahn, Vector Optimization, Second Edition, Springer, Berlin, 2011.
K. Miettinen, Nonlinear Multiobjective Optimization, Springer, New York, 2004.
Y. Sawaragi, H. Nakayama, T. Tanino, Theory of Multiobjective Optimization, Academic Press, Orlando, FL, 1985.

Englisch

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Von: 1. Okt 2026, 00:00

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