Solution Methods for Multi-Objective Combinatorial Optimization

Prof. Dr. Anthony Przybylski

Teresa Schnepper, M.Sc.

Content

Most of the real-world problems naturally involve several conflicting criteria, and can be formulated as multi-objective mathematical programs. There is generally no feasible solution that minimizes all objectives simultaneously. Consequently, the notion of efficient solutions, that are feasible solutions that cannot be improved on one objective without degrading an- other one, replaces the notion of optimal solution. This course will focus on multi-objective combinatorial optimization (MOCO) problems.

• Introduction to Multi-objective Optimization (Mathematical Formulation, contexts of solution methods, notion of efficiency and nondominance, scalarization methods)
• Main properties of Multi-objective Combinatorial Optimization problems
• ε-constraint method with adaptive step
• Two-phase method
• Multi-objective Branch and Bound
• Multi-objective metaheuristics
  

Preknowledge

Linear and integer programming (Bachelor OR I and OR II), Preknowledge in Multicriteria Optimization is not necessary.

Dates

Lecture: Tuesdays 12.15 am - 1.45 pm in G.15.20, Thursdays 10.15 am - 11.45 am in HS 27 (first lecture on October 18th, 2016)
Tutorials: Wednesdays 10.15 am - 11.45 am in D.13.15 (first tutorial on October 26th, 2016)

Moodle

Will be announced later.

Literature

• Matthias Ehrgott. Multicriteria Optimization, second edition. Springer, 2005.
• Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Edited by Matthias Ehrgott and Xavier Gandibleux.

Lecture, tutorials and examinations will be in English! On request, the examination can be carried out in German by another Professor.