## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-51-13-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-51-13-M-7 Multicriteria Optimization 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Ruzika, Stefan, Prof. Dr. (PROF | DEPT: MAT) Ruzika, Stefan, Prof. Dr. (PROF | DEPT: MAT) Schöbel, Anita, Prof. Dr. (PROF | DEPT: MAT) [MAT-OPT] Optimisation [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-51-13-K-7
Multicriteria Optimization
P 84 h 186 h - - PL1 9.0 irreg.
• About [MAT-51-13-K-7]: Title: "Multicriteria Optimization"; Presence-Time: 84 h; Self-Study: 186 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86310 ("Multicriteria Optimization")

## Contents

• Necessity of modelling with more than one objective function,
• Structures of order and concept of optimality,
• Characterisation of efficient and non-dominating solutions,
• Scalarisation methods,
• Multicriteria linear programmes,
• Multicriteria combinatorial optimization.

In the lecture and the exercise classes one of the topics listed above or a further research topic may be extensively discussed. Details are to be found in the information system KIS.

## Competencies / intended learning achievements

Upon successful completion of the module, the students are able to cope with advanced methods and algorithms to solve multicriteria optimization problems. They can model and solve real problems of scientific, technical and physical research areas via mathematical methods. They understand the mathematical background required for the algorithms and can critically assess the possibilities and limitations of the use of the same. They understand the proofs and are able to reproduce and explain them. They can critically assess, what conditions are necessary for the validity of the statements.

By solving the given exercise problems, they have gained a precise and independent handling of terms, propositions and methods of the lecture. In addition, they have learned to apply the methods to new problems, analyze them and develop solution strategies indepently or by team work.

## Literature

• M. Ehrgott: Multicriteria Optimization.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

## Requirements for attendance of the module (informal)

Depending on the current focus additional knowledge from the course [MAT-50-11-K-4] may be required.

None

## References to Module / Module Number [MAT-51-13-M-7]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science [Core Modules (non specialised)] Formal Fundamentals [WP] Compulsory Elective
Module-Pool Name
[MAT-52-MPOOL-7] Specialisation Mathematical Optimisation (M.Sc.)
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)