MSE Master of Science in Engineering

The Swiss engineering master's degree

Jedes Modul umfasst 3 ECTS. Sie wählen insgesamt 10 Module/30 ECTS in den folgenden Modulkategorien:

  • ​​​​12-15 ECTS in Technisch-wissenschaftlichen Modulen (TSM)
    TSM-Module vermitteln Ihnen profilspezifische Fachkompetenz und ergänzen die dezentralen Vertiefungsmodule.
  • 9-12 ECTS in Erweiterten theoretischen Grundlagen (FTP)
    FTP-Module behandeln theoretische Grundlagen wie die höhere Mathematik, Physik, Informationstheorie, Chemie usw. Sie erweitern Ihre abstrakte, wissenschaftliche Tiefe und tragen dazu bei, den für die Innovation wichtigen Bogen zwischen Abstraktion und Anwendung spannen zu können.
  • 6-9 ECTS in Kontextmodulen (CM)
    CM-Module vermitteln Ihnen Zusatzkompetenzen aus Bereichen wie Technologiemanagement, Betriebswirtschaft, Kommunikation, Projektmanagement, Patentrecht, Vertragsrecht usw.

In der Modulbeschreibung (siehe: Herunterladen der vollständigen Modulbeschreibung) finden Sie die kompletten Sprachangaben je Modul, unterteilt in die folgenden Kategorien:

  • Unterricht
  • Dokumentation
  • Prüfung
Optimization (FTP_Optimiz)

This course offers an introduction to optimization, emphasizing basic methodologies and underlying mathematical structures. Optimization refers to the application of mathematical models and algorithms to decision making.  A large number of quantitative real-world problems can be formulated and solved in this general framework. Applications of optimization comprise, for instance, decision problems in production planning, supply chain management, transportation networks, machine and workforce scheduling, blending of components, telecommunication network design, airline fleet assignment, and revenue management.

Eintrittskompetenzen

Linear algebra:

  • Systems of linear equations, Gauss algorithm
  • Basics of vector and matrix algebra, linear spaces

Analysis:

  • Calculus with functions of one variable
  • Zeros of functions (Newton algorithm)

Programming:

  • Basics of procedural programming and ability to implement small programs in an arbitrary language, e.g. Python, Matlab, R, Java, C#, C++, C, etc.

Lernziele

  • The student has an overview of the various fields and approaches to optimization.
  • The student has a basic mathematical and algorithmic understanding of the major optimization methods used in practice (Linear Programming (LP), Integer Programming (ILP), Nonlinear Programming, Optimization in Graphs, Metaheuristics).
  • The student is able to analyze basic real-world decision problems and formulate appropriate optimization models.
  • The student is able to implement and solve basic LP/ILP models in a spreadsheet.
  • The student has developed a certain intuition on how to approach and analyze real-world optimization problems, to correctly estimate their complexity, and to choose appropriate modeling approaches and implementation tools.

Modulinhalt

Week

Topics

1

PART 1:

Introduction to Optimization

  • Basic concepts: models, variables, parameters, constraints, objective, optima
  • Examples of problems and models of different types: linear/nonlinear, discrete/continuous, deterministic/stochastic, constrained/unconstrained
  • Solution methods: exact algorithms, constructive heuristics, improvement heuristics
  • Global vs. local optima, basic ideas of convex optimization

2

3

Linear Programming

  • Mathematical formulation and terminology, canonical and standard form, transformations
  • Geometry: linear inequalities, polyhedra, graphical representation, examples
  • Simplex algorithm

4

5

6

Integer Programming

  • Basic concepts
  • Branch-and-Bound method
  • Cutting Planes method
  • Various applications and modeling techniques

7

8

PART 2:
Nonlinear Optimization

  • Unconstrained multidimensional optimization: optimality conditions, Gradient- and Newton-methods

9

Graphs and Networks

  • Optimization in graphs
  • Paths and cycles
  • Network flows
  • Selected combinatorial optimization problems

10

11

12

Heuristics and Metaheuristics

  • Trajectory-based methods: hill climbing, tabu search, simulated annealing, ...
  • Population-based methods: evolutionary algorithms, ant colony optimization, ...

13

14

Lehr- und Lernmethoden

Lectures and exercises 

Vollständige Modulbeschreibung herunterladen

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