MSE Master of Science in Engineering

The Swiss engineering master's degree


Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories: 

  • 12-15 ECTS in technical scientific modules (TSM)
    TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules.
  • 9-12 ECTS in fundamental theoretical principles modules (FTP)
    FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation.
  • 6-9 ECTS in context modules (CM)
    CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.

In the module description (download pdf) you find the entire language information per module divided into the following categories:

  • instruction
  • documentation
  • examination 
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.

Prerequisites

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.

Learning Objectives

  • 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.

Contents of Module

 

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

 

Teaching and Learning Methods

Lectures and exercises 

Download full module description

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