MSE Master of Science in Engineering

The Swiss engineering master's degree

Ogni modulo equivale a 3 crediti ECTS. È possibile scegliere un totale di 10 moduli/30 ECTS nelle seguenti categorie: 

  • 12-15 crediti ECTS in moduli tecnico-scientifici (TSM)
    I moduli TSM trasmettono competenze tecniche specifiche del profilo e si integrano ai moduli di approfondimento decentralizzati.
  • 9-12 crediti ECTS in basi teoriche ampliate (FTP)
    I moduli FTP trattano principalmente basi teoriche come la matematica, la fisica, la teoria dell’informazione, la chimica ecc. I moduli ampliano la competenza scientifica dello studente e contribuiscono a creare un importante sinergia tra i concetti astratti e l’applicazione fondamentale per l’innovazione 
  • 6-9 crediti ECTS in moduli di contesto (CM)
    I moduli CM trasmettono competenze supplementari in settori quali gestione delle tecnologie, economia aziendale, comunicazione, gestione dei progetti, diritto dei brevetti, diritto contrattuale ecc.

La descrizione del modulo (scarica il pdf) riporta le informazioni linguistiche per ogni modulo, suddivise nelle seguenti categorie:

  • Insegnamento
  • Documentazione
  • Esame
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.

Requisiti

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.

Obiettivi di apprendimento

  • 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.

Contenuti del modulo

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

Metodologie di insegnamento e apprendimento

Lectures and exercises 

Scarica il descrittivo completo del modulo

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