- Docente: Valentina Cacchiani
- Credits: 6
- SSD: MAT/09
- Language: English
- Moduli: Valentina Cacchiani (Modulo 1) Valentina Cacchiani (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Automation Engineering (cod. 8891)
Also valid for Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)
Second cycle degree programme (LM) in Electrical Energy Engineering (cod. 9066)
Second cycle degree programme (LM) in Telecommunications Engineering (cod. 9205)
Learning outcomes
At the end of the course, the students know the foundations of mathematical optimization and graph theory, are able to model optimization problems, and know the main algorithms used for their solution.
Course contents
Requirements: a good knowledge of the basics of set theory, and vectorial and matricial calculus is required.
The course is given in English: slides and exercises are in English. The exam must be taken in English.
The course focuses on optimization problems arising in decision making, with particular emphasis on Combinatorial Optimization problems. The first goal of the course is to teach the theory of Linear Programming and Integer Linear Programming, and how to formulate mathematical models for optimization problems belonging to these classes. The classical Integer Linear Programming problems are also presented. The second goal is to teach algorithms to solve these problems. In addition, the basics of computational complexity of problems and algorithms are introduced, and graph theory concepts and the classical problems modelled on graphs are described. The last part of the course is dedicated to practical applications: more complex real-world optimization problems are presented and the use of optimization tools is shown.
Readings/Bibliography
Slides on IOL (Insegnamenti On Line)
Further readings:
Fischetti M. Introduction to Mathematical Optimization. Kindle Direct Publishing, 2019.
Christos H. Papadimitriou and Ken Steiglitz, Combinatorial optimization: algorithms and complexity. Dover, 1998.
D. Bertsimas and J. Tsitsiklis, Introduction to linear programming. Dynamic Ideas and Athena Scientific, Belmont, Massachusetts, 2008.
D. Bertsimas, D. and R. Weismantel, Optimization over integers. Dynamic Ideas, Belmont, Massachusetts, 2005.
Teaching methods
The course consists of lectures and class exercises.
Assessment methods
The exam consists of a written test in which some exercises on topics of the course have to be solved (about 60 minutes). One or two days after the written test, an oral discussion covering topics of the written test and all topics of the course (including theorems and proofs) completes the exam.
If, due to the pandemic, an online exam will be used: the written test will be done by using EOL and ZOOM, and the oral discussion with TEAMS. More details will be given during the course.
Teaching tools
Optimization software tools
Office hours
See the website of Valentina Cacchiani