73414 - Algorithms for Decision Making M

Learning outcomes

The course introduces mathematical models for optimization problems arising in many branches of engineering, industry and complex systems. General solution methods and software tools (commercial and freeware) are presented.

Course contents

Requirements: a good knowledge of linear algebra and basic mathematics is required.

The course is given in English: slides and exercises are in English. The exam must be taken in English.

Contents

The first part of the course is about:

• Linear Programming and duality theory;

• Integer Linear Programming and branch-and-bound algorithm;

• computational complexity.

The second part of the course is about:

• mathematical formulations for classical combinatorial optimization problems;

• exponential-size models, continuous relaxation;

• column generation and constraint separation;

• solution methods for exponetial-size models;

• examples of real-life applications.

Readings/Bibliography

Slides on virtuale.unibo.it (at the web page of the course)

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 exam and an oral exam. In the written exam, some exercises on topics of the course have to be solved. On the day after the written exam, the students who have passed the written exam, take an oral exam covering all topics of the course to complete the exam.

The final mark is given by the average of written and oral exam marks.

Written and oral exams must be done in the same exam round.

Teaching tools

Slides on virtuale.unibo.it (at the web page of the course) and optimization software tools

Office hours

See the website of Valentina Cacchiani