Discrete optimization

Have you ever wondered what is the shortest route to join the office? What is the best way to plan a trip through several cities? You have maybe already played with magical squares? Then you have met one of the nu- merous instances of discrete optimization. Discrete optimization is a field of mathematics which deals with any problem where parts of the solutions cannot be divided or fractional. And as one may guess, this is the case in many real-life problems.
This poster is divided in three main topics. The first part focuses on formulating those problems. We will start from one of the industrial appli- cations and show how we can model it as a mathematical problem.
In the second part we sketch the main tools and algorithms used to tackle those problems. In particular we point out the fact that requiring integrality leads to extremely hard problems to solve. We show that despite this fact, we are able to solve problems of substantial size.
However there remain some problems that are hard to solve using the state-of-the-art techniques. In the third part we indicate what are the chal- lenges of the field. In particular we will give an overview of the research car- ried out in the universities supported by the Marie-Curie network ADONET.