Optimization: principles and algorithms - Network and discrete optimization

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

The course is structured into 5 sections.

• Networks: you will be introduced to the mathematical formalism of graphs and networks.
• Transhipment: you will learn about the transhipment problem (also called "minimum cost flow problem"), its properties, and some special instances.
• Shortest path: you will learn about algorithms to find the shortest path in a network.
• Discrete optimization: you will learn how to specify a discrete optimization problem.
• Exact methods for discrete optimization: you will be introduced to two algorithms to solve discrete optimization problems.