Network and Discrete Optimization

Course Description

Welcome to our intermediate-level course on Network and Discrete Optimization, offered by EPFLx. This engaging and comprehensive course delves into the fascinating world of mathematical networks and explores two crucial optimization problems: the transshipment problem and the shortest path problem. As you progress through the course, you'll also gain valuable insights into discrete optimization, including classical problems and advanced algorithms like branch and bound.

What You'll Learn

• Mathematical formalism of graphs and networks
• Transshipment problem (minimum cost flow problem) and its properties
• Algorithms for finding the shortest path in a network
• Specification of discrete optimization problems
• Introduction to exact methods for solving discrete optimization problems

Pre-requisites

• Familiarity with linear optimization (recommended to take the companion course if needed)
• Knowledge of Python programming is beneficial but not mandatory

Course Content

• Introduction to networks and graph theory
• Transshipment problem and its special instances
• Shortest path algorithms and applications
• Discrete optimization problem formulation
• Branch and bound algorithm
• Concept of cuts in optimization
• Modeling power of discrete optimization
• Classical optimization problems

Who Should Take This Course

This course is ideal for students, professionals, and researchers interested in:

• Mathematics and computer science
• Operations research and optimization
• Data science and analytics
• Engineering and logistics
• Anyone looking to enhance their problem-solving skills using advanced mathematical concepts

Real-World Applications

The skills acquired in this course have numerous practical applications:

• Supply chain management and logistics optimization
• Transportation and route planning
• Network design and analysis (e.g., social networks, communication networks)
• Resource allocation in various industries
• Data analysis and decision-making in complex systems
• Algorithm development for efficient problem-solving
• Optimization of business processes and operations

Course Structure

The course is structured into 5 main sections:

1. Networks
2. Transshipment
3. Shortest path
4. Discrete optimization
5. Exact methods for discrete optimization

Conclusion

By enrolling in this course, you'll gain a solid foundation in network and discrete optimization, equipping you with powerful tools to tackle real-world problems across various domains. The combination of theoretical knowledge and practical applications will make you a valuable asset in any field requiring advanced problem-solving and optimization skills. Don't miss this opportunity to expand your mathematical horizons and enhance your career prospects!