Network and Discrete Optimization Essentials
Master fundamental concepts in network optimization and discrete optimization, from graph theory to advanced algorithms.
Master fundamental concepts in network optimization and discrete optimization, from graph theory to advanced algorithms.
Explore the fascinating world of network and discrete optimization in this comprehensive course. Dive into the mathematical foundations of graphs and networks, and learn to solve complex problems such as the transshipment problem and shortest path algorithms. The course covers essential topics in discrete optimization, introducing you to powerful modeling techniques and exact solution methods. You'll gain practical skills in formulating and solving optimization problems, with a focus on both theoretical understanding and algorithmic implementation. Ideal for students and professionals in mathematics, computer science, and operations research, this course provides a solid foundation for tackling real-world optimization challenges.
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What you'll learn
Understand and apply the mathematical formalism of graphs and networks
Formulate and solve transshipment (minimum cost flow) problems
Implement and analyze shortest path algorithms for various applications
Specify and model discrete optimization problems
Apply exact methods, including branch and bound and cutting planes, to solve discrete optimization problems
Analyze the computational complexity of network and discrete optimization algorithms
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, exams
Access on Mobile, Tablet, Desktop
Limited Access access
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Module Description
This course provides a comprehensive introduction to network and discrete optimization, covering both theoretical foundations and practical algorithms. The curriculum is structured into five main sections: 1) Networks: introducing the mathematical formalism of graphs and networks; 2) Transshipment: exploring the minimum cost flow problem and its properties; 3) Shortest path: focusing on algorithms to find the shortest path in a network; 4) Discrete optimization: learning how to specify discrete optimization problems; 5) Exact methods for discrete optimization: introducing algorithms to solve discrete optimization problems, including branch and bound and cutting plane methods. Throughout the course, students will learn to apply these concepts to real-world optimization problems, with optional Python programming exercises to implement the algorithms discussed. The course emphasizes both mathematical rigor and practical problem-solving skills, preparing students for advanced study or application of optimization techniques in various fields.
Fee Structure
Instructor
5 Courses
Pioneer in Transportation Systems and Operations Research
Michel Bierlaire, born in 1967 in Namur, Belgium, is a Belgian-Swiss applied mathematician and Full Professor at École polytechnique fédérale de Lausanne (EPFL), where he directs the Transport and Mobility Laboratory since 2006. After earning his Ph.D. in Mathematical Sciences from the University of Namur in 1996, he worked at MIT's Intelligent Transportation Systems Program (1995-1998) developing real-time traffic simulation tools. He joined EPFL in 1998 as a senior scientist, progressing to Associate Professor in 2006 and Full Professor in 2012. His research focuses on transportation modeling, discrete choice models, and operations research, with significant contributions to demand modeling and traffic management systems. He founded the European Association for Research in Transportation and developed Biogeme, an open-source project for discrete choice model estimation. His scholarly output includes over 150 papers in international journals, 4 books, and numerous book chapters and conference proceedings. He has served as director of TraCE Transportation Center (2009-2022) and head of the Civil Engineering Institute (2017-2021), while maintaining leadership roles in various international research organizations
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