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Optimization

principles and algorithms - Network and discrete optimization

Michel Bierlaire

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.

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Learning objectives

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.
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.
The course is structured into 5 sections.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops skills and knowledge in network modeling, helpful for studying communication and transportation networks

Taught by experienced instructor Michel Bierlaire, recognized for their work in network optimization

Examines core techniques in discrete optimization, such as branch and bound and cuts

Introduces the concept of networks and their applications in real-world scenarios

Provides a comprehensive overview of transhipment and shortest path problems, fundamental in network analysis

Requires a background in mathematics and computing, suitable for students with a strong quantitative foundation

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Optimization: principles and algorithms - Network and discrete optimization with these activities:

Review Network Fundamentals

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Review basic network concepts and terminology to strengthen your foundation.

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Read textbooks or online articles covering fundamental network concepts.
Review your notes or past coursework on network fundamentals.

Organize and Review Course Materials

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To ensure a strong foundation, systematically organize your lecture notes, assignments, and other course materials for easy access and review.

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Gather all your relevant course materials.
Create a logical system to organize the materials.

Solve Network Optimization Problems

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Engage in solving practice problems to improve your understanding and problem-solving skills.

Browse courses on Network Optimization

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Find online resources or textbooks with practice problems on network optimization.
Attempt to solve the problems independently.

Two other activities

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Explore Branch and Bound Algorithm

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Follow online tutorials or videos to gain a deeper understanding of the concepts and implementation of the branch and bound algorithm.

Browse courses on Branch and Bound

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Identify online tutorials or videos that provide clear explanations.
Follow the tutorials and try to implement the algorithm yourself.

Develop a Network Modeling Tool

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Create a software tool or script that can perform network modeling tasks, solidifying your knowledge through practical application.

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Identify a specific network modeling task to work on.
Design and implement the software tool or script.

Career center

Learners who complete Optimization: principles and algorithms - Network and discrete optimization will develop knowledge and skills that may be useful to these careers:

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve problems in a wide variety of industries. They use their knowledge of networks and optimization to develop solutions that improve the efficiency and effectiveness of operations. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in operations research.

See salaries and explore the career path for Operations Research Analyst

Logistics Manager

Logistics Managers are responsible for planning, implementing, and controlling the movement of goods and services. They use their knowledge of networks and optimization to develop efficient and cost-effective logistics solutions. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in logistics management.

See salaries and explore the career path for Logistics Manager

Transportation Analyst

Transportation Analysts play a vital role in the planning, design, and operation of transportation systems. They use their knowledge of networks and optimization to develop solutions that improve the efficiency and effectiveness of transportation systems. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in transportation planning and management.

See salaries and explore the career path for Transportation Analyst

Statistician

Statisticians use their knowledge of networks and optimization to analyze data. They use mathematical and analytical techniques to develop models that can predict the future and make informed decisions. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in statistics.

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Software Engineer

Software Engineers design, develop, and maintain software systems. They use their knowledge of networks and optimization to develop efficient and scalable software solutions. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in software engineering.

See salaries and explore the career path for Software Engineer

Data Analyst

Data Analysts use their knowledge of networks and optimization to extract insights from data. They use mathematical and analytical techniques to develop algorithms that can solve complex problems in a variety of industries. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in data analysis.

See salaries and explore the career path for Data Analyst

Management Consultant

Management Consultants use their knowledge of networks and optimization to help businesses improve their operations. They use mathematical and analytical techniques to identify and solve problems that are costing businesses money. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in management consulting.

See salaries and explore the career path for Management Consultant

Risk Analyst

Risk Analysts use mathematical and statistical techniques to assess and manage risk. They use their knowledge of networks and optimization to develop models that can predict the likelihood and severity of risks. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in risk analysis.

See salaries and explore the career path for Risk Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data. They use their knowledge of networks and optimization to develop models that can predict the performance of financial assets. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in quantitative finance.

See salaries and explore the career path for Quantitative Analyst

Economist

Economists use their knowledge of networks and optimization to analyze economic data. They use mathematical and analytical techniques to develop models that can predict the future and make informed decisions. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in economics.

See salaries and explore the career path for Economist

Systems Analyst

Systems Analysts use their knowledge of networks and optimization to design and implement computer systems. They use mathematical and analytical techniques to ensure that systems are efficient and effective. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in systems analysis.

See salaries and explore the career path for Systems Analyst

Computer Programmer

Computer Programmers use their knowledge of networks and optimization to develop software systems. They use mathematical and analytical techniques to ensure that software is efficient and effective. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in computer programming.

See salaries and explore the career path for Computer Programmer

Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data. They use their knowledge of networks and optimization to develop models that can predict the performance of financial assets. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in financial analysis.

See salaries and explore the career path for Financial Analyst

Data Scientist

Data Scientists use mathematical and statistical techniques to extract insights from data. They use their knowledge of networks and optimization to develop algorithms that can solve complex problems in a variety of industries. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in data science.

See salaries and explore the career path for Data Scientist

Business Analyst

Business Analysts use their knowledge of networks and optimization to help businesses improve their operations. They use mathematical and analytical techniques to identify and solve problems that are costing businesses money. This course provides a strong foundation in the mathematical concepts of networks and optimization, which are essential for success in this field. You will learn about the transhipment problem, the shortest path problem, and other important optimization problems on networks. You will also learn about discrete optimization, which is used to solve a wide variety of problems in business analysis.

See salaries and explore the career path for Business Analyst

Reading list

We've selected 15 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Optimization: principles and algorithms - Network and discrete optimization.

Network Flows

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This well-regarded textbook comprehensively covers graph theory, network optimization, and the algorithms used to solve network optimization problems. It includes chapters on topics such as the transshipment problem, the shortest path problem, and network flows, which would provide valuable background and depth to this course.

Optimization

principles and algorithms - Network and discrete optimization

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What's inside

Learning objectives

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