The University of Melbourne

Discrete Optimization

Taught in English

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71,575 already enrolled

Course

Gain insight into a topic and learn the fundamentals

Professor Pascal Van Hentenryck
Dr. Carleton Coffrin

Instructors: Professor Pascal Van Hentenryck

4.8

(755 reviews)

Intermediate level
Some related experience required
65 hours to complete
3 weeks at 21 hours a week
Flexible schedule
Learn at your own pace

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There are 8 modules in this course

These lectures and readings give you an introduction to this course: its philosophy, organization, and load. They also tell you how the assignments are a significant part of the class. This week covers the common input/output organization of the assignments, how they are graded, and how to succeed in this class.

What's included

4 videos2 readings1 programming assignment

These lectures introduce optimization problems and some optimization techniques through the knapsack problem, one of the most well-known problem in the field. It discusses how to formalize and model optimization problems using knapsack as an example. It then reviews how to apply dynamic programming and branch and bound to the knapsack problem, providing intuition behind these two fundamental optimization techniques. The concept of relaxation and search are also discussed.

What's included

9 videos1 programming assignment

Constraint programming is an optimization technique that emerged from the field of artificial intelligence. It is characterized by two key ideas: To express the optimization problem at a high level to reveal its structure and to use constraints to reduce the search space by removing, from the variable domains, values that cannot appear in solutions. These lectures cover constraint programming in detail, describing the language of constraint programming, its underlying computational paradigm and how it can be applied in practice.

What's included

13 videos1 reading2 programming assignments

Local search is probably the oldest and most intuitive optimization technique. It consists in starting from a solution and improving it by performing (typically) local perturbations (often called moves). Local search has evolved substantially in the last decades with a lot of attention being devoted on which moves to explore. These lectures explore the theory and practice of local search, from the concept of neighborhood and connectivity to meta-heuristics such as tabu search and simulated annealing.

What's included

10 videos1 programming assignment

Linear programming has been, and remains, a workhorse of optimization. It consists in optimizing a linear objective subject to linear constraints, admits efficient algorithmic solutions, and is often an important building block for other optimization techniques. These lectures review fundamental concepts in linear programming, including the infamous simplex algorithm, simplex tableau, and duality. .

What's included

6 videos

Mixed Integer Programming generalizes linear programming by allowing integer variables, which dramatically changes the complexity of the problems but also broadens the potential applications significantly. These lectures review how to model problems in mixed-integer programming and how to solve mixed-integer programs using branch and bound. Advanced techniques such as cutting planes and polyhedral cuts are also covered.

What's included

6 videos1 programming assignment

These lectures cover some more advanced concepts in optimization. They introduce constraint-programming techniques for scheduling and routing.

What's included

2 videos1 programming assignment

These lectures continues to cover some more advanced concepts in optimization. They introduce large neighborhood search, which often combines constraint programming and local search, and column generation which decomposes an optimization model into a master and pricing problem, using more complex variables.

What's included

2 videos1 reading

Instructors

Instructor ratings
4.8 (159 ratings)
Professor Pascal Van Hentenryck
The University of Melbourne
1 Course71,575 learners
Dr. Carleton Coffrin
The University of Melbourne
2 Courses73,373 learners

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