About this course: Tired of solving Sudokus by hand? This class teaches you how to solve complex search problems with discrete optimization concepts and algorithms, including constraint programming, local search, and mixed-integer programming. Optimization technology is ubiquitous in our society. It schedules planes and their crews, coordinates the production of steel, and organizes the transportation of iron ore from the mines to the ports. Optimization clears the day-ahead and real-time markets to deliver electricity to millions of people. It organizes kidney exchanges and cancer treatments and helps scientists understand the fundamental fabric of life, control complex chemical reactions, and design drugs that may benefit billions of individuals. This class is an introduction to discrete optimization and exposes students to some of the most fundamental concepts and algorithms in the field. It covers constraint programming, local search, and mixed-integer programming from their foundations to their applications for complex practical problems in areas such as scheduling, vehicle routing, supply-chain optimization, and resource allocation.

Who is this class for: Good programming skills, knowledge of fundamental algorithms, and linear algebra.

Created by: The University of Melbourne

Taught by: Professor Pascal Van Hentenryck
Taught by: Dr. Carleton Coffrin, Adjunct Lecturer
Computing and Information Systems

Level	Intermediate
Commitment	8 weeks of study, 10-15 hours per week
Language	English
How To Pass	Pass all graded assignments to complete the course.
User Ratings	4.9 stars Average User Rating 4.9See what learners said

Syllabus

WEEK 1

Welcome

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, ...

4 videos, 3 readings

Graded: Any Integer

WEEK 2

Knapsack

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 r...

9 videos

Graded: Knapsack

WEEK 3

Constraint Programming

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 s...

13 videos, 1 reading

Graded: Graph Coloring

WEEK 4

Local Search

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 decad...

10 videos

Graded: Traveling Salesman

WEEK 5

Linear Programming

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 technique...

6 videos

WEEK 6

Mixed Integer Programming

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-i...

6 videos

Graded: Facility Location

WEEK 7

Advanced Topics: Part I

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

2 videos

Graded: Vehicle Routing

WEEK 8

Advanced Topics: Part II

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 an...

2 videos

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Coursework

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Creators

The University of Melbourne

The University of Melbourne is an internationally recognised research intensive University with a strong tradition of excellence in teaching, research, and community engagement. Established in 1853, it is Australia's second oldest University.

Ratings and Reviews

Rated 4.9 out of 5 of 83 ratings

The course Materials and instructors are awesome.

This course is very good and essential in my point of view for researchers.

Just excellent. Exceptional teaching and well-formed, realistic assignments. Highly recommended.

Wonderful!

I learned a lot in this course and it's definitely well managed and well taught by an amazing professor.

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Discrete Optimization

Discrete Optimization

Discrete Optimization