About this Course

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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.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Intermediate Level

Approx. 65 hours to complete

English

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Skills you will gain

Constraint Programming
Branch And Bound
Discrete Optimization
Linear Programming (LP)

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Intermediate Level

Approx. 65 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructors

Instructor rating

4.79/5 (139 Ratings)

Professor Pascal Van Hentenryck

63,607 Learners

1 Course

Dr. Carleton Coffrin

Adjunct Lecturer

Computing and Information Systems

65,416 Learners

2 Courses

Syllabus - What you will learn from this course

Content Rating95%(4,304 ratings)

Week

1

Week 1

2 hours to complete

Welcome

2 hours to complete

4 videos (Total 43 min), 2 readings, 1 quiz

Week

2

Week 2

7 hours to complete

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 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.

7 hours to complete

9 videos (Total 101 min)

Week

3

Week 3

17 hours to complete

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 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.

17 hours to complete

13 videos (Total 248 min), 1 reading, 2 quizzes

13 videos

CP 1 - intuition, computational paradigm, map coloring, n-queens27m

CP 2 - propagation, arithmetic constraints, send+more=money26m

CP 3 - reification, element constraint, magic series, stable marriage16m

CP 4 - global constraint intuition, table constraint, sudoku19m

CP 5 - symmetry breaking, BIBD, scene allocation18m

CP 6 - redundant constraints, magic series, market split11m

CP 7 - car sequencing, dual modeling18m

CP 8 - global constraints in detail, knapsack, alldifferent33m

CP 9 - search, first-fail, euler knight, ESDD25m

CP 10 - value/variable labeling, domain splitting, symmetry breaking in search28m

Graph Coloring6m

Optimization Tools5m

Set Cover8m

1 reading

Optimization Tools10m

Week

4

Week 4

13 hours to complete

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 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.

13 hours to complete

10 videos (Total 191 min)

10 videos

LS 1 - intuition, n-queens13m

LS 2 - swap neighborhood, car sequencing, magic square15m

LS 3 - optimization, warehouse location, traveling salesman, 2-opt, k-opt23m

LS 4 - optimality vs feasibility, graph coloring22m

LS 5 - complex neighborhoods, sports scheduling21m

LS 6 - escaping local minima, connectivity15m

LS 7 - formalization, heuristics, meta-heuristics introduction22m

LS 8 - iterated location search, metropolis heuristic, simulated annealing, tabu search intuition18m

LS 9 - tabu search formalized, aspiration, car sequencing, n-queens26m

Traveling Salesman10m

Week

5

Week 5

2 hours to complete

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 techniques. These lectures review fundamental concepts in linear programming, including the infamous simplex algorithm, simplex tableau, and duality. .

2 hours to complete

6 videos (Total 130 min)

Week

6

Week 6

12 hours to complete

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-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.

12 hours to complete

6 videos (Total 136 min)

Week

7

Week 7

11 hours to complete

Advanced Topics: Part I

11 hours to complete

2 videos (Total 51 min)

Week

8

Week 8

1 hour to complete

Advanced Topics: Part II

1 hour to complete

2 videos (Total 32 min), 1 reading

Reviews

4.8

164 reviews

5 stars
89.04%
4 stars
8.25%
3 stars
0.99%
2 stars
0.14%
1 star
1.56%

TOP REVIEWS FROM DISCRETE OPTIMIZATION

by KDSep 3, 2018

i wish there was 6 start rating so i can give this prof his due, he made a very complicated subject look very simple and easy to understand thanks a million

by ASAug 25, 2022

it needs creativity:) assignments are specially hard! doing this course will increase your problem solving skill!

by MJun 2, 2020

This is, without a doubt, one of the most interesting courses I have ever taken. You will be challenged to create your own ideas and you will get to know what NP hard means in practice.

by HDOct 26, 2016

Too good course! One of the very best courses on Coursera!

Thank you so much. It is a wonder to follow your course.

View all reviews

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.
• What are the pre-requisites for the class?
Good programming skills, knowledge of algorithms and linear algebra.
• What programming language will be used in this class?
A minimal knowledge of python is necessary to integrate with the course infrastructure. Outside of that, students are free to use any language of their choice.
• How difficult is this class?
A motivated student spending the time on the programming assignment will succeed in this class.
• Where can I get one of those T-Shirts?
At the discrete optimization store: http://www.zazzle.com.au/discreteoptimization

More questions? Visit the Learner Help Center.

Discrete Optimization