Discrete Optimization

The University of Melbourne

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.

Learner Career Outcomes

40%

started a new career after completing these courses

40%

got a tangible career benefit from this course

17%

got a pay increase or promotion

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 65 hours to complete

English

Subtitles: English

Skills you will gain

Constraint ProgrammingBranch And BoundDiscrete OptimizationLinear Programming (LP)

Learner Career Outcomes

40%

started a new career after completing these courses

40%

got a tangible career benefit from this course

17%

got a pay increase or promotion

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 65 hours to complete

English

Subtitles: English

Instructors

Instructor rating

4.88/5 (46 Ratings)

Professor Pascal Van Hentenryck

43,070 Learners

1 Course

Dr. Carleton Coffrin

Adjunct Lecturer

Computing and Information Systems

44,917 Learners

2 Courses

Offered by

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.

Syllabus - What you will learn from this course

Content Rating95%(3,247 ratings)

Week

Week 1

2 hours to complete

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, how they are graded, and how to succeed in this class.

2 hours to complete

4 videos (Total 43 min), 3 readings, 1 quiz

4 videos

Course Promo1m

Course Motivation - Indiana Jones, challenges, applications20m

Course Introduction - philosophy, design, grading rubric11m

Assignments Introduction & Any Integer9m

3 readings

Start of Course Survey10m

Socialize10m

Course Syllabus10m

Week

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)

9 videos

Knapsack 1 - intuition2m

Knapsack 2 - greedy algorithms7m

Knapsack 3 - modeling8m

Knapsack 4 - dynamic programming17m

Knapsack 5 - relaxation, branch and bound14m

Knapsack 6 - search strategies, depth first, best first, least discrepancy14m

Assignments Getting Started13m

Knapsack & External Solver10m

Exploring the Material - open course design, optimization landscape, picking your adventure10m

Week

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

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

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)

6 videos

LP 1 - intuition, convexity, geometric view23m

LP 2 - algebraic view, naive algorithm13m

LP 3 - the simplex algorithm32m

LP 4 - matrix notation, the tableau20m

LP 5 - duality derivation22m

LP 6 - duality interpretation and uses17m

Week

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)

6 videos

MIP 1 - intuition, relaxation, branch and bound, knapsack, warehouse location26m

MIP 2 - modeling, big-M, warehouse location, graph coloring28m

MIP 3 - cutting planes, Gomory cuts20m

MIP 4 - convex hull, polyhedral cuts, warehouse location, node packing, graph coloring19m

MIP 5 - cover cuts, branch and cut, seven bridges, traveling salesman31m

Facility Location9m

Week

Week 7

11 hours to complete

Advanced Topics: Part I

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

11 hours to complete

2 videos (Total 51 min)

2 videos

Scheduling - jobshop, disjunctive global constraint37m

Vehicle Routing14m

Week

Week 8

1 hour to complete

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 and pricing problem, using more complex variables.

1 hour to complete

2 videos (Total 32 min), 1 reading

2 videos

Large Neighborhood Search - asymmetric TSP with time windows8m

Column Generation - branch and price, cutting stock23m

1 reading

End of course survey10m

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.
What is the refund policy?
You will be eligible for a full refund until two weeks after your payment date, or (for courses that have just launched) until two weeks after the first session of the course begins, whichever is later. You cannot receive a refund once you’ve earned a Course Certificate, even if you complete the course within the two-week refund period. See our full refund policy.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You’ll be prompted to complete an application and will be notified if you are approved. Learn more.
• 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
Will I earn university credit for completing the Course?
This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.

More questions? Visit the Learner Help Center.

Discrete Optimization