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.
Discrete Optimization
The University of MelbourneAbout this Course
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Learner Career Outcomes
33%
started a new career after completing these courses
21%
got a tangible career benefit from this course
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: French, Portuguese (Brazilian), Russian, English, Spanish
Skills you will gain
Constraint ProgrammingBranch And BoundDiscrete OptimizationLinear Programming (LP)
Learner Career Outcomes
33%
started a new career after completing these courses
21%
got a tangible career benefit from this course
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: French, Portuguese (Brazilian), Russian, English, Spanish
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
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 Motivation - Indiana Jones, challenges, applications20m
Course Introduction - philosophy, design, grading rubric11m
Assignments Introduction & Any Integer9m
3 readings
Start of Course Survey10m
Socialize10m
Course Syllabus10m
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 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
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 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
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 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
Reviews
TOP REVIEWS FROM DISCRETE OPTIMIZATION
by SKMay 29, 2019
Exceptional coverage of optimization fundamentals. Learning of practical applied methods. Real university level course, no water down "data science". Absolutely love it! Thank you professor Pascal.
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 AMFeb 5, 2017
I like the instructor teaching approach and the evaluation system, the subject itself took me a lot of effort and i think the LNS technique should be teached just after local search.
by ADJun 5, 2019
Excellent course! The course video are very clear and build on each other as the course progress. It is well structured. The assignments have the right amount of difficulty.
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