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 |
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, how they are graded, and how to succeed in this class.
4 videos, 3 readings
- Video: Course Motivation - Indiana Jones, challenges, applications
- Reading: Start of Course Survey
- Reading: Socialize
- Video: Course Introduction - philosophy, design, grading rubric
- Reading: Course Syllabus
- Video: Assignments Introduction & Any Integer
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 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.
9 videos
- Video: Knapsack 2 - greedy algorithms
- Video: Knapsack 3 - modeling
- Video: Knapsack 4 - dynamic programming
- Video: Knapsack 5 - relaxation, branch and bound
- Video: Knapsack 6 - search strategies, depth first, best first, least discrepancy
- Video: Assignments Getting Started
- Video: Knapsack & External Solver
- Video: Exploring the Material - open course design, optimization landscape, picking your adventure
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 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.
13 videos, 1 reading
- Video: CP 2 - propagation, arithmetic constraints, send+more=money
- Video: CP 3 - reification, element constraint, magic series, stable marriage
- Video: CP 4 - global constraint intuition, table constraint, sudoku
- Video: CP 5 - symmetry breaking, BIBD, scene allocation
- Video: CP 6 - redundant constraints, magic series, market split
- Video: CP 7 - car sequencing, dual modeling
- Video: CP 8 - global constraints in detail, knapsack, alldifferent
- Video: CP 9 - search, first-fail, euler knight, ESDD
- Video: CP 10 - value/variable labeling, domain splitting, symmetry breaking in search
- Video: Graph Coloring
- Video: Optimization Tools
- Reading: Optimization Tools
- Video: Set Cover
- Ungraded Programming: Set Cover
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 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.
10 videos
- Video: LS 2 - swap neighborhood, car sequencing, magic square
- Video: LS 3 - optimization, warehouse location, traveling salesman, 2-opt, k-opt
- Video: LS 4 - optimality vs feasibility, graph coloring
- Video: LS 5 - complex neighborhoods, sports scheduling
- Video: LS 6 - escaping local minima, connectivity
- Video: LS 7 - formalization, heuristics, meta-heuristics introduction
- Video: LS 8 - iterated location search, metropolis heuristic, simulated annealing, tabu search intuition
- Video: LS 9 - tabu search formalized, aspiration, car sequencing, n-queens
- Video: Traveling Salesman
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 techniques. These lectures review fundamental concepts in linear programming, including the infamous simplex algorithm, simplex tableau, and duality. .
6 videos
- Video: LP 2 - algebraic view, naive algorithm
- Video: LP 3 - the simplex algorithm
- Video: LP 4 - matrix notation, the tableau
- Video: LP 5 - duality derivation
- Video: LP 6 - duality interpretation and uses
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-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.
6 videos
- Video: MIP 2 - modeling, big-M, warehouse location, graph coloring
- Video: MIP 3 - cutting planes, Gomory cuts
- Video: MIP 4 - convex hull, polyhedral cuts, warehouse location, node packing, graph coloring
- Video: MIP 5 - cover cuts, branch and cut, seven bridges, traveling salesman
- Video: Facility Location
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
- Video: Vehicle Routing
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 and pricing problem, using more complex variables.
2 videos
- Video: Column Generation - branch and price, cutting stock
FAQs
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The University of Melbourne
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Ratings and Reviews
Good course. The instructor is really a fast talker and it may be hard to grasp everything at the first time you watch the videos. About the assignments: The assignments are really hard. Yes! Really really hard. I've never taken any MOOC course where the assignments are so hard. Al in all, I can say that this course really thought me something about discrete optimization, and I would love to learn even more about this interesting field.
Great instructor, course is taught with passion pouring from the screen. It inspires me a lot!
I love this course!
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Great course, very challenging as problems are NP-hard and hence force you to find the right approaches for various problem set sizes. After a while, you get hooked and tried to find better and better solutions, reviewing videos for overlooked information, looking at research papers and available resources on the net. Programming times are only a minimum and I spent much more time than indicated.