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.
Discrete Optimization
proposé par
The University of Melbourne
À propos de ce cours
4.9
230 notes
Compétences que vous acquerrez
Constraint ProgrammingBranch And BoundDiscrete OptimizationLinear Programming (LP)
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Welcome
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 (Total 43 min), 3 lectures, 1 quiz
4 vidéos
Course Promo1 min
Course Motivation - Indiana Jones, challenges, applications20 min
Course Introduction - philosophy, design, grading rubric11 min
Assignments Introduction & Any Integer9 min
3 lectures
Start of Course Survey10 min
Socialize10 min
Course Syllabus10 min
Semaine
2Knapsack
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 (Total 101 min), 1 quiz
9 vidéos
Knapsack 2 - greedy algorithms7 min
Knapsack 3 - modeling8 min
Knapsack 4 - dynamic programming17 min
Knapsack 5 - relaxation, branch and bound14 min
Knapsack 6 - search strategies, depth first, best first, least discrepancy14 min
Assignments Getting Started13 min
Knapsack & External Solver10 min
Exploring the Material - open course design, optimization landscape, picking your adventure10 min
Semaine
3Constraint 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 (Total 248 min), 1 lecture, 2 quiz
13 vidéos
CP 2 - propagation, arithmetic constraints, send+more=money26 min
CP 3 - reification, element constraint, magic series, stable marriage16 min
CP 4 - global constraint intuition, table constraint, sudoku19 min
CP 5 - symmetry breaking, BIBD, scene allocation18 min
CP 6 - redundant constraints, magic series, market split11 min
CP 7 - car sequencing, dual modeling18 min
CP 8 - global constraints in detail, knapsack, alldifferent33 min
CP 9 - search, first-fail, euler knight, ESDD25 min
CP 10 - value/variable labeling, domain splitting, symmetry breaking in search28 min
Graph Coloring6 min
Optimization Tools5 min
Set Cover8 min
1 lecture
Optimization Tools10 min
Semaine
4Local 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 (Total 191 min), 1 quiz
10 vidéos
LS 2 - swap neighborhood, car sequencing, magic square15 min
LS 3 - optimization, warehouse location, traveling salesman, 2-opt, k-opt23 min
LS 4 - optimality vs feasibility, graph coloring22 min
LS 5 - complex neighborhoods, sports scheduling21 min
LS 6 - escaping local minima, connectivity15 min
LS 7 - formalization, heuristics, meta-heuristics introduction22 min
LS 8 - iterated location search, metropolis heuristic, simulated annealing, tabu search intuition18 min
LS 9 - tabu search formalized, aspiration, car sequencing, n-queens26 min
Traveling Salesman10 min
4.9
50 avis33%
a commencé une nouvelle carrière après avoir terminé ces cours
83%
a bénéficié d'un avantage concret dans sa carrière grâce à ce cours
Meilleurs avis
par AM•Feb 6th 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.
par KD•Sep 4th 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
Enseignants
Dr. Carleton Coffrin
Adjunct LecturerComputing and Information Systems
À propos de 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.
Foire Aux Questions
Quand aurai-je accès aux vidéos de cours et aux devoirs ?
Une fois que vous êtes inscrit(e) pour un Certificat, vous pouvez accéder à toutes les vidéos de cours, et à tous les quiz et exercices de programmation (le cas échéant). Vous pouvez soumettre des devoirs à examiner par vos pairs et en examiner vous-même uniquement après le début de votre session. Si vous préférez explorer le cours sans l'acheter, vous ne serez peut-être pas en mesure d'accéder à certains devoirs.
À quoi ai-je droit si j'achète le Certificat ?
Lorsque vous achetez un Certificat, vous bénéficiez d'un accès à tout le contenu du cours, y compris les devoirs notés. Lorsque vous avez terminé et réussi le cours, votre Certificat électronique est ajouté à votre page Accomplissements. À partir de cette page, vous pouvez imprimer votre Certificat ou l'ajouter à votre profil LinkedIn. Si vous souhaitez seulement lire et visualiser le contenu du cours, vous pouvez accéder gratuitement au cours en tant qu'auditeur libre.
Quelle est la politique de remboursement ?
Une aide financière est-elle possible ?
• 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
D'autres questions ? Visitez le Centre d'Aide pour les Etudiants.
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