Basic Modeling for Discrete Optimization

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Basic Modeling for Discrete Optimization

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About this course: Optimization is a common form of decision making, and is ubiquitous in our society. Its applications range from solving Sudoku puzzles to arranging seating in a wedding banquet. The same technology can schedule planes and their crews, coordinate the production of steel, and organize the transportation of iron ore from the mines to the ports. Good decisions in manpower and material resources management also allow corporations to improve profit by millions of dollars. Similar problems also underpin much of our daily lives and are part of determining daily delivery routes for packages, making school timetables, and delivering power to our homes. Despite their fundamental…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: Optimization is a common form of decision making, and is ubiquitous in our society. Its applications range from solving Sudoku puzzles to arranging seating in a wedding banquet. The same technology can schedule planes and their crews, coordinate the production of steel, and organize the transportation of iron ore from the mines to the ports. Good decisions in manpower and material resources management also allow corporations to improve profit by millions of dollars. Similar problems also underpin much of our daily lives and are part of determining daily delivery routes for packages, making school timetables, and delivering power to our homes. Despite their fundamental importance, all of these problems are a nightmare to solve using traditional undergraduate computer science methods. This course is intended for students interested in tackling all facets of optimization applications. You will learn an entirely new way to think about solving these challenging problems by stating the problem in a state-of-the-art high level modeling language, and letting library constraint solving software do the rest. This will allow you to unlock the power of industrial solving technologies, which have been perfected over decades by hundreds of PhD researchers. With access to this advanced technology, problems that are considered inconceivable to solve before will suddenly become easy. Watch the course promotional video here: https://www.youtube.com/watch?v=hc3cBvtrem0&t=8s

Who is this class for: The course is for penultimate/final year undergraduates and graduates in computing and related disciplines. You will need to have basic computer programming skills, and knowledge of fundamental algorithms, discrete mathematics, logic and linear algebra in order to take this course. Please note that this course is also available wholly in Chinese, see: https://www.coursera.org/learn/lisan-youhua-jianmo-jichupian

Created by:  The University of Melbourne, The Chinese University of Hong Kong
  • Taught by:  Prof. Peter James Stuckey, Professor

    Computing and Information Systems
  • Taught by:  Prof. Jimmy Ho Man Lee, Professor

    Department of Computer Science and Engineering
Level Intermediate Commitment 4 weeks of study, 6-12 hours/week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Coursework

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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. The Chinese University of Hong Kong Founded in 1963, The Chinese University of Hong Kong (CUHK) is a forward looking comprehensive research university with a global vision and a mission to combine tradition with modernity, and to bring together China and the West. CUHK teachers and students hail from all corners of the world. CUHK graduates are connected worldwide through an expansive alumni network.

Syllabus


WEEK 1


MiniZinc introduction



In this first module, you will learn the basics of MiniZinc, a high-level modeling language for discrete optimization problems. Combining the simplicity of MiniZinc with the power of open-source industrial solving technologies, you will learn how to solve applications such as knapsack problems, graph coloring, production planning and tricky Cryptarithm puzzles, with great ease.


20 videos, 6 readings expand


  1. Video: Welcome to Basic Modeling for Discrete Optimization
  2. Reading: Course Overview
  3. Reading: Start of Course Survey
  4. Video: 1.1.1 First Steps
  5. Video: 1.1.2 Second Model
  6. Video: 1.1.3 Third Model
  7. Video: 1.1.4 Models and Instances
  8. Video: 1.1.5 Modeling Objects
  9. Video: 1.1.6 Arrays and Comprehensions
  10. Video: 1.1.7 Global Constraints
  11. Video: 1.1.8 Module 1 Summary
  12. Reading: Getting MiniZinc
  13. Reading: Workshop 0: First Steps
  14. Video: Workshop 0 Solution
  15. Reading: Workshop 1: Temperature
  16. Video: Workshop 1 Solution
  17. Video: Assignment Submission - IDE
  18. Video: Assignment Submission - CLI
  19. Reading: About the Reference Material
  20. Video: Reference 1: Basic Features
  21. Video: Reference 2: Booleans Expressions
  22. Video: Reference 3: Sets, Arrays, Comprehensions
  23. Video: Reference 4: Enumerated Types
  24. Video: Reference 5: Strings and Output
  25. Video: Reference 6: Option Types
  26. Video: Reference 7: Command Line Interface

Graded: Cryptarithms for Seven Paces Verse

WEEK 2


Modeling with Sets



In this module, you will learn how to model problems involving set selection. In particular, you will see different ways of representing set variables when the variable has no constraints on its cardinality, has fixed cardinality and bounded cardinality. You also have to ensure all model decisions are valid decisions, and each valid decision corresponds to exactly one model decision.


6 videos, 1 reading expand


  1. Video: 1.2.1 Selecting a Set
  2. Video: 1.2.2 Choosing a Set Representation
  3. Video: 1.2.3 Choosing a Fixed Cardinality Set
  4. Video: 1.2.4 Sets with Bounded Cardinality
  5. Video: 1.2.5 Module 2 Summary
  6. Reading: Workshop 2: Surrender Negotiations
  7. Video: Workshop 2 Solution

Graded: Raid Planning

WEEK 3


Modeling with Functions



In this module, you will learn how to model pure assignment problems and partition problems, which are functions in disguise. These problems find applications in rostering and constrained clustering. In terms of modeling techniques, you will see the power of common subexpression elimination and intermediate variables, and encounter the global cardinality constraint for the first time. MiniZinc also provides constraints for removing value symmetries.


7 videos, 1 reading expand


  1. Video: 1.3.1 Modeling Functions
  2. Video: 1.3.2 Another Assignment Problem Example
  3. Video: 1.3.3 Modeling Partitions
  4. Video: 1.3.4 Global Cardinality Constraint
  5. Video: 1.3.5 Pure Partitioning
  6. Video: 1.3.6 Module 3 Summary
  7. Reading: Workshop 3: Feast Trap
  8. Video: Workshop 3 Solution

Graded: Dance Trap

WEEK 4


Multiple Modeling



In the final module of this course you will see how discrete optimization problems can often be seen from multiple viewpoints, and modeled completely differently from each viewpoint. Each viewpoint may have strengths and weaknesses, and indeed the different models can be combined to help each other.


6 videos, 2 readings expand


  1. Video: 1.4.1 Multiple Modeling
  2. Video: 1.4.2 Permutation
  3. Video: 1.4.3 Permutation Problem
  4. Video: 1.4.4 Multiple Models
  5. Video: 1.4.5 Module 4 Summary
  6. Reading: Workshop 4: Composition
  7. Video: Workshop 4 Solution
  8. Reading: End of Course Survey

Graded: Royal Hunt
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