Solving Algorithms for Discrete Optimization from Coursera

Discrete Optimization aims to make good decisions when we have many possibilities to choose from. Its applications are ubiquitous throughout 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 on the use of scarce or expensive resources such as staffing and material resources also allow corporations to improve their 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, these problems are a nightmare to solve using traditional undergraduate computer science methods.

This course is intended for students who have completed Advanced Modelling for Discrete Optimization. In this course, you will extend your understanding of how to solve challenging discrete optimization problems by learning more about the solving technologies that are used to solve them, and how a high-level model (written in MiniZinc) is transformed into a form that is executable by these underlying solvers. By better understanding the actual solving technology, you will both improve your modeling capabilities, and be able to choose the most appropriate solving technology to use.

Watch the course promotional video here: https://www.youtube.com/watch?v=-EiRsK-Rm08

What's inside

Syllabus

Basic Constraint Programming

This module starts by using an example to illustrate the basic machinery of Constraint Programming solvers, namely constraint propagation and search. While domains represent possibilities for variables, constraints are actively used to reason about domains and can be encoded as domain propagators and bounds propagators. You will learn how a propagation engine handles a set of propagators and coordinates the propagation of constraint information via variable domains. You will also learn basic search, variable and value choices, and how propagation and search can be combined in a seamless and efficient manner. Last but not least, this module describes how to program search in MiniZinc.

Advanced Constraint Programming

In this module, you will see how Branch and Bound search can solve optimization problems and how search strategies become even more important in such situations. You will be exposed to advanced search strategies, including restart search and impact-based search. The module also uncovers the inner workings of such global constraints as alldifferent and cumulative.

Mixed Integer Programming

This module starts by introducing linear programming and the Simplex algorithm for solving continuous linear optimization problems, before showing how the method can be incorporated into Branch and Bound search for solving Mixed Integer Programs. Learn Gomory Cuts and the Branch and Cut method to see how they can speed up solving.

Local Search

This module takes you into the exciting realm of local search methods, which allow for efficient exploration of some otherwise large and complex search space. You will learn the notion of states, moves and neighbourhoods, and how they are utilized in basic greedy search and steepest descent search in constrained search space. Learn various methods of escaping from and avoiding local minima, including restarts, simulated annealing, tabu lists and discrete Lagrange Multipliers. Last but not least, you will see how Large Neighbourhood Search treats finding the best neighbour in a large neighbourhood as a discrete optimization problem, which allows us to explore farther and search more efficiently.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Fits well for learners who want to solve challenging discrete optimization problems

Taught by experienced instructors, Prof. Peter James Stuckey and Prof. Jimmy Ho Man Lee

Develops capabilities in modeling, helping learners improve their problem-solving skills

Covers advanced topics like Branch and Bound search, Local Search, and Mixed Integer Programming

Provides a strong foundation in Discrete Optimization, making it suitable for learners who want to pursue further studies or careers in the field

Learners are expected to have completed 'Advanced Modelling for Discrete Optimization' before taking this course

Reviews summary

Solving algorithms for discrete optimization

Learners say that Solving Algorithms for Discrete Optimization is challenging and often requires more time to complete than the first two courses in the series, despite this, many found the course rewarding and worthwhile. One learner recommended reviewing the subtitles on all three discrete optimization problems, because there are many errors that need to be corrected. Some assignments have unclear instructions, so it may also be helpful to consult the forums. This course is part of a three-course series, and it covers topics such as simulated annealing, tabu search, large neighborhood search, and constrained optimizers.

Part of a Series

"This course is part of a three-course series"

Worthwhile Experience

"I'm not sure that it was enjoyable, but I'm glad I did it, completed it, and finished it having achieved higher marks than I did on the first two courses."

Simulated Annealing, Constrained Optimizers

"We also learned about local search algorithms like simulated annealing, tabu search and (particularly cool) large neighbourhood search."

"We learned about how to use MiniZinc's annotations to improve search performance."

Subtitles Need Review

"Someone should review the subtitles on all 3 discrete optimization problems, there is an abundance of errors that need to be corrected."

Challenging Course

"This was harder work than the first two courses in the series."

Consult Forums

"I needed to consult the forums for the Parade assignment as the instructions PDF was quite unclear."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Solving Algorithms for Discrete Optimization with these activities:

Review Discrete Optimization Basics

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Recall the basic concepts and terminologies of Discrete Optimization to reinforce your understanding.

Browse courses on Discrete Optimization

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Reread lecture notes and textbooks from previous courses
Revisit online resources and tutorials
Attempt practice problems and exercises

Organize Course Materials

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Compile resources, notes, and study materials from different sources and organize them systematically for easy access and review.

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Gather lecture notes, slides, and assignments
Review and organize materials by topic
Create a digital or physical study hub
Annotate and highlight key concepts

Explore Constraint Programming Resources

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Enhance your understanding of Constraint Programming (CP) by following online tutorials and resources to strengthen your practical skills.

Browse courses on Constraint Programming

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Identify reputable CP learning platforms and tutorials
Follow step-by-step guides and examples
Experiment with different CP tools and libraries
Apply CP concepts to solve sample problems
Consult online forums and documentation for additional support

Four other activities

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Solve Discrete Optimization Problems

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Sharpen your problem-solving abilities by practicing a variety of Discrete Optimization problems, covering different techniques and domains.

Browse courses on Discrete Optimization

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Access online platforms with problem sets and challenges
Attempt to solve problems independently
Analyze solution strategies and identify optimization techniques
Compare your solutions with others and seek feedback

Develop a Discrete Optimization Model

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Demonstrate your modeling proficiency by designing and implementing a Discrete Optimization model using MiniZinc to solve a real-world problem.

Browse courses on Discrete Optimization

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Identify a suitable problem domain
Formulate the problem as a Discrete Optimization model
Implement the model in MiniZinc
Validate and test the model
Analyze and interpret the results

Attend Industry Conferences and Meetups

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Expand your network and stay up-to-date by engaging with industry professionals at conferences and meetups dedicated to Discrete Optimization and related fields.

Browse courses on Discrete Optimization

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Identify relevant conferences and meetups
Attend sessions and presentations
Network with experts and practitioners
Explore potential collaborations

Contribute to Open-Source Discrete Optimization Projects

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Enhance your practical skills and gain valuable experience by contributing to real-world Discrete Optimization projects on platforms like Github.

Browse courses on Discrete Optimization

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Identify open-source projects in need of assistance
Review codebases and documentation
Identify areas for improvement or contribution
Submit pull requests with bug fixes or enhancements
Engage with project maintainers and community

Career center

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