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# Advanced Modeling for Discrete Optimization

### Overview

##### Class Central Tips
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 who have completed Basic Modelling for Discrete Optimization. In this course you will learn much more about solving challenging discrete optimization 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 course will focus on debugging and improving models, encapsulating parts of models in predicates, and tackling advanced scheduling and packing problems. As you master this advanced technology, you will be able to tackle problems that were inconceivable to solve previously.

Watch the course promotional video here: https://www.youtube.com/watch?v=hc3cBvtrem0&t=8s

### Syllabus

• Debugging and Improving Models
• Similar to computer programs, models can have bugs. In this module, you will see the symptoms (unsatisfiability, too many solutions, too few solutions) of different bugs, and learn methods to discover what is going wrong with your model and how to fix it. Equipped with these tools, you will be able to develop and debug complex models.
• Predicates
• In this module, you will learn how to encapsulate a complex constraint definition in a predicate definition to enable its reuse. This will enable the construction of far more complex models with improved readability in a modular manner. You will also encounter for the first time a problem with multiple objectives and learn how to compress them into one single objective. In addition to this, you will learn how to model the banquet seating problem, which will assist you in many occasions in life.
• Scheduling
• Learn how to tackle complex project scheduling problems of various forms, progressively from ones with only basic precedence requirements to ones with unary resources and even cumulative resources. You will see how to model some of the complex constraints that arise in these applications.
• Packing
• In this module, you will learn the important application of packing, from the packing of squares to rectilinear shapes with and without rotation. Again, you will see how to model some of the complex constraints that arise in these applications.
• Symmetry and Dominance
• This final module looks at the various forms of symmetries that can appear in discrete optimization problems. You will learn various methods and special constraints to break such symmetries so as to increase solving efficiency. You will also learn the notion of dominance, which is a generalization of symmetries, and also dominance breaking techniques.

### Taught by

Jimmy Ho Man Lee and Prof. Peter James Stuckey