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.
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Solving Algorithms for Discrete Optimization
Instructors: Prof. Jimmy Ho Man Lee
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There are 4 modules in this course
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.
What's included
8 videos4 readings1 programming assignment
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.
What's included
7 videos1 reading1 programming assignment
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.
What's included
6 videos1 reading1 programming assignment
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.
What's included
10 videos2 readings1 programming assignment
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