Lecture10 - Integer Programming IE418 Lecture 10 Dr Ted...

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Integer Programming IE418 Lecture 10 Dr. Ted Ralphs
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IE418 Lecture 10 1 Reading for This Lecture Wolsey Chapter 7 Nemhauser and Wolsey Sections II.3.1, II.3.6, II.4.1, II.4.2, II.5.4
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IE418 Lecture 10 2 Computational Integer Programming We now shift our focuse to how difficult classes of integer programs are solved in practice. Computationally, the most important aspect of solving integer programs is obtaining good bounds on the value of the optimal solution. In this lecture, we will motivate this fact by introducing the branch and bound algorithm. We will then look at various methods of obtaining bounds. Later, we will examine branch and bound in more detail.
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IE418 Lecture 10 3 Branch and Bound Branch and bound is the most commonly-used algorithm for solving MILPs. It is a divide and conquer approach. Suppose F is the feasible region for some MILP and we wish to solve max x F c x . Consider a partition of F into subsets F 1 , . . . F k . Then max x F c x = max { 1 i k } { max x F i c x } . In other words, we can optimize over each subset separately. Idea : If we can’t solve the original problem directly, we might be able to solve the smaller subproblems recursively.
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