Lecture22

Lecture22 - Advanced Operations Research Techniques IE316...

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Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 22 Dr. Ted Ralphs IE316 Lecture 22 1 Reading for This Lecture Bertsimas Sections 10.2, 10.3, 11.1, 11.2 IE316 Lecture 22 2 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 min x F c T x . Consider a partition of F into subsets F 1 ,...F k . Then min x F c T x = min { 1 i k } { min x F i c T x } . In other words, we can optimize over each subset separately. Idea : If we cant solve the original problem directly, we might be able to solve the smaller subproblems recursively. Dividing the original problem into subproblems is called branching . Taken to the extreme, this scheme is equivalent to complete enumeration. IE316 Lecture 22 3 Branch and Bound Next, we discuss the role of bounding . For the rest of the lecture, assume all variables have finite upper and lower bounds....
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Lecture22 - Advanced Operations Research Techniques IE316...

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