Lecture26-4-01-2002

# Lecture26-4-01-2002 - MAE 552 Heuristic Optimization...

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MAE 552 – Heuristic Optimization Lecture 26 April 1, 2002 Topic:Branch and Bound

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Branch and Bound We have seen this semester that the size of real-world problems grows very large as the number of design variables increases. Recall that there are (n-1)!/2 different solutions for the Travelling Salesman Problem (TSP). Exhaustive search is impractical when n>20 It would be helpful of we could reduce the size of the search space where we know the optimum solution will not exist.
Branch and Bound Branch and Bound works on the idea of successively partitioning the design space. 1st we need some means on determining a lower bound on the cost of any particular solution. A lower bound on a solution means the solution will cost at least the value of this lower bound. If we are maximizing the we need to find an upper bound on a solution - a value which this solution cannot exceed

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Branch and Bound For minimization If we have a solution 1 with a cost c AND we know that another solution 2 has lower bound that is greater than c THEN we do not need to evaluate 2 because we know that 2 will exceed 1.
Branch and Bound For maximization If we have a solution 1 with a cost c AND we know that another solution 2 has upper bound that is less than c THEN we do not need to evaluate 2 because we know that 2 will never exceed 1.

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We can determine an lower or upper bound by partially evaluating a particular solution. Example using TSP: Say we evaluate a partial tour of a TSP with 15 cities and after 8 cities it already exceeds our best solution so far. 1
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## This note was uploaded on 07/09/2011 for the course MAE 522 taught by Professor Hacker during the Spring '10 term at SUNY Buffalo.

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Lecture26-4-01-2002 - MAE 552 Heuristic Optimization...

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