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

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