Lecture5-2-1-2002

Lecture5-2-1-2002 - MAE 552 Heuristic Optimization Lecture...

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MAE 552 – Heuristic Optimization Lecture 5 February 1 , 2002
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Traditional Search Methods Exhaustive Search checks each and every solution in the search space until the solution has been found. Works well and is easy to code for small search problem. For large problems it is not practical Recall that for the 50 city TSP there are 10 62 possible tours If to evaluate each tour took, .00001 seconds it would take >10 45 years to evaluate them all !!!!!
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Exhaustive Search Methods Exhaustive Search requires only that all of the solutions be generated in some systematic way. The order the solutions are evaluated is irrelevant because all of them have to be looked at. The basic question is how can we generate all the solutions to a particular problem??
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Exhaustive Search Methods For the SAT problem the structure of the problem may allow some solutions to be pruned so they do not have to be searched. X 1 =T X 1 =F X 2 =T X 2 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 2 =T X 2 =F . . .
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Exhaustive Search Methods Pruning is possible if after examining the values of a few variables it is clear that the candidate is not optimal. X 1 =T X 1 =F X 2 =T X 2 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 2 =T X 2 =F If there was a clause in the SAT: ) ( 2 1 x x Means x 1 and x 2 must be present
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Exhaustive Search Methods • All the the branches with either x 1 and x 2 FALSE could be pruned without ever looking at x 3 leaving a much smaller S X 1 =T X 1 =F X 2 =T X 2 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 3 =T X 3 =F X 2 =T X 2 =F Each node is traversed in order in a Depth-First Search
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Enumerating the TSP For some problems, including the TSP you cannot simply generate all possible solutions as many will not be feasible. For example in many TSP problems all of the cities are not ‘fully
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Lecture5-2-1-2002 - MAE 552 Heuristic Optimization Lecture...

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