Branch and Bound

Jan 31, 2013

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Example Problem. Travelling Salesman ProblemInput: connected, weighted digraphG = (V = {1,2,,n},E), w : E -> ROutput: Minimum weighted cycle that visits each vertex exactly once[i1,i2,in] such that ?1 = k = n ik ? V and (ik, ik 1) ? E and ?

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Branch and Bound

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Backtracking And Branch And Bound

Backtracking And Branch And Bound. Subset & Permutation Problems. Subset problem of size n . Nonsystematic search of the space for the answer takes O(p2 n ) time, where p is the time needed to evaluate each member of the solution space. Permutation problem of size n .

403 views • 16 slides

Branch & Bound

0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10. Branch & Bound. UPPER =  LOWER = 0. 0. 0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10. Branch & Bound. UPPER =  LOWER = 2. 0. 2. 0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10.

538 views • 10 slides

Branch and bound

Branch and bound. branch and bound methods economize the search for the best trees by backing out of dead alleys. The Traveling Salesman Problem. the technique can be used to solve the traveling salesman problem. The Traveling Salesman Problem. an arbitrary route. d=5.4342.

367 views • 12 slides

Branch and Bound Example

Branch and Bound Example. Initial lower bound. Use 1 machine preemptive schedule as lower bound Job 2 has a lateness of 5, this is a lower bound on Lmax. J1. J3. J4. J3. J2. 10. 5. 4. 17. 15. Initial upper bound. Find some schedule. Lmax is 7. J3. J4. J1. J2. 12. 6. 4. 17.

415 views • 14 slides

Branch and Bound

Branch and Bound. Similar to backtracking in generating a search tree and looking for one or more solutions Different in that the “objective” is constrained to maximization or minimization of a given function We will consider minimization problems in this section.

492 views • 7 slides