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I am trying to implement branch and bound technique for covering points with axis parallel lines. for each sub problem I am considering my LP solution as the LB and iterative rounding solution as the UB. At first I am considering a fractional valued variable (after applying LP) and for 0 and 1 value I am considering SP1 and SP2 as my sub-problems. for each SP1 I have UB1 and LB1 and for each SP2 I have UB2 and LB2 as mentioned earlier. Then I am checking

i) if (LB1=UB1 or LB2=UB2) then stop

ii) if (UB1 >= LB2) then solving SP2

iii) if (UB2 >= LB1) then solving SP1

I am not sure that, I am considering the right approach. Because in most of the nodes both cases ii) and iii) are happening(though at a time just one 'if' is executing). Am I using the right approach?? any help will be appreciated.

Thanks.

Cherry
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1 Answers1

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I am not familiar with your "iterative rounding" procedure, but I will assume it is correct.

If you compare upper and lower bound you will probably have conditions ii) and iii) satisfied, specially in the beginning of the solution procedure, since your solution GAP might be big. A more common approach is to solve the sub-problem with the most promising lower bound from all available sup-problems.

Does the answer you are getting seems reasonable?

pbc1303
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  • thanks :). I am still working on it. will let you know when I am done – Cherry May 09 '15 at 20:38
  • Ok! (= Keep in mind that there are several branching rules possible. The one I told you is just one I know is frequently used. – pbc1303 May 09 '15 at 20:51