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RINS: Relaxation induced neighborhood search, firstly introduced by Danna et.al in 2004 in "Exploring relaxation induced neighborhoods to improve MIP solutions"

I wanted to design an example how the RINS algorithm works to make sure that I have it completly understood completly.

As it turns out, I do not know what happens if I am currently at a node where RINS should be applied and there are no values in the incumbent and the relaxation solution that equal to each other? How do I decide on which node to branch then?

Or can someone forward me to a very insightful example? I mean the overall procedure is clear, I am just not sure about the details. Thanks!

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