Originally posted by: Heungjo

Here, I will assume that the problem is the min problem.

It seems that CPLEX B&B routine generates monotonic increasing "Best Node" values in min problem.

The "Best Node" is defined as the following.
: the "best node" is the open node with minimal objective function value for the LP relaxation at the node.
(https://www.ibm.com/developerworks/forums/thread.jspa?messageID=14425005&#14425005)

However, I think that it would be possible that the "Best Node" value could fluctuate (i.e., increase, but sometimes decrease), because "Best Node" is based only on the open nodes.
So, I am wondering how CPLEX generates monotonic increasing "Best Node" values in min problem.

Please anybody help me.

Thank you.
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Originally posted by: SystemAdmin

I think you are missing an important fact here: For a minimization problem, if you have a node N and create a child node C by way of branching then the optimal objective function value for the LP relaxation of C will never be smaller than the optimal objective function value of the LP relaxation of N (this is because C has more constraints than N).
Consequently, the LP relaxation of a newly created node can never have an optimal objective function value that is smaller than the minimum of all open nodes.
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Originally posted by: Heungjo

I was foolish.
My B&B code may have some problem.

Thank you so much for quick and clear reply.
I really appreciate that.
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