Hi,

I'm triyng to solve MILP with CPLEX where the objective is a sum of integer variables.

When looking at the logs, I noticed that the Best Bound is often a non-integer value, e.g., 14.63, I don't understand why CPLEX does not update this directly to integer value to obtain tighter bound? If the best bound is 14.63, then the actual best bound would be 15 (for a minimization problem), which is much better.

Any reason why this is not done? Any way to force this?

Thanks,

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Mikaël
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Hi Mikaël,
Is the variable/expression to minimize is explicitly declared as Integer before to be set as the objective ?
What Cplex interface are you using ? 

Yes - My objective is the sum of binary variables, I also tried using a single integer variable and I get the same behavior. I am using docplex to build and solve the model.

Say your problem is a minimization one.

The best bound is by definition the 'best' value of the relaxation of the open nodes, eg the one with the smallest LP_relaxation. Its is no surprise that it can be  fractional

On the other hand, you're right that CPLEX could/should take into account of the integrality of the objective function to derive a better best bound but if this is done, I guess this is done through a cutting plane approach or something similar

I know the best bound is from the relaxation, but adding a "rounding cut" should be trivial. If you have code to add a cut through callback using the Python API, then I'd like to try it, because it seems overly complicated for such a simple thing.