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I have this MIP optimization problem, with couple of binary variables; however when I relax one of the binary variables the optimal solution of the objective does not change. But the solving time increase drastically. How could this happen? I noticed that this only happens for just when only I relax that specific variable, not for the rest. Does it like this that when you relax a variable the solution space does not change? is the some MIP optimization logic or property behind this?

Thank you for your help.

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