I have a MIP problem A with a set of variables Va and a problem B with a set of variables Vb = Va + Vb’. The objective of the root relaxation is the same for both problems before postprocessing. However, after the postprocessing on the root node which generates cutting planes and tries various heuristic to reduce the problem size, the objective of the root relaxation is better for the problem A (gap of 10% for A and 20% for B).
In theory, is it possible ? Is the generation of cutting planes a heuristic ?
In the practice case it happens, the size of the problems are the following: |Va| = 90’000, |Vb’| = 10’000 and so |Vb| = 100’000.
Thank you for your reply!
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