Complexity of branch-and-bound and cutting planes in mixed-integer optimization – II [article]

Amitabh Basu, Michele Conforti, Marco Di Summa, Hongyi Jiang
2021 arXiv   pre-print
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut framework can be orders of magnitude more efficient than employing these tools on their own. In particular, we give general conditions under which a cutting plane strategy and a branching scheme give a provably exponential advantage in efficiency when combined
more » ... into branch-and-cut. The efficiency of these algorithms is evaluated using two concrete measures: number of iterations and sparsity of constraints used in the intermediate linear/convex programs. To the best of our knowledge, our results are the first mathematically rigorous demonstration of the superiority of branch-and-cut over pure cutting planes and pure branch-and-bound.
arXiv:2011.05474v4 fatcat:eq6yh256anbszfro2mxs6sjlse