Online Learning for Strong Branching Approximation in Branch-and-Bound

We present an online learning approach to variable branching in branch-and-bound for mixed-integer linear problems. Our approach consists in learning strong branching scores in an online fashion and in using them to take branching decisions. More specifically, numerical scores are used to rank the branching candidates. If, for a given variable, the learned approximation is … Read more

Machine Learning to Balance the Load in Parallel Branch-and-Bound

We describe in this paper a new approach to parallelize branch-and-bound on a certain number of processors. We propose to split the optimization of the original problem into the optimization of several subproblems that can be optimized separately with the goal that the amount of work that each processor carries out is balanced between the … Read more

An algorithm for the separation of two-row cuts

We consider the question of finding deep cuts from a model constructed with two rows of a simplex tableau. To do that, we show how to reduce the complexity of setting up the polar of such model from a quadratic number of integer hull computations to a linear number of integer hull computations. Furthermore we … Read more

Split Rank of Triangle and Quadrilateral Inequalities

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. (2007) and Cornuejols and Margot (2007) showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from … Read more