Faster MIP solutions via new node selection rules

When a branch and bound method is used to solve a linear mixed integer program (MIP), the order in which the nodes of the branch and bound tree are explored significantly affects how quickly the MIP is solved. In this paper, new methods are presented that exploit correlation and distribution characteristics of branch and bound trees to trigger backtracking and to choose the next node to solve when backtracking. A new method is also presented that determines when the cost of using a node selection method outweighs its benefit, in which case it is abandoned in favor of a simpler method. Empirical experiments show that these proposed methods outperform the current state of the art.