The available technology to solve Mixed Integer Linear Programs (MILPs) has experienced dramatic improvements in the past two decades. Pushing this algorithmic progress further is essential for solving even more complex optimization problems that arise in practice. This thesis examines various methods to enhance Branch-and-Bound (B&B) based MILP solvers, focusing on areas such as branching and Machine Learning (ML) assisted rules. Through our analysis of current methodologies and the introduction of novel techniques, this thesis contributes to the development of more efficient and adaptive MILP solvers...

Branch-and-bound for integer optimization typically uses single-variable disjunctions. Enumerative methods for integer optimization with theoretical guarantees use a non-binary search tree with general disjunctions based on lattice structure. These disjunctions are expensive to compute and challenging to implement. Here we compare two lattice reformulations that can be used to heuristically obtain general disjunctions in the original space, we develop a new lattice-based variant, and compare the derived disjunctions computationally with those produced by the algorithm of Lovász and Scarf.