MILP Acceleration: A Survey from Perspectives of Simplex Initialization and Learning-Based Branch and Bound

Mixed integer linear programming (MILP) is an NP-hard problem, which can be solved by the branch and bound algorithm by dividing the original problem into several subproblems and forming a search tree. For each subproblem, linear programming (LP) relaxation can be solved to find the bound for making the following decisions. Recently, with the increasing dimension of MILPs in different applications, how to accelerate the solution process becomes a huge challenge. In this survey, we summarize techniques and trends to speed up MILP solving from two perspectives. First, we present different approaches in simplex initialization, which can help to accelerate the solution of LP relaxation for each subproblem. Second, we introduce the learning-based technologies in branch and bound algorithms to improve decision making in tree search. We also propose several potential directions and extensions to further enhance the efficiency of solving different MILP problems.