A Parallel Macro Partitioning Framework for Solving Mixed Integer Programs

Abstract

Mixed Integer Programs are a class of optimization problems which have a vast range of applications in engineering, business, science, health care, and other areas. For many applications, however, problems of realistic size can take a an impractical amount of time to solve on a single workstation. However, using parallel computing resources to solve MIP is difficult, as parallelizing the standard branch-and-bound framework presents an array of challenges. In this paper we present a novel framework called a Parallel Macro Partitioning (PMaP) framework for solving mixed integer programs in parallel. The framework exploit ideas from modern MIP heuristics to partition the problem at a high-level into MIP subproblems, each of which can be solved on a separate processor by an MIP algorithm. Initial computational resources suggest that PMaP has significant promise as a framework capable of bringing many processors to bear effectively on difficult problems.