Hyper-Graph Partitioning for a Multi-Agent Reformulation of Large-Scale MILPs

Abstract

This letter addresses the challenge of solving large-scale Mixed Integer Linear Programs (MILPs). A resolution scheme is proposed for the class of MILPs with a hidden constraint-coupled multi-agent structure. In particular, we focus on the problem of disclosing such a structure to then apply a computationally efficient decentralized optimization algorithm recently proposed in the literature. The multi-agent reformulation problem consists in manipulating the matrix defining the linear constraints of the MILP so as to put it in a singly-bordered block-angular form, where the blocks define local constraints and decision variables of the agents, whereas the border defines the coupling constraints. We translate the matrix reformulation problem into a hyper-graph partitioning problem and introduce a novel algorithm which accounts for the specific requirements on the singly-bordered block-angular form to best take advantage of the decentralized optimization approach. Numerical results show the effectiveness of the proposed hyper-graph partitioning algorithm.