A decentralized approach to multi-agent MILPs: Finite-time feasibility and performance guarantees

We address the optimization of a large scale multi-agent system where each agent has discrete and/or continuous decision variables that need to be set so as to optimize the sum of linear local cost functions, in presence of linear local and global constraints. The problem reduces to a Mixed Integer Linear Program (MILP) that is here addressed according to a decentralized iterative scheme based on dual decomposition, where each agent determines its decision vector by solving a smaller MILP involving its local cost function and constraint given some dual variable, whereas a central unit enforces the global coupling constraint by updating the dual variable based on the tentative primal solutions of all agents. An appropriate tightening of the coupling constraint through iterations allows to obtain a solution that is feasible for the original MILP. The proposed approach is inspired by a recent paper to the MILP approximate solution via dual decomposition and constraint tightening, but shows finite-time convergence to a feasible solution and provides sharper performance guarantees by means of an adaptive tightening. The two approaches are compared on a plug-in electric vehicles optimal charging problem.