A Distributed Iterative Algorithm for Multi-Agent MILPs: Finite-Time Feasibility and Performance Characterization

We deal with decision making in a large-scale multi-agent system, where each agent aims at minimizing a local cost function subject to local constraints, and the local decision variables of all agents are coupled through a global constraint. We consider a cooperative framework where the multi-agent decision problem is formulated as a constrained optimization program with the sum of the local costs as global cost to be minimized with respect to the local decision variables of all agents, subject to both local and global constraints. We focus on a non-convex linear set-up where all costs and constraints are linear but local decision variables are discrete or include a discrete component, and propose a distributed iterative scheme based on dual decomposition and consensus to solve the resulting mixed integer linear program. Our approach extends recent results in the literature to a distributed set-up with a time-varying communication network and allows to: reduce the computational and communication effort, achieve resilience to communication failures, and also preserve privacy of local information. The approach is demonstrated on a numerical example of optimal charging of plug-in electric vehicles.