A novel decentralized approach to large-scale multi-agent MILPs

We address the optimal operation of a large-scale multi-agent system where agents have to set their own continuous and/or discrete decision variables so as to jointly minimize the sum of local linear performance indices while satisfying local and global linear constraints. When the number of discrete decision variables is large, solving the resulting Mixed Integer Linear Program becomes computationally demanding, and often impossible in practice. Inspired by some recent methods in the literature, we propose a decentralized iterative scheme that recovers computational tractability by decomposing the dual of the MILP problem into lower-dimensional MILPs, one per agent, and obtains feasibility of the recovered primal solution by introducing a fictitious tightening of the global constraints. The tightening is updated in an adaptive fashion according to an heuristic strategy which allows it to both increase and decrease throughout the iterations, depending on the mismatch between the recovered mixed-integer primal solution and the solution to the relaxed linear problem associated with the current tightening. The procedure is shown to be effective and to outperform state-of-the-art alternative resolution schemes in a benchmark example on optimal charging of a fleet of electric vehicles.