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

## TL;DR

This paper proposes a decentralized iterative scheme for large-scale multi-agent MILPs that guarantees finite-time feasibility and improved performance guarantees, demonstrated through electric vehicle charging examples.

## Contribution

It introduces a novel decentralized dual decomposition method with constraint tightening that ensures finite-time feasibility for multi-agent MILPs, enhancing existing approaches.

## Key findings

- Guarantees finite-time feasibility of solutions.
- Provides improved performance bounds over previous methods.
- Validated through numerical experiments on electric vehicle charging.

## Abstract

We address the optimal design 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 method to the MILP approximate solution via dual decomposition and constraint tightening, and presents the advantage of guaranteeing feasibility in finite-time and providing better performance guarantees. The two approaches are compared on a numerical example on plug-in electric vehicles optimal charging.