A Privacy-Aware Distributed Approach for Loosely Coupled Mixed Integer Linear Programming Problems

TL;DR

This paper introduces two exact distributed algorithms for solving mixed integer linear programming problems with multiple agents, ensuring data privacy and addressing non-convexity challenges.

Contribution

The paper presents novel distributed algorithms that incorporate primal cuts and Lagrangian relaxation to solve MILPs exactly in a privacy-preserving manner.

Findings

Algorithms converge finitely for binary and continuous variables.

Effective on unit commitment problem, with advantages over centralized methods.

Highlights trade-offs and limitations of the proposed distributed approach.

Abstract

In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex nature of MILPs, classical distributed and decentralized optimization approaches cannot be applied directly to find their optimal solutions. The proposed exact algorithms are based on adding primal cuts and restricting the Lagrangian relaxation of the original MILP problem. We show finite convergence of these algorithms for MILPs with only binary and continuous variables. We test the proposed algorithms on the unit commitment problem and discuss its pros and cons comparing to the central MILP approach.