Distributed Mixed-Integer Linear Programming via Cut Generation and Constraint Exchange

TL;DR

This paper introduces distributed algorithms for solving mixed-integer linear programs in peer-to-peer networks, enabling finite-time convergence to optimal or near-optimal solutions despite unreliable communication.

Contribution

It proposes novel distributed algorithms that work asynchronously and reliably in unreliable networks, with guarantees of finite-time convergence for both optimal and approximate solutions.

Findings

Algorithms converge in finite time under certain conditions.

Robustness to packet loss demonstrated in multi-task assignment.

Scalability analyzed through numerical simulations.

Abstract

Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. At each communication round, agents locally solve a small linear program, generate suitable cutting planes and communicate a fixed number of active constraints. Within the distributed framework, we first propose an algorithm that, under the assumption of integer-valued optimal cost, guarantees finite-time convergence to an optimal solution. Second, we propose an algorithm for general problems that provides a suboptimal solution up to a given tolerance in a finite number of communication rounds. Both algorithms work under asynchronous, directed, unreliable networks. Finally, through numerical computations, we analyze the algorithm scalability in terms of the network size. Moreover, for a multi-agent multi-task assignment problem, we show, consistently with the theory, its robustness to packet loss.