A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

TL;DR

This paper introduces a distributed cutting plane algorithm for solving mixed integer linear programs in peer-to-peer networks, ensuring finite convergence to the optimal solution with limited communication.

Contribution

It presents a novel distributed algorithm that uses local LP solves and cutting planes, guaranteeing finite convergence without a central coordinator.

Findings

Algorithm converges in finite steps for integer costs.

Performance analyzed as a function of network size.

Effective in distributed cyber-physical systems.

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 algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.