Distributed Primal Decomposition for Large-Scale MILPs

TL;DR

This paper introduces a distributed primal decomposition algorithm for large-scale, NP-hard mixed-integer linear programs with coupling constraints, providing feasible solutions with guaranteed suboptimality bounds.

Contribution

It presents a novel fully distributed algorithm that handles integer decision variables and coupling constraints, with proven feasibility and suboptimality guarantees.

Findings

Algorithm guarantees feasible solutions in finite time.

Achieves extremely low suboptimality bounds in simulations.

Applicable to large-scale, nonconvex MILPs in control applications.

Abstract

This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints and a linear coupling constraint involving all the decision variables. A key, challenging feature of the considered set-up is that some components of the decision variables must assume integer values. The addressed MILPs are NP-hard, nonconvex and large-scale. Moreover, several additional challenges arise in a distributed framework due to the coupling constraint, so that feasible solutions with guaranteed suboptimality bounds are of interest. We propose a fully distributed algorithm based on a primal decomposition approach and an appropriate tightening of the coupling constraint. The algorithm is guaranteed to provide feasible solutions in finite time. Moreover, asymptotic and finite-time suboptimality bounds are established for the computed solution. Montecarlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm.