Distributed Primal Decomposition for Large-Scale MILPs
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.
Cite
@article{arxiv.2010.14446,
title = {Distributed Primal Decomposition for Large-Scale MILPs},
author = {Andrea Camisa and Ivano Notarnicola and Giuseppe Notarstefano},
journal= {arXiv preprint arXiv:2010.14446},
year = {2021}
}