Distributed Primal Decomposition for Large-Scale MILPs

This article deals with a distributed Mixed-Integer Linear Programming (MILP) setup 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 v...

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Published in:	IEEE transactions on automatic control Vol. 67; no. 1; pp. 413 - 420
Main Authors:	Camisa, Andrea, Notarnicola, Ivano, Notarstefano, Giuseppe
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.01.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Approximation algorithms Constraint-coupled optimization Cost function Coupling Couplings Decomposition Distributed algorithms distributed optimization Heuristic algorithms Integer programming Linear programming Mixed integer mixed-integer linear programming Resource management Task analysis
ISSN:	0018-9286, 1558-2523
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Abstract	This article deals with a distributed Mixed-Integer Linear Programming (MILP) setup 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 setup 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. Monte Carlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm.
AbstractList	This article deals with a distributed Mixed-Integer Linear Programming (MILP) setup 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 setup 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. Monte Carlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm.
Author	Notarstefano, Giuseppe Camisa, Andrea Notarnicola, Ivano
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SubjectTerms	Algorithms Approximation algorithms Constraint-coupled optimization Cost function Coupling Couplings Decomposition Distributed algorithms distributed optimization Heuristic algorithms Integer programming Linear programming Mixed integer mixed-integer linear programming Resource management Task analysis
Title	Distributed Primal Decomposition for Large-Scale MILPs
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