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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Veröffentlicht in:IEEE transactions on automatic control Jg. 67; H. 1; S. 413 - 420
Hauptverfasser: Camisa, Andrea, Notarnicola, Ivano, Notarstefano, Giuseppe
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3057061