Distributed Mixed-Integer Linear Programming via Cut Generation and Constraint Exchange

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 algorithmic framework to solve this class of optimization problems in a peer-to-peer netw...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 65; no. 4; pp. 1456 - 1467
Main Authors: Testa, Andrea, Rucco, Alessandro, Notarstefano, Giuseppe
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Communication
Convergence
Cutting planes
Cyber-physical systems
Distributed algorithms
distributed optimization
Integer programming
Integers
Linear programming
Mixed integer linear programming
mixed-integer
multi-agent multi-task assignment
Multiagent systems
Operations research
Optimization
Peer to peer computing
Robustness (mathematics)
Social networks
Task analysis
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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 algorithmic framework to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. At each communication round, agents locally solve a small linear program, generate suitable cutting planes, and communicate a fixed number of active constraints. Within the distributed framework, we first propose an algorithm that, under the assumption of integer-valued optimal cost, guarantees finite-time convergence to an optimal solution. Second, we propose an algorithm for general problems that provides a suboptimal solution up to a given tolerance in a finite number of communication rounds. Both algorithms work under asynchronous, directed, unreliable networks. Finally, through numerical computations, we analyze the algorithm scalability in terms of the network size. Moreover, for a multi-agent multi-task assignment problem, we show, consistently with the theory, its robustness to packet loss.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2920812