A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

Andrea Testa; Alessandro Rucco; Giuseppe Notarstefano

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arXiv · 1712.01621

A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

Andrea Testa·Alessandro Rucco·Giuseppe Notarstefano

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Abstract

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 algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.

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BibTeX RIS

Andrea Testa, Alessandro Rucco, Giuseppe Notarstefano. 2017-12-05. A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming. https://arxiv.org/abs/1712.01621

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