  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.
