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.

中文翻译：

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通过切割生成和约束交换的分布式混合整数线性规划

许多对信息物理网络系统感兴趣的问题可以表述为混合整数线性程序，其中约束分布在代理之间。在本文中，我们提出了一种分布式算法框架，以在没有协调器且计算和通信能力有限的对等网络中解决此类优化问题。在每一轮交流中，代理在本地解决一个小的线性程序，生成合适的切割平面，并交流固定数量的活动约束。在分布式框架内，我们首先提出一种算法，在整数值最优成本的假设下，保证有限时间收敛到最优解。第二，我们为一般问题提出了一种算法，该算法在有限数量的通信轮次中提供了达到给定容差的次优解决方案。这两种算法都在异步、有向、不可靠的网络下工作。最后，通过数值计算，我们从网络规模的角度分析了算法的可扩展性。此外，对于多智能体多任务分配问题，我们与理论一致地展示了它对丢包的鲁棒性。