MILP, pseudo-boolean, and OMT solvers for optimal fault-tolerant placements of relay nodes in mission critical wireless networks

In critical infrastructures like airports, much care has to be devoted in protecting radio communication networks from external electromagnetic interference. Protection of such mission-critical radio communication networks is usually tackled by exploiting radiogoniometers: at least three suitably deployed radiogoniometers, and a gateway gathering information from them, permit to monitor and localise sources of electromagnetic emissions that are not supposed to be present in the monitored area. Typically, radiogoniometers are connected to the gateway through relay nodes. As a result, some degree of fault-tolerance for the network of relay nodes is essential in order to offer a reliable monitoring. On the other hand, deployment of relay nodes is typically quite expensive. As a result, we have two conflicting requirements: minimise costs while guaranteeing a given fault-tolerance. In this paper, we address the problem of computing a deployment for relay nodes that minimises the relay node network cost while at the same time guaranteeing proper working of the network even when some of the relay nodes (up to a given maximum number) become faulty (fault-tolerance). We show that, by means of a computation-intensive pre-processing on a HPC infrastructure, the above optimisation problem can be encoded as a 0/1 Linear Program, becoming suitable to be approached with standard Artificial Intelligence reasoners like MILP, PB-SAT, and SMT/OMT solvers. Our problem formulation enables us to present experimental results comparing the performance of these three solving technologies on a real case study of a relay node network deployment in areas of the Leonardo da Vinci Airport in Rome, Italy.