Optimization of monitoring, data collecting, and energy resupplying tasks with scarce resources

We study an optimization problem which involves wireless power transmission and data collection technologies. The addressed problem is a variant of the Covering Tour Problem (CTP), where the resource consumption is taken into account. It is called Resource Constrained CTP (RCCTP). We consider nodes (smart devices) deployed in a given area, that have to be covered. An agent starts its tour from an origin node, visits portions of the area, and reaches a destination node. The agent, associated with a covering radius, has to cover all the nodes when performing her/his tour. The task of the agent is to provide a service to the covered nodes, i.e., power transmission and/or data collection. Moving in the area and performing the task require a certain amount of resource. The resource consumption depends on the tour and the nodes covered. Hence, the agent can choose the positions, from which it starts to deliver the service to cover a certain number of nodes at a time. The RCCTP aims at covering all the nodes through the agent, such that the total quantity of resource, consumed to perform the task and travel along the tour, does not exceed a certain threshold. We provide a formal definition of the problem along with a mathematical formulation. A computational phase is carried out on instances generated starting from benchmarks for the CTP.