Covering tour problem with varying coverage: Application to marine environmental monitoring

In this paper, we present a novel variant of the Covering Tour Problem (CTP), called the Covering Tour Problem with Varying Coverage (CTP-VC). We consider a simple graph ?????? = (??????, ??????), with a measure of importance assigned to each node in ??????. A vehicle with limited battery capacity visits the nodes of the graph and has the ability to stay in each node for a certain period of time, which determines the coverage radius at the node. We refer to this feature as stay-dependent varying coverage or, in short, varying coverage. The objective is to maximize a scalarization of the weighted coverage of the nodes and the negation of the cost of moving and staying at the nodes. This problem arises in the monitoring of marine environments, where pollutants can be measured at locations far from the source due to ocean currents. To solve the CTP-VC, we propose a mathematical formulation and a heuristic approach, given that the problem is NP-hard. Depending on the availability of solutions yielded by an exact solver, we evaluate our heuristic approach against the exact solver or a constructive heuristic on various instance sets and show how varying coverage improves performance. Additionally, we use an offshore CO2 storage site in the Gulf of Mexico as a case study to demonstrate the problem's applicability. Our results demonstrate that the proposed heuristic approach is an efficient and practical solution to the problem of stay-dependent varying coverage. We conduct numerous experiments and provide managerial insights.