A multi-objective bi-level location problem for heterogeneous sensor networks with hub-spoke topology

An heterogeneous sensor network (hSN) consists of different types of sensor nodes with varying coverage capability, range, and sensing quality. hSNs are used by military and other defense organizations for a number of purposes such as monitoring critical facilities, surveilling an area of interest, tracking enemies, or protecting borders. Therefore, the deployment problem of such networks to form an effective coverage and surveillance is of high importance. In this study, we consider the problem of locating an hSN along a two-dimensional belt-shaped border region which includes a number of critical facilities that need protection against intruders. Assuming a hub-spoke location topology, we allow the use of cooperative and gradual covering, multiple types of sensors, critical facilities and intruders. We developed two competing multi-objective mixed integer nonlinear program formulations as well as their equivalent mixed integer linear program (MILP) reformulations which adopt a goal programming approach. The MILP formulations are then solved by a commercial optimizer for a set of problem instances using the branch-and-cut (B&C) procedure with various branching and node selection strategies as well as different user defined optimality gap and goal settings. Our results indicate that the performance of formulations are significantly affected by the B&C variable selection strategy as well as the goal levels determined by the decision-makers. We also observe that, using proper settings, the majority of the problem instances can be solved within a maximum of 10% optimality gap in reasonable computing times.