The goal of environmental monitoring is to collect information from the environment and to generate an accurate model for a specific phenomena of interest. We can distinguish environmental monitoring applications into two macro areas that have different strategies for acquiring data from the environment. On one hand the use of fixed sensors deployed in the environment allows a constant monitoring and a steady flow of information coming from a predetermined set of locations in space. On the other hand the use of mobile platforms allows to adaptively and rapidly choose the sensing locations based on needs. For some applications (e.g. water monitoring) this can significantly reduce costs associated with monitoring compared with classical analysis made by human operators. However, both cases share a common problem to be solved. The data collection process must consider limited resources and the key problem is to choose where to perform observations (measurements) in order to most effectively acquire information from the environment and decrease the uncertainty about the analyzed phenomena. We can generalize this concept under the name of information gathering. In general, maximizing the information that we can obtain from the environment is an NP-hard problem. Hence, optimizing the selection of the sampling locations is crucial in this context. For example, in case of mobile sensors the problem of reducing uncertainty about a physical process requires to compute sensing trajectories constrained by the limited resources available, such as, the battery lifetime of the platform or the computation power available on board. This problem is usually referred to as Informative Path Planning (IPP). In the other case, observation with a network of fixed sensors requires to decide beforehand the specific locations where the sensors has to be deployed. Usually the process of selecting a limited set of informative locations is performed by solving a combinatorial optimization problem that model the information gathering process. This thesis focuses on the above mentioned scenario. Specifically, we investigate diverse problems and propose innovative algorithms and heuristics related to the optimization of information gathering techniques for environmental monitoring applications, both in case of deployment of mobile and fixed sensors. Moreover, we also investigate the possibility of using a quantum computation approach in the context of information gathering optimization
