Reasoning with incomplete and imprecise preferences

Preferences are present in many real life situations but it is often difficult to quantify them giving a precise value. Sometimes preference values may be missing because of privacy reasons or because they are expensive to obtain or to produce. In some other situations the user of an automated system may have a vague idea of whats he wants. In this thesis we considered the general formalism of soft constraints, where preferences play a crucial role and we extended such a framework to handle both incomplete and imprecise preferences. In particular we provided new theoretical frameworks to handle such kinds of preferences. By admitting missing or imprecise preferences, solving a soft constraint problem becomes a different task. In fact, the new goal is to find solutions which are the best ones independently of the precise value the each preference may have. With this in mind we defined two notions of optimality: the possibly optimal solutions and the necessary optimal solutions, which are optimal no matter we assign a precise value to a missing or imprecise preference. We provided several algorithms, bases on both systematic and local search approaches, to find such kind of solutions. Moreover, we also studied the impact of our techniques also in a specific class of problems (the stable marriage problems) where imprecision and incompleteness have a specific meaning and up to now have been tackled with different techniques. In the context of the classical stable marriage problem we developed a fair method to randomly generate stable marriages of a given problem instance. Furthermore, we adapted our techniques to solve stable marriage problems with ties and incomplete lists, which are known to be NP-hard, obtaining good results both in terms of size of the returned marriage and in terms of steps need to find a solution.

Dynamics of coastal aquifers: data-driven forecasting and risk analysis

This work is focused on the study of saltwater intrusion in coastal aquifers, and in particular on the realization of conceptual schemes to evaluate the risk associated with it. Saltwater intrusion depends on different natural and anthropic factors, both presenting a strong aleatory behaviour, that should be considered for an optimal management of the territory and water resources. Given the uncertainty of problem parameters, the risk associated with salinization needs to be cast in a probabilistic framework. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters are modeled as random variables, and global sensitivity analysis is used to determine their influence on the position of saltwater interface. The analyses presented in this work rely on an efficient model reduction technique, based on Polynomial Chaos Expansion, able to combine the best description of the model without great computational burden. When the assumptions of classical analytical models are not respected, and this occurs several times in the applications to real cases of study, as in the area analyzed in the present work, one can adopt data-driven techniques, based on the analysis of the data characterizing the system under study. It follows that a model can be defined on the basis of connections between the system state variables, with only a limited number of assumptions about the "physical" behaviour of the system.