Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

Abstracting soft constraints: framework, properties, examples

Soft constraints are very and expressive. However, they also are very complex to handle. For this reason, it may be reasonable in several cases to pass to an abstract version of a given soft constraint problem, and then to bring some useful information from the abstract problem to the concrete one. This will hopefully make the search for a solution, or for an optimal solution, of the concrete problem, faster. In this paper we propose an abstraction scheme for soft constraint problems and we study its main properties. We show that processing the abstracted version of a soft constraint problem can help us in finding good approximations of the optimal solutions, or also in obtaining information that can make the subsequent search for the best solution easier. We also show how the abstraction scheme can be used to devise new hybrid algorithms for solving soft constraint problems, and also to import constraint propagation algorithms from the abstract scenario to the concrete one. This may be useful when we don\u27t have any (or any efficient) propagation algorithm in the concrete setting

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

Optimization and inference under fuzzy numerical constraints

Εκτεταμένη έρευνα έχει γίνει στους τομείς της Ικανοποίησης Περιορισμών με διακριτά (ακέραια) ή πραγματικά πεδία τιμών. Αυτή η έρευνα έχει οδηγήσει σε πολλαπλές σημασιολογικές περιγραφές, πλατφόρμες και συστήματα για την περιγραφή σχετικών προβλημάτων με επαρκείς βελτιστοποιήσεις. Παρά ταύτα, λόγω της ασαφούς φύσης πραγματικών προβλημάτων ή ελλιπούς μας γνώσης για αυτά, η σαφής μοντελοποίηση ενός προβλήματος ικανοποίησης περιορισμών δεν είναι πάντα ένα εύκολο ζήτημα ή ακόμα και η καλύτερη προσέγγιση. Επιπλέον, το πρόβλημα της μοντελοποίησης και επίλυσης ελλιπούς γνώσης είναι ακόμη δυσκολότερο. Επιπροσθέτως, πρακτικές απαιτήσεις μοντελοποίησης και μέθοδοι βελτιστοποίησης του χρόνου αναζήτησης απαιτούν συνήθως ειδικές πληροφορίες για το πεδίο εφαρμογής, καθιστώντας τη δημιουργία ενός γενικότερου πλαισίου βελτιστοποίησης ένα ιδιαίτερα δύσκολο πρόβλημα. Στα πλαίσια αυτής της εργασίας θα μελετήσουμε το πρόβλημα της μοντελοποίησης και αξιοποίησης σαφών, ελλιπών ή ασαφών περιορισμών, καθώς και πιθανές στρατηγικές βελτιστοποίησης. Καθώς τα παραδοσιακά προβλήματα ικανοποίησης περιορισμών λειτουργούν βάσει συγκεκριμένων και προκαθορισμένων κανόνων και σχέσεων, παρουσιάζει ενδιαφέρον η διερεύνηση στρατηγικών και βελτιστοποιήσεων που θα επιτρέπουν το συμπερασμό νέων ή/και αποδοτικότερων περιορισμών. Τέτοιοι επιπρόσθετοι κανόνες θα μπορούσαν να βελτιώσουν τη διαδικασία αναζήτησης μέσω της εφαρμογής αυστηρότερων περιορισμών και περιορισμού του χώρου αναζήτησης ή να προσφέρουν χρήσιμες πληροφορίες στον αναλυτή για τη φύση του προβλήματος που μοντελοποιεί.Extensive research has been done in the areas of Constraint Satisfaction with discrete/integer and real domain ranges. Multiple platforms and systems to deal with these kinds of domains have been developed and appropriately optimized. Nevertheless, due to the incomplete and possibly vague nature of real-life problems, modeling a crisp and adequately strict satisfaction problem may not always be easy or even appropriate. The problem of modeling incomplete knowledge or solving an incomplete/relaxed representation of a problem is a much harder issue to tackle. Additionally, practical modeling requirements and search optimizations require specific domain knowledge in order to be implemented, making the creation of a more generic optimization framework an even harder problem.In this thesis, we will study the problem of modeling and utilizing incomplete and fuzzy constraints, as well as possible optimization strategies. As constraint satisfaction problems usually contain hard-coded constraints based on specific problem and domain knowledge, we will investigate whether strategies and generic heuristics exist for inferring new constraint rules. Additional rules could optimize the search process by implementing stricter constraints and thus pruning the search space or even provide useful insight to the researcher concerning the nature of the investigated problem

A general framework integrating techniques for scheduling under uncertainty

Ces dernières années, de nombreux travaux de recherche ont porté sur la planification de tâches et l'ordonnancement sous incertitudes. Ce domaine de recherche comprend un large choix de modèles, techniques de résolution et systèmes, et il est difficile de les comparer car les terminologies existantes sont incomplètes. Nous avons cependant identifié des familles d'approches générales qui peuvent être utilisées pour structurer la littérature suivant trois axes perpendiculaires. Cette nouvelle structuration de l'état de l'art est basée sur la façon dont les décisions sont prises. De plus, nous proposons un modèle de génération et d'exécution pour ordonnancer sous incertitudes qui met en oeuvre ces trois familles d'approches. Ce modèle est un automate qui se développe lorsque l'ordonnancement courant n'est plus exécutable ou lorsque des conditions particulières sont vérifiées. Le troisième volet de cette thèse concerne l'étude expérimentale que nous avons menée. Au-dessus de ILOG Solver et Scheduler nous avons implémenté un prototype logiciel en C++, directement instancié de notre modèle de génération et d'exécution. Nous présentons de nouveaux problèmes d'ordonnancement probabilistes et une approche par satisfaction de contraintes combinée avec de la simulation pour les résoudre. ABSTRACT : For last years, a number of research investigations on task planning and scheduling under uncertainty have been conducted. This research domain comprises a large number of models, resolution techniques, and systems, and it is difficult to compare them since the existing terminologies are incomplete. However, we identified general families of approaches that can be used to structure the literature given three perpendicular axes. This new classification of the state of the art is based on the way decisions are taken. In addition, we propose a generation and execution model for scheduling under uncertainty that combines these three families of approaches. This model is an automaton that develops when the current schedule is no longer executable or when some particular conditions are met. The third part of this thesis concerns our experimental study. On top of ILOG Solver and Scheduler, we implemented a software prototype in C++ directly instantiated from our generation and execution model. We present new probabilistic scheduling problems and a constraintbased approach combined with simulation to solve some instances thereof

Embedding Preference Elicitation Within the Search for DCOP Solutions

The Distributed Constraint Optimization Problem(DCOP)formulation is a powerful tool to model cooperative multi-agent problems, especially when they are sparsely constrained with one another. A key assumption in this model is that all constraints are fully specified or known a priori, which may not hold in applications where constraints encode preferences of human users. In this thesis, we extend the model to Incomplete DCOPs (I-DCOPs), where some constraints can be partially specified. User preferences for these partially-specified constraints can be elicited during the execution of I-DCOP algorithms, but they incur some elicitation costs. Additionally, we propose two parameterized heuristics that can be used in conjunction with Synchronous Branch-and-Bound to solve I-DCOPs. These heuristics allow users to trade-off solution quality for faster runtimes and a smaller number of elicitations. They also provide theoretical quality guarantees for problems where elicitations are free. Our model and heuristics thus extend the state of the art in distributed constraint reasoning to better model and solve distributed agent-based applications with user preferences