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We hypothesize and confirm that probabilistic reasoning is closely related to constraint satisfaction at a formal level, and that this relationship yields effective algorithms for guiding constraint satisfaction and constraint optimization solvers. By taking a unified view of probabilistic inference and constraint reasoning in terms of graphical models, we first associate a number of formalisms and techniques between the two areas. For instance, we characterize search and inference in constraint reasoning as summation and multiplication (or disjunction and conjunction) in the probabilistic space; necessary but insufficient consistency conditions for solutions to constraint problems (like arc-consistency) mirror approximate objective functions over probability distributions (like the Bethe free energy); and the polytope of feasible points for marginal probabilities represents the linear relaxation of a particular constraint satisfaction problem. While such insights synthesize an assortment of existing formalisms from varied research communities, they also yield an entirely novel set of “bias estimation” techniques that contribute to a growing body of research on applying probabilistic methods to constraint problems. In practical terms, these techniques estimate the percentage of solutions to a constraint satisfaction or optimization problem wherein a given variable is assigned a given value. By devising search methods that incorporate such information as heuristic guidance for variable and value ordering, we are able to outperform existing solvers on problems of interest from constraint satisfaction and constraint optimization–-as represented here by the SAT and MaxSAT problems. Further, for MaxSAT we present an equivalent transformation” process that normalizes the weights in constraint optimization problems, in order to encourage prunings of the search tree during branch-and-bound search. To control such computationally expensive processes, we determine promising situations for using them throughout the course of an individual search process. We accomplish this using a reinforcement learning-based control module that seeks a principled balance between the exploration of new strategies and the exploitation of existing experiences.

We hypothesize and confirm that probabilistic reasoning is closely related to constraint satisfaction at a formal level, and that this relationship yields effective algorithms for guiding constraint satisfaction and constraint optimization solvers. By taking a unified view of probabilistic inference and constraint reasoning in terms of graphical models, we first associate a number of formalisms and techniques between the two areas. For instance, we characterize search and inference in constraint reasoning as summation and multiplication (or disjunction and conjunction) in the probabilistic space; necessary but insufficient consistency conditions for solutions to constraint problems (like arc-consistency) mirror approximate objective functions over probability distributions (like the Bethe free energy); and the polytope of feasible points for marginal probabilities represents the linear relaxation of a particular constraint satisfaction problem. While such insights synthesize an assortment of existing formalisms from varied research communities, they also yield an entirely novel set of “bias estimation” techniques that contribute to a growing body of research on applying probabilistic methods to constraint problems. In practical terms, these techniques estimate the percentage of solutions to a constraint satisfaction or optimization problem wherein a given variable is assigned a given value. By devising search methods that incorporate such information as heuristic guidance for variable and value ordering, we are able to outperform existing solvers on problems of interest from constraint satisfaction and constraint optimization–-as represented here by the SAT and MaxSAT problems. Further, for MaxSAT we present an equivalent transformation” process that normalizes the weights in constraint optimization problems, in order to encourage prunings of the search tree during branch-and-bound search. To control such computationally expensive processes, we determine promising situations for using them throughout the course of an individual search process. We accomplish this using a reinforcement learning-based control module that seeks a principled balance between the exploration of new strategies and the exploitation of existing experiences.

ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, California / This paper describes a model of how to configure settings on instrumentation. For any given instrument there may be 100s of settings that can be set to various values. However, randomly selecting values for each setting is not likely to produce a valid configuration. By "valid" we mean a set of setting values that can be implemented by each instrument. The valid configurations must satisfy a set of dependency rules between the settings and other constraints. The formalization provided allows for identification of different sets of configurations settings under control by different systems and organizations. Similarly, different rule sets are identified. A primary application of this model is in the context of a multi-vendor system especially when including vendors that maintain proprietary rules governing their systems. This thus leads to a discussion of an application user interface (API) between different systems with different rules and settings.

Declarative, object-oriented configuration management systems are widely used, and there is a desire to extend such systems with automated analysis and decision-making. This thesis introduces a new formulation for configuration management problems based on the tools and techniques of constraint programming, which enables automated decision-making. We present ConfSolve, an object-oriented declarative configuration language, in which logical constraints on a system can be specified. Verification, impact analysis, and the generation of valid configurations can then be performed. This is achieved via translation to the MiniZinc constraint programming language, which is in turn solved via the Gecode constraint solver. We formally define the syntax, type system, and semantics of ConfSolve, in order to provide it with a rigorous foundation. Additionally we show that our implementation outperforms previous work, which utilised an SMT solver, while adding new features such as optimisation. We next develop an extension of the ConfSolve language, which facilitates not only one-off configuration tasks, but also subsequent re-configurations in which the previous state of the system is taken into account. In a practical setting one does not wish for a re-configuration to deviate too far from the existing state, unless the benefits are substantial. Re-configuration is of crucial importance if automated configuration systems are to gain industry adoption. We present a novel approach to incorporating state-change into ConfSolve while remaining declarative and providing acceptable performance.

A wide range of problems can be formalized as a set of constraints that need to be satisfied. In fact, such a model is called a constraint satisfaction problem (CSP). Another way to represent a problem is to express it as a formula in propositional logic, or, in other words, a Boolean satisfiability problem (SAT). In the quest to find efficient algorithms for solving instances of CSP and SAT specialised software has been developed. It is, however, not clear when should we choose a SAT-solver over a constraint solver (and vice versa). CSP-solvers are known for their domain-specific reasoning, whereas SAT-solvers are considered to be remarkably fast on Boolean instances. In this thesis we tackle these issues by investigating the connections between CSP and SAT. In order to answer the question why SAT-solvers are so efficient on certain classes of CSP instances, we first present the various ways one can encode a CSP instance into SAT. Next, we show that with some encodings SAT-solvers simulate the effects of enforcing a form of local consistency, called k-consistency, in expected polynomial-time. Thus SAT-solvers are able to solve CSP instances of bounded-width structure efficiently in contrast to conventional constraint solvers. By considering the various ways one can encode CSP domains into SAT, we give theoretical reasons for choosing a particular SAT encoding for several important classes of CSP instances. In particular, we show that with this encoding many problem instances that can be solved in polynomial-time will still be easily solvable once they are translated into SAT. Furthermore, we show that this is not true for several other encodings. Finally, we compare the various ways one can use a SAT-solver to solve the classical problem of the pigeonhole principle. We perform both theoretical and empirical comparison of the various encodings. We conclude that none of the known encodings for the classical representation of the problem will result in an efficiently-solvable SAT instance. Thus in this case constraint solvers are a much better choice.

<p>The world’s population is ageing. Due to societal improvements in healthcare, living standards, and socio-economic status, more and more people are living to old age. The proportion of the world's population aged 65 or over is expected to increase from 11% in 1998 to 16% in 2025. This causes a major public health issue, because with increased age there is an increased risk of developing a number of age-related diseases. However, there is increasing scientific evidence that many of the biological changes and risks for chronic disease, which have traditionally been attributed to ageing, are in fact caused by malnutrition (sub-optimal diets and nutrient intakes).</p><p>This report presents a constraint satisfaction approach to planning meals while taking into account amongst other things nutritional and economic factors. Two models for generating meal plans are presented and their respective strengths and weaknesses discussed. System design, implementation and the main algorithms used are described in more detail. These algorithms include Depth First Branch and Bound and its various improvements for meal plan generation as well as Item-based Collaborative Filtering for user preferences. Our test runs show that the system works well for smaller applications but runs into problems when the number of available recipes grows or a larger number of meals are planned. The tests also show that the two modelling approaches both have useful applications. Based on the test results some suggestions for further improvement of the system conclude the report.</p>

This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. Theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs. The results also indicate that the new algorithm should be significantly faster when the ODE contains many operations.

This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. Theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs. The results also indicate that the new algorithm should be significantly faster when the ODE contains many operations.