The constraint satisfaction problem is an NP-complete problem that provides a convenient framework for expressing many computationally hard problems. In addition, domain knowledge can be efficiently integrated into CSPs, providing a potentially exponential speedup in some cases. The CSP is closely related to the satisfiability problem and many of the techniques developed for one have been transferred to the other. However, the recent dramatic improvements in SAT solvers that result from learning clauses during search have not been transferred successfully to CSP solvers. In this thesis we propose that this failure is due to a fundamental restriction of \newtext{nogood learning, which is intended to be the analogous to clause learning in CSPs}. This restriction means that nogood learning can exhibit a superpolynomial slowdown compared to clause learning in some cases. We show that the restriction can be lifted, delivering promising results. Integration of nogood learning in a CSP solver, however, presents an additional challenge, as a large body of domain knowledge is typically encoded in the form of domain specific propagation algorithms called global constraints. Global constraints often completely eliminate the advantages of nogood learning. We demonstrate generic methods that partially alleviate the problem irrespective of the type of global constraint. We also show that more efficient methods can be integrated into specific global constraints and demonstrate the feasibility of this approach on several widely used global constraints.

The constraint satisfaction problem is an NP-complete problem that provides a convenient framework for expressing many computationally hard problems. In addition, domain knowledge can be efficiently integrated into CSPs, providing a potentially exponential speedup in some cases. The CSP is closely related to the satisfiability problem and many of the techniques developed for one have been transferred to the other. However, the recent dramatic improvements in SAT solvers that result from learning clauses during search have not been transferred successfully to CSP solvers. In this thesis we propose that this failure is due to a fundamental restriction of \newtext{nogood learning, which is intended to be the analogous to clause learning in CSPs}. This restriction means that nogood learning can exhibit a superpolynomial slowdown compared to clause learning in some cases. We show that the restriction can be lifted, delivering promising results. Integration of nogood learning in a CSP solver, however, presents an additional challenge, as a large body of domain knowledge is typically encoded in the form of domain specific propagation algorithms called global constraints. Global constraints often completely eliminate the advantages of nogood learning. We demonstrate generic methods that partially alleviate the problem irrespective of the type of global constraint. We also show that more efficient methods can be integrated into specific global constraints and demonstrate the feasibility of this approach on several widely used global constraints.

This thesis is about the computational complexity of several classes of combinatorial optimization problems, all related to the constraint satisfaction problems. A constraint language consists of a domain and a set of relations on the domain. For each such language there is a constraint satisfaction problem (CSP). In this problem we are given a set of variables and a collection of constraints, each of which is constraining some variables with a relation in the language. The goal is to determine if domain values can be assigned to the variables in a way that satisfies all constraints. An important question is for which constraint languages the corresponding CSP can be solved in polynomial time. We study this kind of question for optimization problems related to the CSPs. The main focus is on extended minimum cost homomorphism problems. These are optimization versions of CSPs where instances come with an objective function given by a weighted sum of unary cost functions, and where the goal is not only to determine if a solution exists, but to find one of minimum cost. We prove a complete classification of the complexity for these problems on three-element domains. We also obtain a classification for the so-called conservative case. Another class of combinatorial optimization problems are the surjective maximum CSPs. These problems are variants of CSPs where a non-negative weight is attached to each constraint, and the objective is to find a surjective mapping of the variables to values that maximizes the weighted sum of satisfied constraints. The surjectivity requirement causes these problems to behave quite different from for example the minimum cost homomorphism problems, and many powerful techniques are not applicable. We prove a dichotomy for the complexity of the problems in this class on two-element domains. An essential ingredient in the proof is an algorithm that solves a generalized version of the minimum cut problem. This algorithm might be of independent interest. In a final part we study properties of NP-hard optimization problems. This is done with the aid of restricted forms of polynomial-time reductions that for example preserves solvability in sub-exponential time. Two classes of optimization problems similar to those discussed above are considered, and for both we obtain what may be called an easiest NP-hard problem. We also establish some connections to the exponential time hypothesis.

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). 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.

Most commercial CAD systems do not offer sufficient support for the design activity. The reason is that they cannot understand the functional requirements of the design product. The user is responsible for maintaining the functional requirements in different design phases. By incorporating constraint programming concepts, these CAD systems would evolve into systems which would maintain the functional requirements in the design process, and perform analysis and simulation of geometric models. The CAD systems incorporated with constraint programming concepts would reduce design time, avoid human fatigue and error, and also maintain consistency of the geometric constraints imposed on the model. The G+ system addresses these issues by introducing a constraint-based system for geometric modeling by object-oriented methods. The G+ is designed such that available specialized algorithms can be utilized to enable handling of non-linear problems by both iterative and non-iterative schemes.

Many real world problems are naturally distributed, whether they are spatially, cognitively, or otherwise. Distributed problems naturally lend themselves to solutions using multi-agent paradigms. Distributed Constraint Satisfaction Problems (DisCSPs) are a class of such distributed problems. In DisCSPs, variables and constraints are distributed between agents. Most distributed algorithms, although exponential in the worst-case, can have a good performance in the average case. The main purpose of this research is to statistically assess difference between the empirical performances of major state of the art DisCSP algorithms including Multi-Sectioned Constraint Network (MSCN) based algorithms, that have never been empirically compared against other DisCSP algorithms. In this thesis, we select a set of state of the art DisCSP algorithms and compare them on randomly generated instances of binary DisCSPs with a wide range of characteristics. Distributed algorithms ADOPT, DSA, DPOP, and MSCN based algorithms were selected based on a set of high level criteria. We explore how these algorithms relatively compare with each other on a range of DisCSPs with different parameters. Their performances are evaluated according to computation time (in the form of non-concurrent computational steps or NCCCs) and communication load (in the form of number of messages as well as volume of messages). Statistical parametric tests are used to aid interpretation of the performance results. In addition, this thesis discusses privacy issues associated with these DisCSP algorithms.

International Telemetering Conference Proceedings / October 18-21, 2004 / Town & Country Resort, San Diego, California / Several algorithms have been proposed for solving constraint satisfaction and the more general constraint optimization problem in a distributed manner. In this paper we apply two such algorithms to the task of dynamic resource allocation in the sensor network domain using appropriate abstractions. The aim is to effectively track multiple targets by making the sensors coordinate with each other in a distributed manner, given a probabilistic representation of tasks (targets). We present simulation results and compare the performance of the DBA and DSA algorithms under varying experimental settings.

Computational creativity has been called the "final frontier" of artificial intelligence due to the difficulty inherent in defining and implementing creativity in computational systems. Despite this difficulty computer creativity is becoming a more significant part of our everyday lives, in particular music. This is observed in the prevalence of music recommendation systems, co-creational music software packages, smart playlists, and procedurally-generated video games. Significant progress can be seen in the advances in industrial applications such as Spotify, Pandora, Apple Music, etc., but several problems persist. Of more general interest, however, is the question of whether or not computers can exhibit autonomous creativity in music composition. One of the primary challenges in this endeavor is enabling computational systems to create music that exhibits global structure, that can learn structure from data, and which can effectively incorporate autonomy and intention. We seek to address these challenges in the context of a modular machine learning framework called hierarchical Bayesian program learning (HBPL). Breaking the problem of music composition into smaller pieces, we focus primarily on developing machine learning models that solve the problems related to structure. In particular we present an adaptation of non-homogenous Markov models that enable binary constraints and we present a structural learning model, the multiple Smith-Waterman (mSW) alignment method, which extends sequence alignment techniques from bioinformatics. To address the issue of intention, we incorporate our work on structured sequence generation into a full-fledged computational creative system called Pop* which we show through various evaluative means to possess to varying extents the characteristics of creativity and also creativity itself.

Déterminer si un problème de satisfaction de contraintes (CSP) a une solution ou non est NP-complet. Les CSP sont résolus par inférence (c’est-à-dire, en appliquant un algorithme de cohérence), par énumération (c’est-à-dire en effectuant une recherche avec retour sur trace ou backtracking), ou, plus souvent, en intercalant les deux mécanismes. La propriété de cohérence la plus courante appliquée en cours du backtracking est la GAC (Generalized Arc Consistency). Au cours des dernières années, de nouveaux algorithmes pour appliquer des cohérences plus fortes que le GAC ont été proposés et montrés comme étant nécessaires pour résoudre les problèmes difficiles.Nous nous attaquons à la question de balancer d’une part le coût et, d’autre part, le pouvoir d’élagage des algorithmes de cohérence et posons cette question comme étant celle de déterminer où, quand et combien une cohérence doit-elle être appliquée en cours de backtracking. Pour répondre à la question « où », nous exploitons la structure topologique d'une instance du problème et focalisons la cohérence forte là où des structures cycliques apparaissent. Pour répondre à la question « quand », nous proposons une stratégie simple, réactive et efficace qui surveille la performance du backtracking puis déclenche une cohérence forte lorsque l’effort du retour sur trace devient alarmant. Enfin, pour la question du « combien », nous surveillons les mises à jour provoquées par la propagation des contraintes et interrompons le processus dès qu’il devient inactif ou coûteux même avant qu’il n’atteigne un point fixe. Les évaluations empiriques sur des problèmes de référence établissent l’efficacité de nos stratégies. / Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforceconsistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances.We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the ‘where’ question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the ‘when’ question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of ‘how much,’ we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies.

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