Extensible Automated Constraint Modelling

In constraint solving, a critical bottleneck is the formulationof an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature

CONJURE: automatic generation of constraint models from problem specifications

Funding: Engineering and Physical Sciences Research Council (EP/V027182/1, EP/P015638/1), Royal Society (URF/R/180015).When solving a combinatorial problem, the formulation or model of the problem is critical tothe efficiency of the solver. Automating the modelling process has long been of interest because of the expertise and time required to produce an effective model of a given problem. We describe a method to automatically produce constraint models from a problem specification written in the abstract constraint specification language Essence. Our approach is to incrementally refine the specification into a concrete model by applying a chosen refinement rule at each step. Any nontrivial specification may be refined in multiple ways, creating a space of models to choose from. The handling of symmetries is a particularly important aspect of automated modelling. Many combinatorial optimisation problems contain symmetry, which can lead to redundant search. If a partial assignment is shown to be invalid, we are wasting time if we ever consider a symmetric equivalent of it. A particularly important class of symmetries are those introduced by the constraint modelling process: modelling symmetries. We show how modelling symmetries may be broken automatically as they enter a model during refinement, obviating the need for an expensive symmetry detection step following model formulation. Our approach is implemented in a system called Conjure. We compare the models producedby Conjure to constraint models from the literature that are known to be effective. Our empirical results confirm that Conjure can reproduce successfully the kernels of the constraint models of 42 benchmark problems found in the literature.Publisher PDFPeer reviewe

Dynamically weakened constraints in bounded search for constraint optimisation problems

Combinatorial optimisation problems, where the goal is to an optimal solution from the set of solutions of a problem involving resources, constraints on how these resources can be used, and a ranking of solutions are of both theoretical and practical interest. Many real world problems (such as routing vehicles or planning timetables) can be modelled as constraint optimisation problems, and solved via a variety of solver technologies which rely on differing algorithms for search and inference. The starting point for the work presented in this thesis is two existing approaches to solving constraint optimisation problems: constraint programming and decision diagram branch and bound search. Constraint programming models problems using variables which have domains of values and valid value assignments to variables are restricted by constraints. Constraint programming is a mature approach to solving optimisation problems, and typically relies on backtracking search algorithms combined with constraint propagators (which infer from incomplete solutions which values can be removed from the domains of variables which are yet to be assigned a value). Decision diagram branch and bound search is a less mature approach which solves problems modelled as dynamic programming models using width restricted decision diagrams to provide bounds during search. The main contribution of this thesis is adapting decision diagram branch and bound to be the search scheme in a general purpose constraint solver. To achieve this we propose a method in which we introduce a new algorithm for each constraint that we wish to include in our solver and these new algorithms weaken individual constraints, so that they respect the problem relaxations introduced while using decision diagram branch and bound as the search algorithm in our solver. Constraints are weakened during search based on the problem relaxations imposed by the search algorithm: before search begins there is no way of telling which relaxations will be introduced. We attempt to provide weakening algorithms which require little to no changes to existing propagation algorithms. We provide weakening algorithms for a number of built-in constraints in the Flatzinc specifi- cation, as well as for global constraints and symmetry reduction constraints. We implement a solver in Go and empirically verify the competitiveness of our approach. We show that our solver can be parallelised using Goroutines and channels and that our approach scales well. Finally, we also provide an implementation of our approach in a solver which is tailored towards solving extremal graph problems. We use the forbidden subgraph problem to show that our approach of using decision diagram branch and bound as a search scheme in a constraint solver can be paired with canonical search. Canonical search is a technique for graph search which ensures that no two isomorphic graphs are returned during search. We pair our solver with the Nauty graph isomorphism algorithm to achieve this, and explore the relationship between branch and bound and canonical search

Exemplary Practice: Inscribing Conduct Along Upper Canada\u27s Early Frontier

This dissertation studies exemplary conduct along Upper Canada\u27s early frontier. Presuming that exemplars reproduce core ideas of conduct for those who construct them, it is no surprise that exemplars by which authorities sought to make Upper Canada in Britain‟s image appeared in multiple arenas including legal discourse, newspaper publication, writings on conduct, informal notions of gender and domesticity, and travel writing. At the overlap of these different spaces, through special attention to an early burglary trial, the private dwelling house emerges in this dissertation as the moral core of Upper Canada. This claim interprets British legal definitions of human rights and duties, and a specific orientation to intention that these definitions entail, as supporting an intense emphasis on appearances that manifested as notions of conduct. I suggest that the articulation of absolute and relative rights, and their respective duties, creates a gap between individuals as elements unto themselves and individuals defined in terms of social relationships. This gap was reconciled by taking observable acts, including evidence of proper conduct, as measures of elements that were beyond direct observation, intention most crucially, which in turn measured the value of the act. As a consequence, observation—a web of relations involving acts, people observing them, who themselves are observed by others, and so on—got infused with a moral force it would not require if one could read intentions directly. Legal discourse thus put an emphasis on proper conduct that went beyond the letter of laws, whose formal expression had only limited influence on how conduct appeared in casual publications. My theoretical baseline is the practice approach of Ortner (1989), which views action, embodied in individuals, as emergent in analytic tensions between public institutions, particular situations, patterns in history and experience, and unpredictable, extra-systemic input. Since conduct is based in observation, and because the immanent structuring forces of practice entail relationships, I add to Ortner\u27s model the necessary presence of multiple actors who are present to each other. This model helps unpack the concrete bodies, relations, moments, and constraints in which exemplars emerge, and also emphasizes their conservative tendency

Based on a true history?: The impact of popular "Medieval Film" on the public understanding of the Middle Ages

This thesis examines the understanding of the Middle Ages among the UK public and the impact that popular big-budget films which depict the period have on that understanding. Three films released between 2000 and 2009 are chosen for detailed study, their selection being determined by success at the UK box office as a measure of popularity: Lord of the Rings, Return of the King (Jackson, 2003), Kingdom of Heaven (Scott, 2005) and Beowulf (Zemeckis, 2007). Ten focus group interviews were conducted with nineteen participants, all between eighteen and twenty-six years of age, none of whom had studied the Middle Ages at GCSE level (age 14-16) or higher. In these groups, participants discussed their knowledge of the Middle Ages, were shown a film, and then discussed what they had seen. Participants were asked open-ended interview questions to encourage them to respond in their own terms and define what was important to them. As a result, topics ranged widely. In preliminary discussions, participants discussed how they understood the period, their academic, experiential and pop-culture sources of knowledge, their definitions of the similar terms ‘medieval’ and ‘Middle Ages’ and also their ideas about medieval culture, religion, warfare and crusade. After the films, participants discussed what they had seen usually in the context of what they already knew, sometimes constructing false memories of what they had seen which fit with their previous knowledge. Often they used the language of historical veracity to criticise the film for other related reasons (like poor filmmaking or inappropriate accents). They found support for many of their historical misconceptions in the films, but, rather than accepting all they saw as historical truth, they engaged in a complex critical discourse with what they were shown. The findings of this thesis have implications for medieval (and medievalism) studies, public history, and for the delivery of history in primary, secondary and higher education

The classical and the grotesque in the work of Alexander Pope and Jonathan Swift

This thesis takes Mikhail Bakhtin's definitions of the classical and the grotesque, uses various other theorists to problematise and extend these concepts through an engagement with gender categories, and applies them to the work of Alexander Pope and Jonathan Swift. Although the first part deals with the 'theory' of the classical and the grotesque, the following sections on Pope and Swift seek to recognise the historical specificity and complexity of these modes as they intersect with the cultural, material, and psychological circumstances of the writer. The methodology is not solely biographical', 'political', 'cultural', 'feminist' or 'textual', but combines those approaches most relevant to the particular text in question, sometimes engaging more directly with the political environment, for example, at other times placing greater stress on mythological and generic allusions. The thesis shows that the classical and the grotesque emerge from a long social and literary tradition, yet the ways in which they manifest themselves in the time of Pope and Swift are very specific and constructed at least partially in response to contemporary cultural contexts such as the publishing trade, the present monarchy, the situation of Ireland and so on. Extending the work of Susan Gubar, particular attention is paid to the figure of the female grotesque, a common and yet varied image that is made to stand for a variety of cultural and moral ills in the writing of Pope and Swift. In contrast the figure of the 'classical' woman or 'softer man' is found to be symbolic of order as the unruly 'natural' substance of woman is transformed into masculine 'Culture' through social and textual containment. Classical and grotesque constructions of the masculine are also examined, especially in relation to the author's perceptions of his own masculinity. The thesis concludes with a brief analysis of the classical masculine friendship between Pope and Swift