Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling

Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex colouring and introduces a formulation of vertex colouring using a suitable clique partition of the graph. This formulation is applicable in timetabling applications, where such a clique partition of the conflict graph is given implicitly. In contrast with some alternatives, the presented formulation can also be easily extended to accommodate complex performance indicators (``soft constraints'') imposed in a number of real-life course timetabling applications. Its performance depends on the quality of the clique partition, but encouraging empirical results for the Udine Course Timetabling problem are reported

Soft CLP(FD

Abstract Over-constrained problems can be solved with the help of soft constraints. Weighted constraints are a typical representation of soft constraints used to minimize weights of unsatisfied constraints. A natural extension of the CLP(FD) approach is presented which allows handling of weighted soft constraints. To achieve this goal, the costs associated with unsatisfied constraints is accumulated for each problem variable and its value. For the approach proposed, implementation of the soft constraint solver on top of the existing CLP(FD) library of SICStus Prolog is described. A large scale timetabling implementation demonstrates practical application of the approach presented

Rožmberk as a place of memory (Presentation of the ancientness and nobleness by the family of Buquoy)

Rožmberk as a place of memory (Presentation of the ancientness and nobleness by the family of Buquoy) This bachelor essay takes an interest in rebuilding of dolní hrad (i.e. the Lower Castle) at Rožmberk nad Vltavou in the style of romantic Historicism, which was carried out between 1844 -1853. In the first chapter there are shortly presented literature and archival sources for the topic. That means especially the ego-sources from the estate of Georg Johann Buquoy and the institutional sources from the collection Domain Rožmberk. The different iconographic sources were used, too. The castle at Rožmbek was adapted in the style of the Historicism. Historicism, its English inspiration and its expression in the Czech architecture of 19th century are described in the next part. The deciding role by the reconstruction played the personality of Count Georg Johann Buquoy. Because Count Georg Johann was a talented artist {--} dilettante, he interfered with the look of the Lower Castle. Also his ideas and perception of medieval history and family history found the expression in the Lower Castle. After the neogothic rebuilding the Lower castle at Rožmberk was opened for the public as Buquoys`museum. It was a place, which brought near the ancientness and famous family history through the heraldic and picture decoration, through collections of antique furniture and objects d`art. The ancientness of family was especially presented through heraldic decoration of the Lower Castle. In most of the stained-glass windows there were situated the coats of arms that belonged to the members of the family Longueval-Buquoy and to the meaningful families, which were connected with this family. The coats of arms of European sovereigns, who Buquoys served, cannot be forgotten. The names of rooms on the first floor belonged to the celebration of ancestors, too

For God, King and the Fine Art: The Counts of Buquoy and the Visual Arts in the "Long 19th Century

Předkládaná disertační práce se zaměřuje na hraběcí rodinu Longueval-Buquoyů a na její vztah k vizuálním uměním mezi lety 1803 a 1911. Členové této urozené rodiny měli v 19. a na počátku 20. století blízko k rozmanitým formám umění a jejich aktivita může posloužit jako příklad různého šlechtického přístupu k výtvarným uměním (vlastní umělecká tvorba, obchodování s uměleckými předměty, stavební činnost, mecenášství). Do těsného vztahu k vizuálním uměním se promítaly individuální zájmy urozených mužů a žen i dobové šlechtické milieu, a proto se metodologickým východiskem staly tak zvaná nová biografie a tak zvané nové kulturní dějiny.This thesis focuses on the count family of Longueval-Buquoy and its relation to the visual arts between 1803 and 1911. In the 19th and at the beginning of the 20th century, the members of this noble family were close to various forms of art and their activity is able to be an example of different attitude to the fine art (own artistic work, trading in artistic articles, active interest of architecture and building, sponsorship). In the close relation to the visual arts, there were expressed individual interests of noble men and women as well as the then aristocratic milieu. Therefore the so called new biography and new cultural history became the methodological basis.Fakulta filozofickáDoktorandka obsáhle představila svoji disertační práci - její teze, cíle, metody, které využila, a další inspirační východiska, použité prameny a výsledky. Doktorandka byla seznámena s oponentskými posudky, které vyzdvihly vysokou heuristickou a interpretační hodnotu práce a upozornily na několik sporných momentů. Doktorandka zodpověděla vznesené otázky. Vše bylo vyhodnoceno jako vyhovující. Otázky: 1) V jakých ohledech a výsledcích se doktorčino bádání lišilo od buqoyoského projektu NAKI (Krajina - sídlo - obraz)? 2) Jaké jsou kořeny pojetí šlechtického sídla jako muzea? 3) Jaký byl vliv šlechty na směřování vývoje umění? 4) Problematika češtiny a psaní šlechtických jmen. 5) Terminologický problém amaterský (diletantský) profesionální umělec.Dokončená práce s úspěšnou obhajobo