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

Educational timetabling: Problems, benchmarks, and state-of-the-art results

We propose a survey of the research contributions on the field of Educational Timetabling with a specific focus on “standard” formulations and the corresponding benchmark instances. We identify six of such formulations and we discuss their features, pointing out their relevance and usability. Other available formulations and datasets are also reviewed and briefly discussed. Subsequently, we report the main state-of-the-art results on the selected benchmarks, in terms of solution quality (upper and lower bounds), search techniques, running times, and other side settings

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

(Re)-Creating, Interpreting and Appropriating Portuguese Language Policies in the UK

Situated as it is at the intersection of national and international educational policies and practices, state institutions and policy agents at various levels of social and institutional activity, the provision of Portuguese language in schools in England is a particularly interesting case of language policy research as it evidences many of the tensions in the field. The fate of the language provision complies with a particular legal framework which is centrally formulated in Portugal and is then (re)-created, interpreted and appropriated by a network of teachers and their administrator in their day-to-day interactions with head teachers, teachers, pupils and parents in the UK. With the context of language learning in England as a backdrop to the implementation of Portuguese language policies, this study sets out to understand the relationship between the discourses within the Portuguese legal framework – the macro-level of policy creation – and their interpretation and appropriation by a group of four Portuguese teachers and their administrator – the micro and meso levels of policy deployment. Shedding a brighter light on these relationships will help us understand how opportunities are created for Portuguese language learning. It is hoped that studying Portuguese language provision as a resource to schools in England will contribute to improving and incrementing its delivery as well as that of other less-commonly taught languages. This is an ethnography of language policy (McCarty 2011). As such, it combines analysis of macro-level official policy texts with ethnographic collection and analysis of data from the meso and micro levels of policy enactment. The study is based on the theoretical assumption that language policies can be instruments of power and control (Tollefson 1991, Shohamy 2006), but they can also be instruments of empowerment (Hornberger 2006). They can set discursive and structural boundaries on what languages and language varieties can be learned, who can learn them and how. But they can also promote and protect language learning and linguistic diversity and empower minority language users. An official language policy is but one element in a complex, multi-layered and interactively constructed process of multi-levelled social and institutional activity. After detailed analysis of the Portuguese legal framework, the study reports on two years of ethnographic data collection involving the use of timelines (Adriansen 2012) and in-depth three-part interviews (Bagnoli 2009, McCarty 2015) with four Portuguese teachers and their senior administrator. The collection of data also included participant and non-participant observation of the work of these four teachers in their schools. It was all documented in field notes, audio-recordings and photographs. The analysis of the legal framework evidenced significant discursive turning points and problematised the construction of Portuguese as “a great language of international communication” (Decree-Law nº 65-A/2016 of 25 October 2016), aimed at a diverse audience of learners. While the broadening policy discourses are a source of tension (Keating et al. 2014), the findings of the empirical study evidenced disparity in the interpretation and appropriation of the legal framework. For example, the teachers’ engagement with the official policy goals, which will be explored throughout this thesis, was found to be only partial and each teacher had their own individual take on the policy’s intentions and scope. It was also shown how different ideological and structural forces combined to facilitate or constrain opportunities for Portuguese language learning. Thus, the research emphasised the importance of considering the interaction between official language policy discourses and the individual, structural and ideological circumstances (Priestley et al. 2015, Liddicoat 2018) impacting their interpretation and appropriation by its agents (Johnson 2013a), namely teachers and their senior administrators. The conclusion contends for wider participation and collaboration between the Portuguese teachers and their senior administrators, both in England and Lisbon, engaging together in the process of language policy making

Links between devolution and changes in curriculum policy : a case study of year 8-10 social studies curriculum in Western Australia since 1987

This study investigates the links between devolution and Year 8-10 Society and Environment (SAE) curriculum policy in Western Australia (WA) since 1987. It explores whether changes to the structure within which SAE resides, the process through which curriculum decision making occurs, and the content of SAE are consistent with the principles and practice of devolution. An attempt is made in the study to determine whether these changes would have occurred anyway, even if devolution had not been introduced. The investigation is based on a radical humanist model of social inquiry, As such, it uses a critical theory conceptual framework to inform a qualitative research paradigm. Two sources provide qualitative data for the study, namely, interviews and documentary material. The interview material comes from discussions with twenty six senior education officers, school staff, academics and other stakeholders. The documentary material includes key system-wide policy documents, Year 8-10 curriculum frameworks, guidelines and syllabi, and relevant school level publications. Generally, the analysis of data gained from those two sources support the claims made by critical theorists about the impact of devolution upon curriculum policy. More specifically, the findings show that in WA, since 1987, state curriculum development has contributed to a reinforcement of social control, a widening of social inequality and an intensification of the school\u27s role as an agent of narrowly defined economic interests. These links are shown to be consistent with the critical theory argument that devolution is underpinned by corporate managerialism and that it involves not only a decentralisation of responsibility but also a recentralization of power. The study concludes by suggesting that the implications of WA\u27s experience of devolution for China depend largely on whether China\u27s context and needs are examined in terms of a consensus model or a critical theory model of society

Non-aboriginal teachers' perspectives on teaching native studies

Since the mid-1980s, the Saskatchewan Department of Education has approved the instruction of Native Studies courses in provincial high schools. In hope of enhancing the instruction of these courses, this study focused on the perspectives of Non-Aboriginal teachers who were assigned to teach Native Studies. Through a questionnaire, personal interviews, and a focus group, nine Non-Aboriginal high-school teachers examined the following aspects of the courses: formal and informal training of instructors , goals of the courses, key content and pedagogical methodologies, major challenges, and recommendations for improving the delivery of the classes.The literary context for the research was based upon three major areas: Non-Aboriginal teachers' perspectives on teaching Aboriginal students, preparing teachers to teach Native Studies, and preparing teachers to instruct Native Studies to Aboriginal students. Due to the 'single-group' nature of Native Studies curricula, considerable literature examination was focused on multicultural education models. The research data of the study revealed that the majority of interviewees have minimal formal education experience with Aboriginal content or epistemology. In addition, most of the study participants indicated little, if any, informal cultural contact with Aboriginal peoples. Study participants generally acknowledged the limitations of their scant academic and experiential interaction with Aboriginal cultures, and recommended means of various education stakeholders improving the situation.The study also exposed a variety of teacher perspectives about the goals of the courses. While there was unanimity regarding the efficacy of the courses, most teachers believed the goals of Native Studies varied depending on the cultural composition of the class. In addition, a couple of teachers inferred that a major objective of Native Studies courses is the promotion of an anti-establishment' political message. Some teachers also indicated a quandary regarding whether the course curricula required them to "teach Aboriginal culture, or teach about Aboriginal culture."In terms of course content and teaching methodologies, there were numerous opinions on `what was important'. All the interviewees viewed history as a significant ingredient to a `good' Native Studies class, but some of the teachers expressed a reluctance to delve into such issues as Aboriginal spirituality, racism, and 'white-privilege'. There was also hesitation amongst many of the respondents to incorporate traditional Aboriginal epistemologies into course methodologies because they wanted to personalize instruction, not base it upon cultural generalizations.In addition to the aforementioned issues and corresponding challenges associated with the background training for the courses, the goals of the courses, and the content and methodology of the courses, the study participants highlighted other concerns with the teaching of Native Studies: irrelevant curricula, lack of materials, poor course funding, student absenteeism, student perception that the courses are for 'non-academics', lack of flexible timetabling for experiential learning, and lack of staff knowledge and appreciation of Aboriginal cultures. All administrative levels of the education system were identified by the interviewees as influential in helping to mitigate the difficulties associated with the instruction of Native Studies

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes