Relation-algebraic specification and solution of special university timetabling problems

AbstractIn this paper, we are concerned with a special timetabling problem. It was posed to us by the administration of our university and stems from the adoption of the British-American system of university education in Germany. This change led to the concrete task of constructing a timetable that enables the undergraduate education of secondary school teachers within three years in the “normal case” and within four years in the case of exceptional combinations of subjects. We develop two relation-algebraic models of the timetabling problem and in each case algorithms for computing solutions. The latter easily can be implemented in the Kiel RelView tool showing that RelView can be used for timetabling

Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure

Development of a prototype for the automated generation of timetable scenarios specified by the transport service intention

Within the next 5 to 10 years, public transport in Switzerland as well as in other European countries will experience major technological and organisational changes. However, changes will also take place on the customer side, resulting in different mobility behaviour and demand patterns. These changes will lead to additional challenges for transport service providers in private as well as public domains. Time to market will be a key success factor and it is unnecessary to mention that due to these factors the speed and flexibility of business processes in freight as well as in passenger transport industry have to be increased significantly. Within the railway value chain (line planning, timetabling and vehicle scheduling etc.) the coordination of the individual planning steps is a key success factor. SBB as the leading service provider in public transport in Switzerland has recognized this challenge and, together with various partners, initiated the strategic project Smart Rail 4.0. The ZHAW and especially the Institute for Data Analysis and Process Design (IDP) of the School of Engineering wants to be part of this transformation process and to contribute with research and educational activities. The IDP research therefore aims for the transformation of academic and scientific know-how to practical applicability. In a first step this concerns directly the current Smart Rail 4.0 TMS-PAS project activities, that concentrate on timetabling issues. The IDP project team considers the integration of the line planning and the timetabling process as crucial for practical applications. To address this in the current research project, we present an application concept that enables the integration of these two major process steps in the transport service value-chain. Although it turns out from our research, that the technical requirements for the integration of the process can be satisfied, rules and conditions for a closer cooperation of the involved business units, the train operating companies and the infrastructure operating company, have to be improved and to be worked out in more detail. In addition to a detailed application concept with use cases for the timetabling process we propose a methodology for computer aided timetable generation based on the central planning object known as ‘service intention’. The service intention can be used to iteratively develop the timetable relying on a ‘progressive feasibility assessment’, a feature that is requested in practice. Our proposed model is based on the ‘track-choice’ and line rotation extension of the commonly known method for the generation of periodic event schedules ‘PESP’. The extension makes use of the track infrastructure representation which is also used in the line planning and timetabling system Viriato. This system that is widely used by public transport planners and operators. With the help of Viriato, it is rather easy to configure the timetabling problem in sufficient detail. On the other side, the level of detail of the considered data is light enough to algorithmically solve practical timetabling problems of realistic sizes. Taking into consideration the technical and operational constraints given by rolling stock, station and track topology data on one hand, and the commercial requirements defined by a given line concept on the other, the method presented generates periodic timetables including train-track assignments. In the first step, the standardized data structure ‘service intention’ represents the line concept consisting of train paths and frequencies. Due to the utilization of infrastructure-based track capacities, we are also able to assess the feasibility of the line concept given. Additionally, the method allows for handling temporary resource restrictions (e.g. caused by construction sites or operational disturbances). In order to assess the performance of the resulting timetable we present a framework for performance measurement that addresses the customer convenience (in terms of start-to-end travel time) as well as operational stability requirements (in terms of delay sensitivity and critical relations)

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes average perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Peri- odic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that mini- mizes the average perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infras- tructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average per- ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

An approach to computer-based knowledge representation for the business environment using empirical modelling

The motivation for the thesis arises from the difficulties experienced by business people who are non-programmers with the inflexibilities of conventional packages and tools for model-making. After a review of current business software an argument is made for the need for a new computing paradigm that would offer more support for the way that people actually experience their business activities. The Empirical Mod- elling (EM) approach is introduced as a broad theoretical and practical paradigm for computing that can be viewed as a far-reaching generali- sation of the spreadsheet concept. The concepts and principles of EM emphasise the experiential pro- cesses underlying familiar abstractions and by which we come to iden- tify reliable components in everyday life and, in particular, business activities. The emphasis on experience and on interaction leads to the new claim that EM environments offer a framework for combining propositional, experiential and tacit knowledge in a way that is more accessible and supportive of cognitive processes than conventional computer-based modelling. It is proposed that such environments offer an alternative kind of knowledge representation. Turning to the imple- mentation and development of systems, the difficulties inherent in con- ventional methods are discussed and then the practical aspects of EM, and its potential for system building, are outlined. Finally, a more detailed study is made of Decision Support Systems and the ways in which the EM focus on experience, and knowledge through interaction, can contribute to the representation of qualitative aspects of business activities and their use in a more human-centred, but computer-supported, process of decision making. Illustrations of the practical application of EM methods to the requirements of a deci- sion support environment are given by means of extracts from a num- ber of existing EM models