Sophia Daskalaki

An integer programming formulation for a case study in university timetabling

A novel 0–1 integer programming formulation of the university timetabling problem is presented. The model provides constraints for a great number of operational rules and requirements found in most academic institutions. Treated as an optimization problem, the objective is to minimize a linear cost function. With this objective, it is possible to consider the satisfaction of expressed preferences regarding teaching periods or days of the week or even classrooms for specified courses. Moreover, with suitable definition of the cost coefficients in the objective function it is possible to reduce the solution space and make the problem tractable. The model is solvable by existing software tools with IP solvers, even for large departments. The case of a five-year Engineering Department with a large number of courses and teachers is presented along with its solution as resulted from the presented IP formulation. � 2003 Elsevier B.V. All rights reserved.

Efficient solutions for a university timetabling problem through integer programming

Abstract Integer programming has always been an alternative for formulating combinatorial problems such as the university timetabling problem. However, the effort required for modeling complicated operational rules, as well as the computational difficulties that result from the size of real problems have discouraged researchers and made them turn their interest to other approaches. In this paper, a two-stage relaxation procedure that solves efficiently the integer programming formulation of a university timetabling problem is presented. The relaxation is performed in the first stage and concerns the constraints that warrantee consecutiveness in multi-period sessions of certain courses. These constraints, which are computationally heavier than the others, are recovered during the second stage and a number of sub-problems, one for each day of the week, are solved for local optima. Comparing to a solution approach that solves the problem in a single stage, computation time is reduced significantly without any loss in quality for the resulting timetables. The new solution approach gives a chance for further improvements in the final timetables, as well as for certain degree of interaction with the users during the construction of the timetables.

EVALUATION OF CLASSIFIERS FOR AN UNEVEN CLASS DISTRIBUTION PROBLEM

Classification problems with uneven class distributions present several difficulties during the training as well as during the evaluation process of classifiers. A classification problem with such characteristics has resulted from a data mining project where the objective was to predict customer insolvency. Using the data set from the customer insolvency problem, we study several alternative methodologies, which have been reported to better suit the specific characteristics of this type of problem. Three different but equally important directions are examined: (a) the performance measures that should be used for problems in this domain; (b) the class distributions that should be used for the training data sets; and (c) the classification algorithms to be used. The final evaluation of the resulting classifiers is based on a study of the economic impact of classification results. This study concludes to a framework that provides the “best” classifiers, identifies the performance measures that should be used as the decision criterion, and suggests the “best” class distribution based on the value of the relative gain from correct classification in the positive class. This framework has been applied in the customer insolvency problem, but it is claimed that it can be applied to many similar problems with uneven class distributions that almost always require a multi-objective evaluation process.

Data mining for decision support on customer insolvency in telecommunications business

Abstract This paper reports on the findings of a research project that had the objective to build a decision support system to handle customer insolvency for a large telecommunication company. Prediction of customer insolvency, well in advance, and with an accuracy that could make this prediction useful in business terms, was one of the core objectives of the study. In the paper the process of building such a predictive model through knowledge discovery and data mining techniques in vast amounts of heterogeneous as well as noisy data is described. The reported findings are very promising, making the proposed model a useful tool in the decision making process, while some of the discussed problems and limitations are of interest to researchers who intend to use data mining approaches in other similar real-life problems.

An XML format for benchmarks in High School Timetabling

The High School Timetabling Problem is amongst the most widely used timetabling problems. This problem has varying structures in different high schools even within the same country or educational system. Due to lack of standard benchmarks and data formats this problem has been studied less than other timetabling problems in the literature. In this paper we describe the High School Timetabling Problem in several countries in order to find a common set of constraints and objectives. Our main goal is to provide exchangeable benchmarks for this problem. To achieve this we propose a standard data format suitable for different countries and educational systems, defined by an XML schema. The schema and datasets are available online.

The Role of Domain Knowledge in a Large Scale Data Mining Project

Data Mining techniques have been applied in many application areas. A Data Mining project has been often described as a process of automatic discovery of new knowledge from large amounts of data. However the role of the domain knowledge in this process and the forms that this can take, is an issue that has been given little attention so far. Based on our experience with a large scale Data Mining industrial project we present in this paper an outline of the role of domain knowledge in the various phases of the process. This project has led to the development of a decision support expert system for a major Telecommunications Operator. The data mining process is described in the paper as a continuous interaction between explicit domain knowledge, and knowledge that is discovered through the use of data mining algorithms. The role of the domain experts and data mining experts in this process is discussed. Examples from our case study are also provided.

School timetabling for quality student and teacher schedules

The school timetabling problem, although less complicated than its counterpart for the university, still provides a ground for interesting and innovative approaches that promise solutions of high quality. In this work, a Shift Assignment Problem is solved first and work shifts are assigned to teachers. In the sequel, the actual Timetabling Problem is solved while the optimal shift assignments that resulted from the previous problem help in defining the values for the cost coefficients in the objective function. Both problems are modelled using Integer Programming and by this combined approach we succeed in modelling all operational and practical rules that the Hellenic secondary educational system imposes. The resulting timetables are conflict free, complete, fully compact and well balanced for the students. They also handle simultaneous, collaborative and parallel teaching as well as blocks of consecutive lectures for certain courses. In addition, they are highly compact for the teachers, satisfy the teachers’ preferences at a high degree, and assign core courses towards the beginning of each day.

XHSTT: an XML archive for high school timetabling problems in different countries

We present the progress on the benchmarking project for high school timetabling that was introduced at PATAT 2008. In particular, we announce the High School Timetabling Archive XHSTT-2011 with 21 instances from 8 countries and an evaluator capable of checking the syntax of instances and evaluating the solutions.

Comparing forecasting approaches for Internet traffic

Internet traffic is modeled using time series and neural network approaches.FARIMA and ANNs are combined in two different ways for better predictions.A framework for comparison of the different approaches is introduced.Forecasting with a model selected based on non-linearity test is a successful strategy.Alternatively, hybridization between MLP and FARIMA is found to be equally effective. In this paper, we experiment with several different forecasting approaches for Internet traffic and a scheme for their evaluation. First the existence of properties such as Short or Long Range Dependence and non-linearity is explored in order to take advantage of such information and offer a couple of alternatives as forecasting models. The proposed models include FARIMA with Normal and Students t innovations and two different architectures of Artificial Neural Networks, the Multilayer Perceptron and Radial basis function. Next, we construct a model selection scheme based on the Whites Neural Network test for non-linearity or alternatively combine FARIMA and Neural Networks into hybrid forecasting models. The comparison of all suggested approaches is performed using their average position and standard deviation of position when applied to several known datasets of Internet traffic and when the accuracy of forecasts is measured with three different measures. Based on such a data analysis it is shown that hybridization and the selection of a model according to a non-linearity test are more successful as forecasting approaches over all individual models, as well as over other well-known methods such as Holt-Winters, ARIMA/GARCH and FARIMA/GARCH. This result indicates that forecasting approaches which take non-linearity into account lead to better overall forecasts for Internet traffic.

Combining Routing and Buffer Allocation Problems in Series-Parallel Queueing Networks

Given a series-parallel queueing network topology with exponential servers of finite capacity, a systematic design methodology is presented that approximately solves the optimal routing and buffer space allocation problems within the network. The multi-objective stochastic nonlinear programming problem in integer variables is described and a two-stage iterative optimization procedure is presented which interconnects the routing and buffer space allocation problems. The algorithmic procedure couples the Expansion method, a decomposition method for computing performance measures in queueing networks with finite capacity, along with Powells unconstrained optimization procedure which allocates the buffers and a multi-variable search procedure for determining the routing probabilities. The effectiveness and efficiency of the resulting two-stage design methodology is tested and evaluated in a series of experimental designs along with simulations of the network topologies.