A Comparison of Discrete and Continuous Neural Network Approaches to Solve the Class/Teacher Timetabling Problem

This study explores the application of neural network-based heuristics to the class/teacher timetabling problem (CTTP). The paper begins by presenting the basic CTTP characteristics in terms of hard and soft constraints and proposing a formulation for the energy function required to map the problem within the artificial neural network model. There follow two distinct approaches to simulating neural network evolution. The first uses a Potts mean-field annealing simulation based on continuous Potts neurons, which has obtained favorable results in various combi¬natorial optimization problems. Afterwards, a discrete neural network simulation, based on discrete winner-take-all neurons, is proposed. The paper concludes with a comparison of the computational results taken from the application of both heuris¬tics to hard hypothetical and real CTTP instances. This experiment demonstrates that the discrete approach performs better, in terms of solution quality as well as execution time

An application of Soft System Methodology

AbstractThe typical course timetabling problem is assigning Classes of students to appropriate faculty members, suitable classrooms and available timeslots. Hence, it involves a large number of stakeholders including students, teachers and institutional administrators. Different kinds of Hard Operational Research techniques have been employed over the years to address such problems. Due to the computational difficulties of this NP complete problem as well as the size and the complexity of the real world instances, an efficient optimal solution cannot be found easily.As an alternative strategy, this paper investigates the application of Checkland‘s Soft System Methodology (SSM) to the course timetabling problem. Besides giving an ideal course timetable, even to large and complex real problems, application of SSM, generates debate, learning, and understanding; enables key changes; facilitates negotiating the actions to be taken and makes possible the meaningful collaboration among concerned stakeholders. This paper also provides an appropriate course timetable for the management faculty at University of Tehran to show the potential of this application to real problems

A review of timetabling and resource allocation models for light-rail transportation systems

This paper surveys the relevant operations research literature on timetabling and resource allocationproblems with a special attention paid to the transportation systems. The purpose of this review is to define the critical objectives, determine the key components and identify the key issues for developing a comprehensive mathematical model for timetabling of light rail transit vehicles in sequence with the assignment of drivers as an available resource. In doing so, the implications of the emerging timetabling research is discussed, components of the mathematical models proposed are reviewed, and the extend they reflect real business practices are analyzed. Finally, fundamental issues and primary elements of a simple model in association with general timetabling and resource allocation problems are presented

Goal programming approach to solve the timetabling problem at Turkish Military Academy

Cataloged from PDF version of article.The aim of this study is to propose a goal programming model to solve the timetabling problem at Turkish Military Academy. Since the problem is NPcomplete, it’s not easy to find an optimal solution all the time. It takes a lot of time of the people who are responsible to prepare the timetables of TMA. The model consists in all of the requirements, and is tested with the real data provided by Planning and Programming Department. Since the problem is so big to solve at once as a whole, a five-step iterative solution procedure is proposed. There are four priorities, three for teacher preferences and one for teaching loads. The model aims to minimize the deviations from the preferences and teaching loads of the teachers. Solution process produced a feasible and near-optimal timetable after four steps, in a reasonably short time compared to hand-made timetabling procedure. The result was improved by making some modifications in step five. In the conclusion, we mentioned the problems we faced, and presented our suggestions for future research.Şahin, TunaM.S

An Assignment Problem and Its Application in Education Domain: A Review and Potential Path

This paper presents a review pertaining to assignment problem within the education domain, besides looking into the applications of the present research trend, developments, and publications. Assignment problem arises in diverse situations, where one needs to determine an optimal way to assign n subjects to m subjects in the best possible way.With that, this paper classified assignment problems into two, which are timetabling problem and allocation problem. The timetabling problem is further classified into examination, course, and school timetabling problems, while the allocation problem is divided into student-project allocation, new student allocation, and space allocation problems. Furthermore, the constraints, which are of hard and soft constraints, involved in the said problems are briefly elaborated.In addition, this paper presents various approaches to address various types of assignment problem. Moreover, direction and potential paths of problem solving based on the latest trend of approaches are also highlighted.As such, this review summarizes and records a comprehensive survey regarding assignment problem within education domain, which enhances one's understanding concerning the varied types of assignment problems, along with various approaches that serve as solution

Uma proposta baseada em algoritmo genético para o problema timetable escolar compacto

Orientador : Prof. Dr. Sérgio ScheerOrientador : Prof. Dr. Anderson Roges Teixeira GóesDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 11/12/2015Inclui referências : f.74-79Resumo: O início do ano letivo é marcado por um desafio clássico a uma equipe pedagógica: montar a distribuição de aulas e turmas aos professores, um Scholar Timetabling Problem, atendendo necessidades apresentadas pelo corpo docente e garantindo que a carga horária semanal de cada disciplina seja cumprida em sua totalidade para as turmas. É comum, tanto em escolas públicas quanto particulares de pequeno e médio porte, que este trabalho ainda seja realizado manualmente por vários motivos: hábito; desconhecimento ou falta de habilidade com softwares pagos ou gratuitos; gosto pelo desafio ou por envolver custos que poderiam ser evitados. As variáveis do problema envolvem produtos entre as quantidades de professores, turmas, dias letivos na semana e aulas por dia, tornando o universo de possíveis soluções relativamente grande. Dependendo do método escolhido, o processo de busca de uma solução factível é desgastante, árduo e demanda considerável período de tempo normalmente escasso. O atendimento da disponibilidade dos dias em que ministram aulas é de extrema importância para os professores de pequenas escolas, que geralmente mantem outros vínculos empregatícios. É preciso que janelas e aulas isoladas sejam minimizadas e, sendo possível, evitadas. Neste contexto a presente pesquisa visa construir uma interface que receba os dados do problema e, após valida-los, seja capaz de fornecer uma solução ao problema que seja factível e na qual a quantidade de janelas seja mínima. O uso de meta-heurística baseada em Algoritmo Genético neste processamento se dá pela eficiência com que este método se aproxima de soluções com boa qualidade. Foram utilizados dados reais de duas escolas de ensino fundamental de pequeno porte de região de Curitiba-PR para validar os processos desenvolvidos. Inicialmente se conjecturou que reduzindo o número de janelas nas grades horárias dos professores se conseguiria um horário concentrado no mínimo de dias necessários, satisfazendo as restrições apresentadas. A redução de janelas ocorreu devido à penalização destas situações durante a execução da meta-heurística, favorecendo soluções que apresentaram as menores quantidades de janelas. Foram obtidos horários concentrados dentro de um dia letivo, porém dispersos na semana dos professores com maior disponibilidade de dias. Os resultados obtidos demonstram que a redução de janelas é importante, mas não é suficiente para minimizar a quantidade de dias de trabalho. Palavras-chaves: Scholar Timetabling Problem. Otimização. Meta-heurística. Algoritmo Genético.Abstract: The beginning of the school year is marked by a classic challenge for a pedagogical team: assembling a distribution of classes to the teachers, a scholar timetabling problem, by meeting needs presented by the teaching staff and ensuring that the weekly duration of each discipline is fully accomplished for the classes. In both public and private schools, small or medium, it is still common to do this task manually for several reasons: habit; unfamiliarity or lack of skill with paid or free software; a taste for challenge or avoiding unnecessary costs. The variables of the problem involve products between the numbers of teachers, classes, school days a week and classes per day, making the universe of possible solutions relatively large. Depending on the chosen method, the process of searching for a feasible solution is exhausting, difficult and demands a considerable period of time usually scarce. Satisfying the days' availability is of utmost importance for the small schools teachers, who usually maintain other employment relationships. It is required that idle slots and isolated classes be minimized and, if possible, avoided. In this context, the present research aims to build an interface that receives the issue data and, after validating them, is able to provide a feasible solution to the problem, with a minimal amount of idle slots. The use of a metaheuristic based on Genetic Algorithms in this processing is given by the efficiency with which this method approximates to solutions with good quality. Real data from two small primary schools in the region of Curitiba-PR were used to validate the developed processes. Initially, it was conjectured that, by reducing the number of idle slots in the teachers' schedules, it would be possible to get a schedule concentrated on the minimum days needed, satisfying the presented constraints. The reduction of idle slots occurred due to the penalty of these situations during the metaheuristic execution, favoring solutions that had the lowest amounts of slots. Timetables without slots were obtained with lessons concentrated within a school day, yet dispersed in the week of the teachers with greater availability. The obtained results show that the reduction of slots is important, but not sufficient to minimize the number of workdays. Key-words: Scholar Timetabling Problem. Optimization. Metaheuristics. Genetic Algorithm

Uma nova abordagem na resoluçăo do problema do caixeiro viajante /

Orientador: Sergio ScheerCo-orientadora: Maria Teresinha Arns SteinerTese (doutorado) - Universidade Federal do Paraná, Setores de Tecnologia e Cięncias Exatas, Programa de Pós-Graduaçăo em Métodos Numéricos em Engenharia. Defesa: Curitiba, 2005Inclui bibliografi