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  • A multiobjective genetic algorithm for the class/teacher timetabling problem
    Publication . Carrasco, Marco Paulo; Pato, Margarida Vaz
    The drawing up of school timetables is a slow, laborious task, performed by people working on the strength of their knowledge of resources and constraints of a specific institution. This paper begins by presenting the timetabling problems that emerge in the context of educational institutions. This is followed by a description of the basic characteristics of the class/teacher timetabling problem. Timetables are considered feasible provided the so-called hard constraints are respected. However, to obtain high-quality timetabling solutions, other conditions should be satisfied in this case — those of soft constraints — which impose satisfaction of a set of desirable conditions for classes and teachers. A multiobjective genetic algorithm was proposed for this timetabling problem, incorporating two distinct objectives. They concern precisely the minimization of the violations of both types of constraints, hard and soft, while respecting the two competing aspects — teachers and classes. A brief description of the characteristics of a genetic multiobjective metaheuristic is presented, followed by the nondominated sorting genetic algorithm, using a standard fitness-sharing scheme improved with an elitist secondary population. This approach represents each timetabling solution with a matrix—type chromosome and is based on special-purpose genetic operators of crossover and mutation developed to act over a secondary population and a fixed-dimension main population of chromosomes. The paper concludes with a discussion of the favorable results obtained through an application of the algorithm to a real instance taken from a university establishment in Portugal.
  • Skill development patterns and their impact on re-employability : evidence for Portugal
    Publication . Fernandes, Graça Leão; Passos, José; Lopes, Margarida Chagas
    Our main objective is to assess the impact upon reemployment probabilities of school and/or vocational training attendance during unemployment spells. According to Weiss’ (1986) model return to schooling or training, while unemployed, should have an impact on reemployment probabilities since skill developments not only prevent obsolescence but also contribute to human capital growth. We use duration models to assess the impact of skill dynamics on life cycle trajectories, namely on the probability of getting a job after an unemployment spell. The dataset used for estimation was selected from the Portuguese quarterly employment surveys (Inquérito ao Emprego) for the period between the 3rd quarter of 2002 and the 4th quarter of 2003. We present estimates for the Weibull, the Cox proportional hazard (PH) and Prentice and Gloeckler (1978) models assuming continuous-time and discrete-time specifications. There is no much difference in the estimates from these specifications and they seem to confirm that leaving unemployment becomes easier and/or unemployment spells smaller whenever education and/or training are present to compensate for qualifications obsolescence, all other things being equal (ceteris paribus). We end up with some policy implications that might get support from the present as well as future results of this research.