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Bus driver rostering by hybrid methods based on column generation
Publication . Barbosa, Vítor; Respício, Ana Luísa do Carmo Correia, 1965-
Rostering problems arise in a diversity of areas where, according to the business and labor rules, distinct variants of the problem are obtained with different constraints and objectives considered. The diversity of existing rostering problems, allied with their complexity, justifies the activity of the research community addressing them. The current research on rostering problems is mainly devoted to achieving near-optimal solutions since, most of the times, the time needed to obtain optimal solutions is very high. In this thesis, a Bus Driver Rostering Problem is addressed, to which an integer programming model is adapted from the literature, and a new decomposition model with three distinct subproblems representations is proposed. The main objective of this research is to develop and evaluate a new approach to obtain solutions to the problem in study. The new approach follows the concept of search based on column generation, which consists in using the column generation method to solve problems represented by decomposition models and, after, applying metaheuristics to search for the best combination of subproblem solutions that, when combined, result in a feasible integer solution to the complete problem. Besides the new decomposition models proposed for the Bus Driver Rostering Problem, this thesis proposes the extension of the concept of search by column generation to allow using population-based metaheuristics and presents the implementation of the first metaheuristic using populations, based on the extension, which is an evolutionary algorithm. There are two additional contributions of this thesis. The first is an heuristic allowing to obtain solutions for the subproblems in an individual or aggregated way and the second is a repair operator which can be used by the metaheuristics to repair infeasible solutions and, eventually, generate missing subproblem solutions needed. The thesis includes the description and results from an extensive set of computational tests. Multiple configurations of the column generation with three decomposition models are tested to assess the best configuration to use in the generation of the search space for the metaheuristic. Additional tests compare distinct single-solution metaheuristics and our basic evolutionary algorithm in the search for integer solutions in the search space obtained by the column generation. A final set of tests compares the results of our final algorithm (with the best column generation configuration and the evolutionary algorithm using the repair operator) and the solutions obtained by solving the problem represented by the integer programming model with a commercial solver.
Dynamics for schrödinger evolution problems
Publication . Correia, Simão Fernandes, 1990-; Figueira, Mário, 1948-
In this thesis, we study some dynamical aspects related to the nonlinear Schrödinger equation (NLS) and some of its variants, such as the complex Ginzburg-Landau equation and the hyperbolic nonlinear Schrödinger equation. Our focus is the existence and stability of "special" solutions (which includes bound-states, spatial plane waves and so on). Part I is dedicated to the theory of ground-states for a system of weakly coupled nonlinear Schrödinger equations; Part II looks at three variants of the (NLS); Part III presents some new results for the (NLS).
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Fundação para a Ciência e a Tecnologia
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5876
Número da atribuição
UID/MAT/04561/2013