A notion of morphological modularity is often implicit in systematics and paleontology. Indeed, the perception of morphological modularity is manifested in the very existence of anatomy, comparative anatomy, and taxonomy as disciplines, and provides a rational basis for treating organic diversity as a combinatorial problem in development.

[pt] Com o objetivo de desenvolver um sistema de apoio à decisão na área de manutenção embarcada, este trabalho apresenta um modelo para problemas de ordem com restrições: CPSO(mais). Este modelo é a combinação de dois modelos da literatura, o PSO(mais), que apresenta bons resultados em problemas com restrições, e o CPSO, que introduz as modificações necessárias para aplicar o PSO em problemas de ordem. O modelo proposto foi adaptado para resolver o complexo problema de definir a melhor sequência de atividades embarcadas e funcionários alocados, de forma a maximizar o lucro da prestadora de serviço no período de três meses respeitando todas as restrições de prazo de conclusão dos serviços e restrições específicas do segmento offshore. Para avaliar o desempenho deste novo modelo na resolução do problema proposto, duas variantes do CPSO(mais) foram avaliadas frente ao modelo da literatura, CPSO, em seis casos de simulação propostos. Conclui-se pelos resultados das simulações que o modelo CPSO(mais) com inicialização reduzida destaca-se dos demais avaliados por apresentar um tempo de execução moderado e com soluções melhores que as dos demais. / [en] In order to develop an offshore maintenance support system, this work presents a model for constrained combinatorial problems: CPSO(plus). This model is a combination of two models, the PSO(plus), which presented good results in problems with constrains, and the CPSO, which is an adaptation of PSO for application in combinatorial problems. The proposed model has been adapted to solve the complex problem of defining the best sequence of offshore activities and allocated staff so as to maximize service provider profitability within three months while respecting all service completion time constraints and specific offshore work constraints. To evaluate the performance of this new model in solving the proposed problem, two CPSO(plus) variants were evaluated against the literature model, CPSO, in six proposed simulation cases. It is concluded from the results of the simulations that the CPSO(plus) model with reduced initialization outperforms other evaluated models with respect to execution time and solutions to given problem.

O presente trabalho propõe resolver o clássico problema combinatorial conhecido como problema do caixeiro viajante. Foi usado no sistema de otimização de busca do menor caminho uma rede neural recorrente. A topologia de estrutura de ligação das realimentações da rede adotada aqui é conhecida por rede recorrente de Wang. Como regra de treinamento de seus pesos sinápticos foi adotada a técnica de perturbação simultânea com aproximação estocástica. Foi elaborado ainda uma minuciosa revisão bibliográfica sobre todos os temas abordados com detalhes sobre a otimização multivariável com perturbação simultânea. Comparar-se-á também os resultados obtidos aqui com outras diferentes técnicas aplicadas no problema do caixeiro viajante visando propósitos de validação. / This work proposes to solve the classic combinatorial optimization problem known as traveling salesman problem. A recurrent neural network was used in the system of optimization to search the shorter path. The structural topology linking the feedbacks of the network adopted here is known by Wang recurrent network. As learning rule to find the appropriate values of the weights was used the simultaneous perturbation with stochastic approximation. A detailed bibliographical revision on multivariable optimization with simultaneous perturbation is also described. Comparative results with other different techniques applied to the traveling salesman are still presented for validation purposes.

O presente trabalho propõe resolver o clássico problema combinatorial conhecido como problema do caixeiro viajante. Foi usado no sistema de otimização de busca do menor caminho uma rede neural recorrente. A topologia de estrutura de ligação das realimentações da rede adotada aqui é conhecida por rede recorrente de Wang. Como regra de treinamento de seus pesos sinápticos foi adotada a técnica de perturbação simultânea com aproximação estocástica. Foi elaborado ainda uma minuciosa revisão bibliográfica sobre todos os temas abordados com detalhes sobre a otimização multivariável com perturbação simultânea. Comparar-se-á também os resultados obtidos aqui com outras diferentes técnicas aplicadas no problema do caixeiro viajante visando propósitos de validação. / This work proposes to solve the classic combinatorial optimization problem known as traveling salesman problem. A recurrent neural network was used in the system of optimization to search the shorter path. The structural topology linking the feedbacks of the network adopted here is known by Wang recurrent network. As learning rule to find the appropriate values of the weights was used the simultaneous perturbation with stochastic approximation. A detailed bibliographical revision on multivariable optimization with simultaneous perturbation is also described. Comparative results with other different techniques applied to the traveling salesman are still presented for validation purposes.

This diploma thesis deals with combinatorics in primary school teaching methods. The theoretical part is focused on characterisation of mathematical field of combinatorics, briefly describes it's historical evolution and basic types of combinatorial problems. This theoretical knowledge is further supplemented by an analysis of utilization rate of combinatorics in curiculative documents, selected textbooks and mathematical contests for primary school pupils. An essential part of the theoretical part of the work are chapters dealing with solving combinatorial problems. The practical part is based on research of solving combinatorial proceses on tasks for primary school pupils. KEYWORDS Combinatorics, combinatorial problem, typology of combinatorial problems, primary school pupil, solving peoceses, analysis of pupils'solving processes, number of solutions

Cette thèse s'intéresse à la résolution de très grands problèmes d'optimisation combinatoire stochastique. Les recherches sont appliquées au problème de planification des arrêts pour rechargement des centrales nucléaires. Compte-tenu de la part prépondérante de celles-ci dans le mix-électrique, ce problème structure fortement la chaîne de management d’énergie d'EDF. Une première partie propose une formulation étendue bi-niveau dans laquelle les décisions de premier niveau fixent les plannings d’arrêt et des profils de production des centrales, et celles de second niveau évaluent le coût de satisfaction de la demande associé. Cette formulation permet la résolution à l'optimum d'instances industrielles déterministes par un solveur en PLNE. Dans le cas stochastique, une telle résolution directe du problème n'est plus possible. Nous proposons une formulation permettant d’en résoudre la relaxation linéaire par génération de colonnes et de coupes, correspondant respectivement aux reformulations de Danzig-Wolfe du premier niveau et de Benders du second. Une phase heuristique permet ensuite de déterminer des solutions entières de bonne qualité pour des instances, jusqu'à une cinquantaine de scénarios représentatifs de l’incertitude sur les données. L’apport de l’approche est estimé en utilisant les outils industriels exploités par EDF pour évaluer les plannings. Une seconde partie porte sur l'intégration de méthodes d'optimisation robuste pour la prise en compte d’aléas sur la disponibilité des centrales. Nous nous plaçons dans un cadre où les recours possibles sur les dates d'arrêts ne sont pas exercés. Nous comparons des méthodes bi-objectif et probabiliste permettant de rendre le planning robuste pour les contraintes opérationnelles dont la relaxation est envisageable. Pour les autres, nous proposons une méthode basée sur un budget d’incertitude. Cette méthode permet de renforcer la stabilité du planning en limitant les besoins de réorganisation futurs. La prise en compte d’une loi de probabilité de l’aléa permet d’affiner le contrôle du prix de cette robustesse. / The purpose of this Ph.D. thesis is to study optimization techniques for large-scale stochastic combinatorial problems. We apply those techniques to the problem of scheduling EDF nuclear power plant maintenance outages, which is of significant importance due to the major part of the nuclear energy in the French electricity system. We build on a two-stages extended formulation, the first level of which fixes nuclear outage dates and production profiles for nuclear plants, while the second evaluates the cost to meet the demand. This formulation enables the solving of deterministic industrial instances to optimality, by using a MIP solver. However, the computational time increases significantly with the number of scenarios. Hence, we resort to a procedure combining column generation of a Dantzig-Wolfe decomposition with Benders’ cut generation, to account for the linear relaxation of stochastic instances. We then obtain integer solutions of good quality via a heuristic, up to fifty scenarios. We further assume that outage durations are uncertain and that unexpected shutdowns of plants may occur. We investigate robust optimization methods in this context while ignoring possible recourse on power plants outage dates. We report on several approaches, which use bi-objective or probabilistic methods, to ensure the satisfaction of constraints which might be relaxed in the operating process. For other constraints, we apply a budget uncertainty-based approach to limit future re-organizations of the scheduling. Adding probabilistic information leads to better control of the price of the robustness.