This thesis is focused on identifying key aspects of mechanics graphs regarded by students and experts. It also contains observations of student's attention focused on each graph. This data was collected using eye tracking camera. 23 high school students and 14 experts participated in this research. Our group of experts contained graduate and post-graduate students as well as researchers from faculty of Mathematics and Physics at Charles University. Our results suggest that experts were able to memorize more information from each graph than high school students. Difference in focus on relevant parts of graphs was obvious from analyzing correct and incorrect answers of high school students and they consider axes and their labeling as the key parts of graphs in contrast to the students. Incorrectly answering students were more focused on parts with no relevance to the task in question. On the contrary, students with correct answers spent less time looking on non-relevant parts of graphs. Ideas of incorrectly answering students were mostly focused on wrong idea about graph as a sketch of real situation, or picture resembling physical situation.

Cette thèse comporte deux parties majeures : la première partie est dédiée à l'étude du problème sparse CARP déterministe où nous avons développé une transformation du sparse CARP en un sparse CVRP. La seconde est consacrée au problème sparse CARP avec coûts sous incertitude. Nous avons donné une formulation mathématique du problème en min-max. Cette modélisation a permis d'identifier le pire scénario pour le problème robuste. Deux approches algorithmiques ont été proposées pour une résolution approchée. / This dissertation consists of two main parts : in the first part, we study the detreministic capacitated arc routing problem over sparse underlying graphs wher we have developed a new transformation techniquevof sparse CARP into sparse CVRP. The second part is consecrated about the sparse CARP with travel costs uncertainty. We have given a mathematical formulation of the probleme in min-max. A worst scenario for the robust problem is then identified, and two algorithmic approaches are proposed to determine a solution of the studied problem.