This study aims to answer whether a heuristic that trades cycles between the tours in a solution would show good results when trying to solve the Weighted k-Chinese Postman Problem for undirected graphs, of varying size, representing neighbourhoods in Sweden.A tabu search heuristic was implemented with each iteration consisting of giving a cycle from the most expensive tour to the cheapest. The heuristic performed increasingly well for graphs of increasing size, although the solution quality decreased when increasing the number of tours to be used in the solution. It is suspected that the cause for this behavior is due to the heuristic only giving cycles from the most expensive tour, not considering trading cycles from other tours in the solution. It is believed that a heuristic considering more than only the most expensive tour when trading cycles would produce even better solutions.

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.