This thesis addresses two important classes of optimization : multiobjective optimization and bilevel optimization. The investigation concerns their solution methods, applications, and possible links between them. First of all, we develop a procedure for solving Multiple Objective Linear Programming Problems (MOLPP). The method is based on a new characterization of efficient faces. It exploits the connectedness property of the set of ideal tableaux associated to degenerated points in the case of degeneracy. We also develop an approach for solving Bilevel Linear Programming Problems (BLPP). It is based on the result that an optimal solution of the BLPP is reachable at an extreme point of the underlying region. Consequently, we develop a pivoting technique to find the global optimal solution on an expanded tableau that represents the data of the BLPP. The solutions obtained by our algorithm on some problems available in the literature show that these problems were until now wrongly solved. Some applications of these two areas of optimization problems are explored. An application of multicriteria optimization techniques for finding an optimal planning for the distribution of electrical energy in Cameroon is provided. Similary, a bilevel optimization model that could permit to protect any economic sector where local initiatives are threatened is proposed. Finally, the relationship between the two classes of optimization is investigated. We first look at the conditions that guarantee that the optimal solution of a given BPP is Pareto optimal for both upper and lower level objective functions. We then introduce a new relation that establishes a link between MOLPP and BLPP. Moreover, we show that, to solve a BPP, it is possible to solve two artificial M0PPs. In addition, we explore Bilevel Multiobjective Programming Problem (BMPP), a case of BPP where each decision maker (DM) has more than one objective function. Given a MPP, we show how to construct two artificial M0PPs such that any point that is efficient for both problems is also efficient for the BMPP. For the linear case specially, we introduce an artificial MOLPP such that its resolution can permit to generate the whole feasible set of the leader DM. Based on this result and depending on whether the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining efficient solutions are presented

Cette thèse aborde l'optimisation multicritère et l'optimisation à deux niveaux. L'investigation porte principalement sur les méthodes, les applications et les liens possibles entre les deux classes d'optimisation. Premièrement, nous développons une méthode de résolution des problèmes d'optimisation linéaire multicritère. Pour ce faire, nous introduisons une nouvelle caractérisation des faces efficaces et exploitons le résultat selon lequel l'ensemble des tableaux idéaux associés aux sommets extrêmes dégénérés est connexe. Ceci a permis de développer une approche de parcours de sommet extrême pour générer l'ensemble des solutions efficaces. Dans le même ordre d'idée, nous développons une méthode de résolution des problèmes linéaires à deux niveaux. L'approche est basée sur un résultat, que nous avons formalisé et démontré, qui stipule que la solution optimale du problème linéaire à deux niveaux est l'un des sommets extrêmes du domaine admissible. L'implémentation de l'approche a permis de démontrer qu'il existait dans la littérature des problèmes dont les solutions connues étaient fausses. Deuxièmement, en termes d'applications, nous construisons un modèle d'optimisation multicritère pouvant être exploité dans l'optique d'une planification optimale de la distribution de l'énergie électrique au Cameroun. Nous proposons aussi, à partir d'un modèle d'optimisation à deux niveaux, une technique dont la mise en œuvre par l'État pourrait permettre de protéger les industries locales de la concurrence des firmes internationales. Enfin, nous étudions l'interrelation entre l'optimisation multicritère et l'optimisation à deux niveaux. Tout d'abord, nous tirons des conditions de Pareto-optimalité des solutions du problème à deux niveaux. Ensuite, nous montrons qu'il est possible d'obtenir une solution optimale de certaines classes de problèmes d'optimisation à deux niveaux en résolvant deux problèmes particuliers d'optimisation multicritère. Puis, nous étudions le cas de problème à deux niveaux dans lequel chaque décideur possède plusieurs fonctions objectifs conflictuelles, en nous focalisant sur le cas linéaire. Après, nous construisons un problème artificiel d'optimisation linéaire multicritère dont l'ensemble des solutions efficaces est égal au domaine des solutions admissibles du problème du leader. Pour terminer, nous utilisons ce résultat pour proposer deux approches de résolution dépendant chacune des aspirations du leader / This thesis addresses two important classes of optimization : multiobjective optimization and bilevel optimization. The investigation concerns their solution methods, applications, and possible links between them. First of all, we develop a procedure for solving Multiple Objective Linear Programming Problems (MOLPP). The method is based on a new characterization of efficient faces. It exploits the connectedness property of the set of ideal tableaux associated to degenerated points in the case of degeneracy. We also develop an approach for solving Bilevel Linear Programming Problems (BLPP). It is based on the result that an optimal solution of the BLPP is reachable at an extreme point of the underlying region. Consequently, we develop a pivoting technique to find the global optimal solution on an expanded tableau that represents the data of the BLPP. The solutions obtained by our algorithm on some problems available in the literature show that these problems were until now wrongly solved. Some applications of these two areas of optimization problems are explored. An application of multicriteria optimization techniques for finding an optimal planning for the distribution of electrical energy in Cameroon is provided. Similary, a bilevel optimization model that could permit to protect any economic sector where local initiatives are threatened is proposed. Finally, the relationship between the two classes of optimization is investigated. We first look at the conditions that guarantee that the optimal solution of a given BPP is Pareto optimal for both upper and lower level objective functions. We then introduce a new relation that establishes a link between MOLPP and BLPP. Moreover, we show that, to solve a BPP, it is possible to solve two artificial M0PPs. In addition, we explore Bilevel Multiobjective Programming Problem (BMPP), a case of BPP where each decision maker (DM) has more than one objective function. Given a MPP, we show how to construct two artificial M0PPs such that any point that is efficient for both problems is also efficient for the BMPP. For the linear case specially, we introduce an artificial MOLPP such that its resolution can permit to generate the whole feasible set of the leader DM. Based on this result and depending on whether the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining efficient solutions are presented