Decision theory: multicriteria techniques in multilevel optimization

The book addresses two important classes of optimization: multiobjective optimization and bi-level optimization. First, we develop a procedure for solving Multiple Objective Linear Programming. The method is based on a new characterization of efficient faces. It's exploits the connectedness property of the set of ideal tableaux associated to degenerate points in case of degeneracy. We also develop an approach for solving Bilevel Linear Programming Problems. It is based on the result that an optimal solution of the problem is reachable at an extreme point of the underlying region. Some applications of these two areas of optimization techniques are explored. An application of multicriteria optimization approach for finding an optimal planning for the distribution of electrical energy in Cameroon is provided. Similarly, 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 proposed for instance new relations between the solutions of the two classes of optimization problems.