Étude et mise en œuvre d’algorithmes d’optimisation pour résoudre certaines classes de problèmes pratiques

Abstract

In this thesis, we focused on a very interesting subject of application namely: the study and implementation of optimization algorithms to solve some classes of practical problems such as transport problems with capacity in four indices. Initially the problem of transport is studied in a context of linear programming with certain particularities. We call on at the same time to mathematical notions of economy, convex analysis and operational research. We obtained original results by proposing an effective method to solve the degenerate problems. Furthermore, we are interested in non-convex optimization problems. In order to solve this type of problem we proposed an approach which consists in building several quadratic functions into pieces instead of a single quadratic underestimating the objectives function. The results are encouraging and support the assertion in some cases such as quadratic is preferable to another. The study algorithmic of the method gave rise to an encouraging report. The led study is the case of one variable. In order, to generalize this study in the case of several variables while preserving the advantages required, an effective combination of the Alienor method with the branch and bound technic was developed successfully. We have obtained satisfactory results. They show that this method is efficient compared to other current methods.