Abstract EN:

The global solution of minimization problems is of great practical importance and this is one of the reason why evolutionary algorithms received a tremendous interest in recent years. However, the main difficulties with these algorithms remain their computational time, their lack of precision and their slow convergence. The general idea of this work is to propose a new class of algorithms making it possible to improve the globale and local methods of optimization already existing. We present a method basing itself on the determination of ' good' initial conditions. Many optimization algorithms can be viewed as discrete forms of Cauchy problems for a system of ordinary differential equations in the space of control parameters. We will see that if one introduces an extra information on the infimum, solving global optimization problems using these algorithms is equivalent to solving Boundary Value Problems for the same equations. A motivating idea is therefore to apply algorithms solving Boundary Value Problems to perform this global optimization. We illustrate the previous ingredients through various benchmark and industrial optimization problems