Abstract:
Adaptive partitioning algorithms, works on the basis of a successive reduction of the initial feasible region, in such away to select each time the sub-region that may contain the global optimum of a non convex problem. In this thesis we propose an approach to improving the performances of an adaptive partitioning algorithm. The main idea developed here, is to use the information given a set of the best individuals in a given candidate population solution to enhance the algorithm speed of convergence and precision. The process implemented consists in building sub-regions in dynamic manner guided by the the best individuals, where the region that is more probably containing the global optimum will be selected for repartitioning farther more. This construction uses the inclusion propriety of interval analysis, where the integration of such methods in the proposed algorithms permit improving in a considerable way their convergence. A number of adaptive partitioning algorithms were developed, and most of them are based on a new technique which we call ’the generalized circular design’. these algorithms have the objective to reducing the time needed to attain the a near neighbor of the global optimum. We proposed also, a new technique based on reducing the order of the optimization problem. This problem is transformed to an other problem with `a virtual representation of second order, where optimizing in space of order two is much better and easier. Hence, the obtained solution is transformed again to its original order, in order to obtain the final solution. The proposed algorithms in this thesis, were tested with success in different problems of the litterateur, Physics, Mechanics and the diffusive pseudo invariant control. These algorithms permitted to find with certitude a near neighborhood of the global optimum.
