Berlin 2012 – wissenschaftliches Programm
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MM: Fachverband Metall- und Materialphysik
MM 8: Computational Materials Modelling II - Methods
MM 8.5: Vortrag
Montag, 26. März 2012, 12:45–13:00, TC 006
A novel minimum search method for complex optimization problems — •Julian Hirschfeld and Hans Lustfeld — Forschungszentrum Jülich, IAS-1 and PGI-1, Jülich, Germany
Optimization is essential in many scientific and economical areas, as well as in the development of products. In many cases the optimization problem is too complex to be tackled by simple straight forward calculations or by trial and error. The reason is the too large phase space of the optimization problem and a rough potential surface with too many local minima. To find the global minimum, or at least a representative one, there are methods like simulated annealing, which has the chance to escape local minima, or the genetic algorithm, which changes the configurations by combining subsets of different deep minima. The chance to get stuck in a local minimum or to escape is proportional to the depth of the minimum in these methods.
Here we present a new method, which is complementary to the established ones. The chance to get stuck in a local minimum or to escape is independent of the minimum’s depth but depends on the minimum’s attractor size. Therefore, it can overcome local minima and high barriers equally well. Even though it does not get stuck in local minima of small attractor size, it is especially advantageous when searching for a minimum with a small basin of attraction. We successfully applied the method to find the ground states of the phosphorus P4 and P8 molecules as well as the arsenic As4 and As8 molecules. In the case of P8 we were able to find a new stable configuration.