Recently, a new optimization procedure that combines the power of artificial neural-networks with the versatility of the genetic algorithm ͑GA͒ was introduced. This method, called neural-network-assisted genetic algorithm ͑NAGA͒, uses a neural network to restrict the search space and it is expected to speed up the solution of global optimization problems if some previous information is available. In this paper, we have tested NAGA to determine the ground-state geometry of Si n (10рnр15) according to a tight-binding total-energy method.Our results indicate that NAGA was able to find the desired global minimum of the potential energy for all the test cases and it was at least ten times faster than pure genetic algorithm.

ABSTRACT:To represent the solution of a differential equation by an artificial neural network (ANN) was an idea introduced by Lagaris. Sugawara applied this concept to solve Schrödinger's equation for select systems. We have submitted their method to a new kind of application. Here, for the first time, the approach is applied to the equations derived from density functional theory (DFT). At first, we have tested the procedure for two simple systems: the double harmonic oscillator and the hydrogen atom. The ANN solutions obtained for these simple systems reproduced the analytical results easily. Next, we have moved to the Tomas-Fermi theory and the Kohn-Sham formulation of DFT. In order to show the feasibility of the ANN representation of electronic density, we have solved the Hooke model-atom and two light atoms: helium and lithium. The ANN results match well with the analytical solution to the Hooke model-atom and with the numerical solutions for helium and lithium.

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We have compared the recently introduced generalized simulated annealing ͑GSA͒ with conventional simulated annealing ͑CSA͒. GSA was tested as a tool to obtain the ground-state geometry of molecules. We have used selected silicon clusters (Si n , nϭ4 -7,10) as test cases. Total energies were calculated through tightbinding molecular dynamics. We have found that the replacement of Boltzmann statistics ͑CSA͒ by Tsallis's statistics ͑GSA͒ has the potential to speed up optimizations with no loss of accuracy. Next, we applied the GSA method to study the ground-state geometry of a 20-atom silicon cluster. We found an original geometry, apparently lower in energy than those previously described in the literature.