Genetic algorithm approach to calculation of geometric configurations of 2D clusters of uniformly charged classical particles

The genetic algorithms in the variant developed earlier and in that improved by the mechanism of niches have been exploited in the analysis of global and local minima of the potential energy depending either on the inverse distance between particles (as in Coulomb interactions) or on the logarithm of this distance. The number N   of point-charge particles is finite and they are confined by the parabolic potential. Solutions of the optimization problems yield for 9⩽N⩽309⩽N⩽30 the ground-state configurations and a number of the metastable configurations as well as some saddle points. For the model with the logarithmic interactions, the new ground-state configuration is found for N=20N=20, whereas for the Coulomb model, some new configurations, observed earlier in the molecular dynamics simulations, are determined.