A considerable number of astrometric binaries whose positions on the sky do
not obey the standard model of mean position, parallax and linear proper
motion, were observed by the Hipparcos satellite. Some of them remain
non-discovered, and their observational data have not been properly processed
with the more adequate astrometric model that includes nonlinear orbital
motion. We develop an automated algorithm based on "genetic optimization", to
solve the orbital fitting problem with no prior information about the orbital
elements is available (from, e.g., spectroscopic data or radial velocity
monitoring). We test this method on Hipparcos stars with known orbital
solutions in the catalog, and further apply it to stars with stochastic
solutions, which may be unresolved binaries. At a confidence level of 99%,
orbital fits are obtained for 65 stars, most of which have not been known as
binary. A few of the new probable binaries with A-type primaries with periods
444-2015 d are chemically peculiar stars, including Ap and \lambda Boo type.
The anomalous spectra of these stars are explained as admixture of the light
from the unresolved, sufficiently bright and massive companions. We estimate
the apparent orbits of four stars which have been identified as members of the
300 Myr-old UMa kinematic group. Another four new nearby binaries may include
low-mass M-type or brown dwarf companions. Similar astrometric models and
algorithms can be used for binary stars and planet hosts observed by SIM
PlanetQuest and Gaia