  We present a new method that investigates the evolutionary history of the
pulsating DB white dwarf GD358 using asteroseismology. This is done considering
the internal C/O profile, which describes the relative abundances of carbon and
oxygen from the core of the star to its surface. Different evolutionary
channels lead to the generation of different C/O profiles, and these affect the
pulsation periods. We used C/O profiles associated with white dwarfs that
evolved through binary evolution channels where the progenitor experienced one
or two episodes of mass loss during one or two common envelope (CE) phases, and
two profiles from single star evolution. We computed models using these
different profiles and used a genetic algorithm (GA) to optimize the search in
the parameter space in order to find the best-fit to the observed pulsation
periods. We used three-parameter models, adjusting the stellar mass, the
effective temperature, and the helium mass of the external layer. Our results
suggest that binary evolution profiles may provide a better match to the
pulsation periods of GD 358. The best-fit to the observations is obtained using
a profile related to an evolutionary history where two episodes of mass loss
happen during two CE phases. The best-fit model has a mass close to the mean
mass for DB white dwarfs found in various works, and a temperature consistent
with UV spectra obtained with the IUE satellite.
