  White dwarf asteroseismology offers the opportunity to probe the structure
and composition of stellar objects governed by relatively simple physical
principles. The observational requirements of asteroseismology have been
addressed by the development of the Whole Earth Telescope, but the analysis
procedures still need to be refined before this technique can yield the
complete physical insight that the data can provide. We have applied an
optimization method utilizing a genetic algorithm to the problem of fitting
white dwarf pulsation models to the observed frequencies of the most thoroughly
characterized helium-atmosphere pulsator, GD 358. The free parameters in this
initial study included the stellar mass, the effective temperature, the surface
helium layer mass, the core composition, and the internal chemical profile. For
many years, astronomers have promised that the study of pulsating white dwarfs
would ultimately lead to useful information about the physics of matter under
extreme conditions of temperature and pressure. The optimization approach
developed in this dissertation has allowed us to finally make good on that
promise by exploiting the sensitivity of our models to the core composition. We
empirically determine that the central oxygen abundance in GD 358 is 84 +/- 3
percent. We use this value to place a preliminary constraint on the
C12(alpha,gamma)O16 nuclear reaction cross-section of S_300 = 295 +/- 15 keV
barns. We find a thick helium layer solution for GD 358 that provides a better
match to the data than previous fits, and helps to resolve a problem with the
evolutionary connection between PG 1159 stars and DBVs. [abridged]
