Optimization photoionization models are computed for nine planetary nebulae with various metallicities with the aim of determining their chemical compositions. The algorithm used to compute the models is based on identifying best-fit values of the physical parameters of the nebulae by minimizing the χ2 residual for fits to the observed spectra of these objects. The reliability of the results is investigated. The abundances of He, C, N, O, Ne, Si, S, and Ar are derived, as well as the physical characteristics of the nebulae. The Y -Z dependences (where Y and Z are the mass abundances of helium and heavy elements, respectively) are analyzed for the planetary nebulae together with HII regions in blue compact dwarf galaxies. The primordial helium abundance, Yp = 0.2479 ± 0.0014, and dY/dZ = 2.99 ± 0.32 are determined, and found to be close to the corresponding values obtained using ionization correction factors.
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