This paper will present a novel genetic-algorithm-based code (GASPED), developed for the analysis of fine features (e.g., satellite structure and line shifts) in X-ray spectra emitted by hot dense plasmas. The problem dependent modification of standard genetic-algorithm concepts allows efficient decomposition of spectra in concrete physical terms, such as resonance and intercombination lines, dielectronic satellites, or prospective nuclear transitions. Two examples of the code application demonstrate the proposed approach. High resolution K-shell spectra emitted from He- and Li-like Al ions immersed in dense, constrained-flow plasma are decomposed into individual pseudo-Voigt components, by using anticipatory theoretical knowledge of the satellite structure simulated by the multilevel collisional-radiative code (MARIA). Line shifts of the He-like resonance and intercombination line are deduced assuming the aggregate plasma-induced shifts of the parent lines and their satellites. The trend in the frequency shifts observed as a function of the variable plasma parameters qualitatively follows the theoretical predictions. The found variations of the exchange energy between the singlet and triplet levels provide a new impact for the line shift theories. The second example concerns the search for low-lying nuclear transitions in hot dense laser-produced plasmas. The spectra of highly ionized Ta are decomposed by combining the GASPED code with results of ab initio atomic data calculations performed by the RELAC code. Upper limits for observation of the controversial radiative decay of Ta nuclei at 6.238 eV are estimated.