The paper analyzes the works on optimization of thermodynamic equations of heterogeneous equilibrium using a multi-objective genetic algorithm (MGA) for calculation and multi-3D modeling of liquidus surfaces, boundaries of stable and metastable states of solid solutions of chalcogenide systems YbTe–SnTe, SnTe–Sb₂Te₃, Bi₂Te₃–Sb₂Te₃–PbTe, SnSb₂Te₄, SnSb₄Sb₇, Tl₉SmTe₆–Tl₉BiTe₆ and Tl₉SmTe₆–Tl₈PbTe₃–Tl₉BiTe₆, BiI₃–Bi₂S₃–Bi₂Te₃  of interest for semiconductor technology, U–Nb alloys of interest as nuclear fuel for fast breeder reactors, H₂O-MMA (methyl methacrylate) and H₂O-furfural systems exhibiting heteroazeotropic behavior. Temperature-concentration dependences of the Gibbs energy of formation of solid solutions from binary compounds, as well as from ternary compounds, are determined using a subregular model of solutions of non-molecular compounds as applied to telluride systems. The uncertainty ranges of temperature and pressure for direct reduction of magnetite to free iron and oxidation of V⁺³ to V⁺³ in titanomagnetite concentrate granules by a mixture of natural gas and hydrogen are determined. The conditions for the precipitation process of aluminum hydroxide from aluminate solutions based on fuzzy logic theory are revealed.

doi.org/10.32737/0005-2531-2025-2-36-51