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Multi-objective parametric optimization problem is presented for overwrapped composite pressure vessels under internal pressure for storage and heating water. It is solved using the developed iterative optimization algorithm. Optimal values of design parameters for the vessel are obtained by varying the set of parameters for composite layers, such as the thickness of layers and radii of polar openings, which influence the distribution of fiber angles along the vessel. The suggested optimization methodology is based on the mechanical solution for composite vessels and the satisfaction of the main failure criteria. An innovative approach lies in the possibility of using the developed optimization methodology for designing vessels with non-symmetrical filament winding, which have unequal polar openings on the domes. This became possible due to the development of a special numerical mechanical finite element model of a composite vessel. A specific Python program provides the creation of a model and controls the exchange of data between the modules of the iterative optimization process. The numerical model includes the determination of the distribution of fiber angles on the domes and cylindrical part of the vessel as well as changes in layer thicknesses. The optimization problem solution is provided using a Multi-Island Genetic Algorithm, this type of method showed its efficiency for such applications, by allowing to avoid local solutions. Thus, optimal parameters of a composite vessel were found by minimizing composite mass and thickness and maximizing the strain energy. Test solutions using the developed methodology are presented for three types of composite materials to evaluate their possibility for integration into the vessel design model.