## 1 Introduction
The application of neural networks shortened the computation time in the considered problem by more than 40%. Neural networks, trained and tested in advance with FE data almost instantly provide their precise prediction from a big set of candidate solutions, and a GA optimization procedure involving ANNs is thus highly efficient and robust. In the proposed technique, GA was included to solve the optimization task because functions that describe the dynamic parameters to be optimized have several variables and usually a great number of minima. GA ignores potential local minima and leads to the best solution. This paper presents the maximization of the fundamental natural frequency by determining the optimal fiber orientation in a cylindrical shell's layers of composite material. The lamination fiber angles are treated as constrained variables that are either continuous or discrete. In the context of improving anti-resonance performance, the maximization of the natural frequency of a structure is a primary task in engineering dynamics because it provides the optimal solution to the resonance problem for all external excitation frequencies between zero and the particular optimum fundamental eigenfrequency. Optimization with respect to higher-order eigenfrequencies produces a considerable gap between the specified excitation frequency and the adjacent lower and upper eigenfrequencies. In the offshore oil and gas exploitation industry, risers are indispensable components that are vulnerable to vortex-induced vibration. Vortex-induced vibration strictly depends on the natural frequencies of the risers, so there is a need for optimizing the design of fiber reinforced polymer composite risers by considering different laminate stacking sequences and different lamina thicknesses [14; 15]. This approach grants the possibility of avoiding resonance if external excitation frequencies are confined to a large interval with finite lower and upper limits [16]. The optimization of the layer stacking sequence of composite structures (plates, panels, cylinders, beams) for the maximization of their fundamental frequency has been analyzed by many authors. Using the weighted summation method, the authors in [11] presented a multi-objective optimization strategy for the optimal stacking sequence of laminated cylindrical panels with respect to the first natural frequency and critical buckling load. In order to improve the speed of the optimization process, ANNs were used to reproduce the behavior of the structure in both free vibration and buckling conditions. In [17], the authors reported the optimization of laminated cylindrical panels based on the fundamental natural frequency. In [18], a study of layer optimization was carried out for the maximum fundamental frequency of laminated composite plates under a combination of three classical edge conditions. The optimal stacking sequences of laminated composite plates were found by means of a GA and ANN procedure. The procedure successfully predicted the natural frequencies of the composite plates, and the predicted frequencies and optimal layered sequences corresponded with those of the Ritz-based layerwise optimization method. The usual goal in the design of vibrating structures is to avoid resonance of the structure in a given interval of external excitation frequencies. This was discussed in [16], in which the design objective was the maximization of specific eigenfrequencies and distances (gaps) between two consecutive eigenfrequencies of the structures. The results demonstrated that the creation of structures with multiple optimum eigenfrequencies is the rule rather than the exception in topology optimization of vibrating structures. The study emphasized that this feature needs special attention. The structural optimization problem of laminated composite materials with a reliability constraint was addressed in [19] by using GA and two types of ANNs.