## 1 Introduction
The optimization process was performed using GA, and a Multilayer Perceptron or Radial Basis ANNs were applied to overcome high computational costs. This methodology can be used without loss of accuracy and with large computational time-savings (even when dealing with nonlinear behavior). As a new concept, a Layerwise Optimization Approach (LOA) to optimizing vibration behavior for the maximum natural frequency of laminated composite plates was proposed in [20]. As design variables, the fiber orientation angles in all layers were selected, and the search for the optimum solution in N-dimensional space was replaced by N repetitions of the optimization, with each repetition in one-dimensional space. This idea is based on the physical consideration of bending plates, during which the outer layer has a greater influence on the structure stiffness than the inner layer and is more important in the determination of the natural frequency. The Layerwise Optimization (LO) scheme was also used in [21] to determine the optimum fiber orientation angles for the maximum fundamental frequency of cylindrically curved laminated panels under general edge conditions. In [22], differential evolution optimization was used to find stacking sequences for the maximization of the natural frequency of symmetric and asymmetric laminates. Optimized stacking sequences for eight-ply asymmetric laminates were presented. The authors in [23] dealt with the maximization of the fundamental frequency of laminated plates and cylinders by finding the optimal stacking sequence for symmetric and balanced laminates with neglected bending-twisting and torsion-curvature couplings. [PERSON] et al. [24] introduce a combined method to obtain the maximum fundamental frequency of thick laminated composite plates by finding the optimum fiber orientation. To find the optimum fiber orientation of a thick plate, a mixed implementable evolutionary algorithm was used, and the particle swarm optimization (PSO) method was added to improve the specified percent of the GA population. Excellent reviews of techniques applied to the optimization of stacking sequence are given in [7; 25]. The use of ANNs in optimization problems in civil engineering have been documented in several other publications. In the vast majority of them, ANNs were applied to reduce the time-consuming evaluations of objective functions that occur in iterative global search algorithms, such as GAs or other evolution strategies [26; 27; 28]. The authors in [27] examined the application of ANNs to reliability-based structural optimization of large-scale structural systems. In [26], a critical assessment of three metaheuristic optimization algorithms--differential evolution, harmony search, and particle swarm optimization--was used to find the optimum design of real-worldstructures. Furthermore, a neural network-based prediction scheme of the structural response, which is required to assess the quality of each candidate design during the optimization procedure, was introduced. In [28], ANN approximation of the limit-state function was proposed in order to find the most efficient methodology for performing reliability analysis in conjunction with the performance-based optimum design under seismic loading. The non-uniqueness of the optimum design of cylindrical shells for vibration requirements was presented in [29], and its implications were discussed in depth. Authors have shown that the design optimization of cylindrical shells for modal characteristics is often non-unique. In the above-mentioned paper, some selected issues, such as the new mode sequence, mode crossing, repeated natural frequencies, and stationary modes, were demonstrated and discussed. The numerical results were compared with the analytically obtained ones. This paper presents a novel method for the maximization of eigenfrequency gaps around external excitation frequencies through stacking sequence optimization in laminated structures.