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We address the window design problem of linear arrays to be used in wide-band beamforming systems. During last decades, stochastic optimization algorithms have proven to be very efficient in optimal beamforming synthesis, but most research interest has focused on linear and two-dimensional arrays under narrow-band excitation. In the present paper, we introduce a general approach, based on the simulated annealing optimization algorithm, to design uniformly spaced wide-band arrays that generate low side-lobe level beam patterns. The effectiveness of different beam pattern formulations is evaluated within the proposed framework; we also consider three different methods to control the side-lobe level, yielding different array performances. Moreover, we investigate the influence of the frequency bandwidth on the optimized beam patterns.