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The bootstrap method is one of the most widely used methods in literature for construction of confidence and prediction intervals. This paper proposes a new method for improving the quality of bootstrap-based prediction intervals. The core of the proposed method is a prediction interval-based cost function, which is used for training neural networks. A simulated annealing method is applied for minimization of the cost function and neural network parameter adjustment. The developed neural networks are then used for estimation of the target variance. Through experiments and simulations it is shown that the proposed method can be used to construct better quality bootstrap-based prediction intervals. The optimized prediction intervals have narrower widths with a greater coverage probability compared to traditional bootstrap-based prediction intervals.