Artificial neural networks are one of the most commonly used methods in machine learning. Performance of network highly depends on the learning method. Traditional learning algorithms are prone to be trapped in local optima and have slow convergence. At the other hand, nature-inspired optimization algorithms are proven to be very efficient in complex optimization problems solving due to derivative-free solutions. Addressing issues of traditional learning algorithms, in this study, an enhanced version of artificial bee colony nature-inspired metaheuristics is proposed to optimize connection weights and hidden units of artificial neural networks. Proposed improved method incorporates quasi-reflection-based learning and guided best solution bounded mechanisms in the original approach and manages to conquer its deficiencies. First, the method is tested on a recent challenging CEC 2017 benchmark function set, then applied for training artificial neural network on five well-known medical benchmark datasets. Further, devised algorithm is compared to other metaheuristics-based methods. The efficiency is measured by five metrics - accuracy, specificity, sensitivity, geometric mean, and area under the curve. Simulation results prove that the proposed algorithm outperforms other metaheuristics in terms of accuracy and convergence speed. The improvement of the accuracy over the other methods on different datasets are between 0.03% and 12.94%. The quasi-refection-based learning mechanism significantly improves the convergence speed of the original artificial bee colony algorithm and together with the guided best solution bounded, the exploitation capability is enhanced, which results in significantly better accuracy.