Hyperbolic tangent function (HTF) is an intensity transformation used to improve the contrast of medical images from diverse modalities. Selection of the \(\alpha\) parameter determines the slope of the HTF and influences the quality of output images. An exhaustive framework comprising a metaheuristic search strategy termed bilateral search within iteratively narrowing space (BSINS) optimization algorithm and a fitness function termed cumulative information preservation and contrast enhancement index (CIPCEI) for automating the selection of the \(\alpha\) parameter of HTF employed for image contrast enhancement applications on MRI is proposed. At the ideal value of the \(\alpha\) located from the CIPCEI, the HTF produces enhanced MRI slices with improved contrast among the structures and minimum shift from the mean brightness of the actual MRI slices. The BSINS has faster convergence than the metaheuristic algorithms used in the literature for optimizing the \(\alpha\) parameter of the HTF, namely the tunicate swarm optimization algorithm and differential evolution.