In this article, we propose an efficient approach to find optimal experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). We consider multiple objectives, including estimating the hemodynamic response function (HRF), detecting activation, circumventing psychological confounds and fulfilling customized requirements. Taking into account these goals, we formulate a family of multi-objective design criteria and develop a genetic-algorithm-based technique to search for optimal designs. Our proposed technique incorporates existing knowledge about the performance of fMRI designs, and its usefulness is shown through simulations. Although our approach also works for other linear combinations of parameters, we primarily focus on the case when the interest lies either in the individual stimulus effects or in pairwise contrasts between stimulus types. Under either of these popular cases, our algorithm outperforms the previous approaches. We also find designs yielding higher estimation efficiencies than m-sequences. When the underlying model is with white noise and a constant nuisance parameter, the stimulus frequencies of the designs we obtained are in good agreement with the optimal stimulus frequencies derived by Liu and Frank, 2004, NeuroImage 21: 387-400. In addition, our approach is built upon a rigorous model formulation.
