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New computer algorithms for finding D-optimal designs of stimulus sequence for functional magnetic resonance imaging (MRI) experiments are proposed. Although functional MRI data are commonly analysed by linear models, the construction of a functional MRI design matrix is much more complicated than in conventional experimental design problems. Inspired by the widely used exchange algorithm technique, our proposed approach implements a greedy search strategy over the vast functional MRI design space for a D-optimal design. Compared with a recently proposed genetic algorithm, our algorithms are superior in terms of computing time and achieved design efficiency in both single-objective and multiobjective problems. In addition, the algorithms proposed are sufficiently flexible to incorporate a constraint that requires the exact number of appearances of each type of stimulus in a design. This realistic design issue is unfortunately not well handled by existing methods.

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