MRI (magnetic resonance imaging) is an important modern imaging modality due, in part, to its variety of contrast mechanisms and control parameters. However, this same wealth of control and contrast mechanisms poses a difficult problem for the design of MRI acquisition strategies. To date, most sequence design has been accomplished using experience and heuristic techniques. Despite the advances made in the field using these strategies, they are inherently limited by the skill of the designer. Many individuals who have a sequence-design need lack the necessary experience, and even experts may develop sub-optimal protocols. In addition, some areas of MRI, such as k-space trajectories, seem to offer advantages, but are still poorly understood even by the experts. In order to overcome these limitations it would be beneficial to use modern optimization algorithms in the design of acquisition techniques. To date, such optimal design has been quite limited in both objectives and parameters, and has led to techniques with limited benefit and applicability. This work overcomes these limitations by investigating a variety of algorithms and applications that should prove important in MRI. First, an optimally precise protocol for DCE-MRI (dynamic contrast enhanced MRI) was developed. Second, a software-based fluoroscopic gridding-reconstruction technique was developed. This makes a variety of pulse sequences, such as spiral imaging, available for iMRI (interventional magnetic resonance imaging) applications and is a necessary step for the remainder of this work. Third, time-optimal k-space trajectories were developed using the calculus of variations and multi-objective GAs (genetic algorithms) were used to develop optimal trajectories with respect to time, aliasing energy, flow-artifact energy, and off-resonance artifact energy. Fourth, these trajectories were tested for improvements in image quality using both objective image-quality measures for experimental phantom images and subjective image-quality measures for in-vivo images. Finally, the multi-objective algorithms were adapted to optimize images acquired using rectilinear sequences with respect to acquisition speed, resolution, and BW (bandwidth). The accomplishment of these goals resulted in improvements for several MRI acquisition techniques and also resulted in the development of techniques that should have wider and more general utility for obtaining similar improvements for other MRI techniques.