Images captured using computed tomography and magnetic resonance angiography are used in the examination of the abdominal aorta and its branches. The examination of all clinically relevant branches simultaneously in a single 2-D image without any misleading overlaps facilitates the diagnosis of vascular abnormalities. This problem is called uncluttered single-image visualization (USIV). We can solve the USIV problem by assigning energy-based scores to visualization candidates and then finding the candidate that optimizes the score; this approach is similar to the manner in which the protein side-chain placement problem has been solved. To obtain near-optimum images, we need to explore the energy space extensively, which is often time consuming. This paper describes a method for exploring the energy space in a massively parallel fashion using graphics processing units. According to our experiments, in which we used 30 images obtained from five patients, the proposed method can reduce the total visualization time substantially. We believe that the proposed method can make a significant contribution to the effective visualization of abdominal vascular structures and precise diagnosis of related abnormalities.