Important insights into many data science problems that are traditionally analyzed via statistical models can be obtained by re-formulating and evaluating within a large-scale optimization framework. However, the theoretical underpinnings of the statistical model may shift the goal of the decision space traversal from a traditional search for a single optimal solution to a traversal with the purpose of yielding a set of high quality, independent solutions. We examine statistical frameworks with astronomical decision spaces that translate to optimization problem but are challenging for standard optimization methodologies. We address the new challenges by designing a hybrid metaheuristic with specialized intensification and diversification protocols in the base search algorithm. Our algorithm is extended to the high performance computing realm using the Stampede2 supercomputer where we experimentally demonstrate the effectiveness of our algorithm to utilize multiple processors to collaboratively hill climb, broadcast messages to one another regarding landscape characteristics, diversify across the solution landscape, and request aid in climbing particularly difficult peaks.