This research considers a new problem called the block relocation problem with weights (BRP-W) in which a set of identically-sized items of different, known weights are to be retrieved from a set of last-in-first-out (LIFO) stacks in a specific order using the minimum amount of energy. Our efforts to address this real-world problem resulted in the creation of a sophisticated algorithm—the global retrieval heuristic (GRH) — that decides where to relocate the items that must be moved to allow access to items below them. The GRH was embedded inside a genetic algorithm (GA)-based optimization method in a simulation-optimization structure in order to identify the best settings of the GRH for a particular item configuration size. Results from the preliminary experiments described here indicate that the GRH and GA have the potential to be effective tools to solve this very difficult problem.