During sampling intervals, pairs of swap scores are assigned to respective pairs of storage devices of a storage system, each swap score pair indicating an amount of system performance improvement for a swap of logical volumes between source and target storage devices of the pair of storage devices. The swap scores are summed over all the intervals. A subset of the storage devices are then selected for a full optimization process based on the summed swap scores, where the full optimization process exhaustively looks for some number of best swaps among the storage devices to improve system performance. By choosing the size of the subset of storage devices, the processing burden required to perform the analysis will be in line with the processing capacity of the processing platform on which the analysis is performed, while achieving system performance improvement commensurate with a worst-case process in which every storage device in the system is analyzed for candidate swaps.