1. A method for balancing a rotating system, comprising: (a) recording vibration data from one or more vibration sensors during operation of a rotating system; (b) generating a plurality of balance solutions based, at least in part, on the recorded vibration data using a plurality of computer-based optimization methods, each of the plurality of computer-based optimization methods generating a respective one of the plurality of balance solutions, and each balance solution being configured to minimize peak vibrations in the one or more vibration sensors during operation of the rotating system; (c) determining an optimal balance solution from the plurality of balance solutions; and (d) attaching to or removing from the rotating system one or more balancing masses each having a respective weight and a respective angular position in accordance with said optimal balance solution.