The Blind Men and the Elephant: Integrated Offline/Online Optimization Under Uncertainty

Optimization problems under uncertainty are traditionally solved either via offline or online methods. Offline approaches can obtain high-quality robust solutions, but have a considerable computational cost. Online algorithms can react to unexpected events once they are observed, but often run under strict time constraints, preventing the computation of optimal solutions. Many real world problems, however, have both offline and online elements: a substantial amount of time and information is frequently available (offline) before an online problem is solved (e.g. energy production forecasts, or historical travel times in routing problems); in other cases both offline (i.e. strategic) and online (i.e. operational) decisions need to be made. Surprisingly, the interplay of these offline and online phases has received little attention: like in the blind men and the elephant tale, we risk missing the whole picture, and the benefits that could come from integrated offline/online optimization. In this survey we highlight the potential shortcomings of pure methods when applied to mixed offline/online problems, we review the strategies that have been designed to take advantage of this integration, and we suggest directions for future research.