Multiple Objectives Satisficing Under Uncertainty

We propose a class of functions, called multiple objective satisficing (MOS) criteria, for evaluating the level of compliance of a set of objectives in meeting their targets collectively under uncertainty. The MOS criteria include the joint targets' achievement probability (joint success probability criterion) as a special case and also extend to situations when the probability distributions are not fully characterized. We focus on a class of MOS criteria that favors diversification, which has the potential to mitigate severe shortfalls in scenarios when any objective fails to achieve its target. Naturally, this class excludes joint success probability. We further propose the shortfall-aware MOS criterion (S-MOS), which is inspired by the probability measure and is diversification favoring. We also show how to build tractable approximations of the S-MOS criterion. Because the S-MOS criterion maximization is not a convex optimization problem, we propose improvement algorithms via solving sequences of convex optimization problems. We report encouraging computational results on a blending problem in meeting specification targets even in the absence of full probability distribution description.