Multiple Objectives Satisficing Under Uncertainty

Abstract

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 targets' achievement probability (success probability criterion) as a special case and also extend to situations when the probability distribution is 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 an objective fails to achieve its target. Naturally, this class excludes success probability and we propose the shortfall-aware MOS criterion (S-MOS), which is diversification favoring and is a lower bound to success probability. We also show how to build tractable approximations of the S-MOS criterion. As 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.

A distributionally robust perspective on uncertainty quantification and chance constrained programming

“…Until recently, such problems were suspected to be generically intractable, and the majority of the literature focused on conservative approximations via Bonferroni's inequality [36], distributionally robust conditional value-at-risk constraints [12,51] and component-wise quasi-concave functions [33]. In the following, we present an exact tractable reformulation of problem (2) for a specific class of ambiguity sets, and we argue that this tractability result is unlikely to extend to more general settings.…”

Routing Optimization Under Uncertainty

“…Lam et al (2013) introduce a shortfall-aware criterion that is inspired by the joint probability of a set of attributes in meeting their targets. While the criterion has similar features with the Collective RV Index, it lacks the property of convexity, which enables us to build tractable models for the routing optimization problems.…”

A Simple Framework for Climate-Change Policy Under Model Uncertainty

“…The goal that decision-makers want to meet (or, alternative, the constraint they want to satisfy) is that of ensuring that consumption losses do not exceed a threshold L. Translated to an environment with multiple probability distributions, this requirement is recast as a lower bound on the proportion of such "virtuous" probability distributions. As such, it is similar to satisficing measures that focus on so-called success probabilities [7,4,17]. In addition, this criterion can be viewed as an approximate special case of the one proposed and axiomatized by Ahn [1].…”

“…Over the years they have been shown to hold significant descriptive power [6] as well as normative appeal [7,4,17]. The specific decision-making criterion we propose can be viewed as an analogue of the well-known success-probability criterion [7,4] adapted to settings characterized by model uncertainty.…”