Robust multicriteria risk-averse stochastic programming models

Abstract

In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional value-at-risk (CVaR). First, we introduce a model that optimizes the worst-case multivariate CVaR and show that its optimal solution lies on a particular type of stochastic efficient frontier. To solve this model, we develop a finitely convergent delayed cut generation algorithm for finite probability spaces. We also show that the proposed model can be reformulated as a compact linear program under certain assumptions. In addition, for the cut generation problem, which is in general a mixed-integer program, we give a stronger formulation than the existing ones for the equiprobable case. Next, we observe that similar polyhedral enhancements are also useful for a related class of multivariate CVaR-constrained optimization problems that has attracted attention recently. In our computational study, we use a budget allocation application to benchmark our proposed maximin type risk-averse model against its risk-neutral counterpart and a related multivariate CVaR-constrained model. Finally, we illustrate the effectiveness of the proposed solution methods for both classes of models.