2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
MB9 - Frontiers of optimization under uncertainty
May 16, 2022 03:30 PM – 05:10 PM
Location: Groupe Cholette (yellow)
Chaired by Jonathan Li
03:30 PM - 03:55 PM
On novel primal and dual bounding techniques for multistage adaptive robust optimization
In this work, we adapt the recent decision rules introduced in the stochastic programming literature to robust optimization both from the primal and the dual perspective. The resulting problems are challenging and require advanced techniques in their solution. Our methodology is illustrated with preliminary results on production planning and transportation problems.
03:55 PM - 04:20 PM
Risk-averse Regret Minimization in Multi-stage Stochastic Programs
Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multi-stage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the hindsight decisions benefit from getting access to the realizations of a certain number of stages ahead. We provide theoretical and numerical insights about this paradigm under popular risk measures and shed light on the effect of the length of the period used by the decision-maker when evaluating regret.
04:20 PM - 04:45 PM
Distributionally robust optimization under distorted expectations
In this talk, I will present a new distributionally robust optimization (DRO) scheme whose objective can be viewed as the "dual" of the utility function commonly applied in the classical DRO for capturing decision makers' risk attitudes. I will highlight many benefits of the new scheme, in terms of the computational tractability of the problem, the ease of specifying a distortion functional, and a more realistic behaviour of the worst-case distributions. I will provide also theoretical justification of why our new scheme can provide a solution that is less conservative than the solutions from classical DRO. Our scheme has a unique property that the solution is always sensitive to the change of risk-aversion, whereas the classical DRO can lack this property. An application of two-stage production and planned problem will be presented, together with our finding of how a decision maker who overly weights very good and very bad outcomes, as depicted by the Cumulative Prospect Theory (CPT), will act when facing distributional ambiguity.
04:45 PM - 05:10 PM
Min-Max-Min robust combinatorial optimization with actual first-stage decision variables
This research provides a new algorithm for solving min-max-min robust combinatorial optimization problems. The main idea of this approach is that the decision-maker prepares K solutions in advance before the realization of uncertain parameters. Then, upon full knowledge of uncertain parameters, decision-makers can choose the best of the K solutions that had been prepared.
Apart from generating better solutions in general compared to the classical robust formulation, the k-adaptability has the advantage that the solutions are more easily accepted by a human user if they do not change each time but are taken from a relatively small set of candidate solutions. Even though the practical application of min-max-min robust combinatorial optimization is studied in several research (Eufinger et al, 2020; Subramanyam et al, 2020; Hanasusanto et al, 2015), solution methods have stayed behind since the problem is hard to solve.
The proposed algorithm has advantages over existing methods. First, this method can be applied to problems with actual first-stage decision variables. Second, the uncertain data can be in both objective function or constraints. The results show that the proposed algorithm can solve large combinatorial problems in a reasonable time.