Robust Discrete Optimization and Its Applications

The robust shortest path problem with interval data via Benders decomposition

“…Methodologies for improving the performance of the method have been proposed in McDaniel and Devine (1977) and Magnanti and Wong (1981). Kouvelis and Yu (1997) derived an algorithm for the scenario version of the robust shortest path problem (see Yu and Jang 1998) by adapting Benders decomposition.…”

“…2, has been chosen to drive optimization. This criterion is discussed in Kouvelis and Yu (1997), a book entirely devoted to robust discrete optimization.…”

Robust maximum weighted independent-set problems on interval graphs

“…These imprecisions are mainly due to the lack of full information about the parameters of the problem and/or the dependence of these parameters on some uncontrolled events [10,14]. The outputs of the deterministic models (where the weight of each vertex is fixed to a single value) usually suffer from these imprecisions, which can make their practical implementation almost impossible in some cases [10]. Recently, researchers have started to develop methods to cope with such uncertainty.…”

“…Recently, researchers have started to develop methods to cope with such uncertainty. Two situations can be distinguished: either the decision maker is able to determine the appropriate probability distributions for modeling the uncertain elements and then builds and solves stochastic models [13], or there is no clear characterization of the uncertainty and all possible scenarios affecting the parameters of the problem are considered [1,3,10]. The latter setting is studied in this article.…”

Computational Decision Support Regret-Based Models for Optimization and Preference Elicitation

“…Minimax regret has been adopted as a optimization criterion for problems in which there is data or objective function uncertainty (Kouvelis and Yu, 1997;Averbakh, 2000;Aissi et al, 2009), but only recently has been proposed as a means for accounting for a DSS's uncertainty regarding DM's utility (Boutilier et al, 2001;Salo and Hämäläinen, 2001;Wang and Boutilier, 2003;Boutilier et al, 2004Boutilier et al, , 2006Braziunas and Boutilier, 2007). 2 Minimax regret has several advantages over Bayesian models from a practical perspective.…”