A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold , over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to approximate the joint chance ...

With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the mode...

For discrete-time linear systems subject to parametric uncertainty described by random variables, we develop a samplingbased Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline sampling approach in the design phase instead of online scenario generation. The paper highlights the structural difference between online and o...

When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated partial information, unknown parameters, or complex relationships between these and the problem decision variables. In this work, we develop a novel Chance Constraint Learning (CCL) methodology focus on mixed-integer linear problems which combines ideas from chance constraint l...

Development of every society is incumbent upon energy sector’s technological and economic effectiveness. The electricity industry is a growing and needs to have a better performance to effectively cover the demand. The industry requires a balance between cost and efficiency through careful design and planning. In this paper, a two-stage stochastic programming model is presented for the design o...

We study stochastic variants of flow-based global constraints as combinatorial chance constraints. As a specific case study, we focus on the stochastic weighted alldifferent constraint. We first show that determining the consistency of this constraint is NP-hard. We then show how the combinatorial structure of the alldifferent constraint can be used to define chance-based filtering, and to comp...

Group decision-making (GDM) in an ambiguous environment has consistently become a research focus the decision science field during past decade. Existing minimum cost consensus models either control total budget deterministic context or on improving utility of makers. In this study, novel model with distributionally robust chance constraint (DRO-MCCM) is explored. First, two constraints are deve...

Practical use of the contamination technique in stress testing for risk measures Value at Risk (VaR) and Conditional Value at Risk (CVaR) and for optimization problems with these risk criteria is discussed. Whereas for CVaR its application is straightforward, the presence of the simple chance constraint in the definition of VaR requires that various distributional and structural properties are ...