1,013 research outputs found
Uncertainty Analysis for Data-Driven Chance-Constrained Optimization
In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.BMWi, 0350013A, ChemEFlex - Umsetzbarkeitsanalyse zur Lastflexibilisierung elektrochemischer Verfahren in der Industrie; Teilvorhaben: Modellierung der Chlor-Alkali-Elektrolyse sowie anderer Prozesse und deren Bewertung hinsichtlich Wirtschaftlichkeit und möglicher HemmnisseDFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
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Distributionally Robust Optimization: A Review
The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization
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