Distributionally robust chance‐constrained optimization with Sinkhorn ambiguity set

• Published in: AIChE journal Vol. 69; no. 10
• Main Authors: Yang, Shu‐Bo, Li, Zukui
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.10.2023; American Institute of Chemical Engineers
• Subjects: Ambiguity; data‐driven optimization; distributionally robust chance‐constrained optimization; joint chance constraint; Optimization; Regularization; Robustness (mathematics); Sinkhorn ambiguity set; Sinkhorn distance; Uncertainty
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.18177

A novel distributionally robust chance‐constrained optimization (DRCCP) method is proposed in this work based on the Sinkhorn ambiguity set. The Sinkhorn ambiguity set is constructed based on the Sinkhorn distance, which is a variant of the Wasserstein distance with the entropic regularization. The proposed method can hedge against more general families of uncertainty distributions than the Wasserstein ambiguity set‐based methods. The presented approach is formulated as a tractable conic model based on the Conditional value‐at‐risk (CVaR) approximation and the discretized kernel distribution relaxation. This model is compatible with more general constraints that are subject to uncertainty than the Wasserstein‐based methods. Accordingly, the presented Sinkhorn DRCCP is a more practical approach that overcomes the limitations of the traditional Wasserstein DRCCP approaches. A numerical example and a nonlinear chemical process optimization case are studied to demonstrate the efficacy of the Sinkhorn DRCCP and its advantages over the Wasserstein DRCCP.