Code and data for strengthened and faster linear approximation to joint chance constraints with Wasserstein ambiguity

Journal article

Many real-world decision-making problems in energy systems, transportation, and finance have uncertain parameters in constraints. Wasserstein distributionally robust joint chance constraints (WDRJCC) offer a promising solution by explicitly guaranteeing the probability of the simultaneous satisfaction of multiple constraints. However, WDRJCC are computationally demanding, and practical applications often require more tractable approaches, especially for large-scale and complex problems such as power system unit commitment problems and multilevel problems with chance constraints in lower levels. To address this, this paper proposes a novel convex inner-approximation for WDRJCC with right-hand-side uncertainties (RHS-WDRJCC). Motivated by the strengthening process that leads to a faster but still exact mixed-integer reformulation, we propose a Strengthened and Faster Linear Approximation (SFLA) by strengthening an existing convex inner-approximation. This strengthening process reduces the number of constraints and tightens the feasible region for ancillary variables, leading to significant computational speedup. We prove that the proposed SFLA does not introduce additional conservativeness and can even be less conservative compared to common approximations such as W-CVaR. We then extend the proposed SFLA to robustness maximization, a decision-making paradigm that can be more interpretable, where the risk level and the Wasserstein radius are determined by maximizing solution robustness subject to a utility degradation limit. We discuss the connection between risk minimization and radius maximization as two formulations of robustness maximization, and show the advantage of radius maximization.

In power system unit commitment, the proposed SFLA achieves up to 10× and on average 3.8× computational speedup compared to the strengthened and exact mixed-integer reformulation in finding comparable high-quality solutions. In a bilevel strategic bidding problem where the exact reformulation is not applicable due to non-convexity, the proposed SFLA can lead to 90× speedup compared to existing convex approximation methods including W-CVaR. In robustness maximization, the proposed SFLA demonstrated over 100× speedup than other convex-approximations.

Authors: Zhou, Y; Xia, Y; Yang, H; Morstyn, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute for Operations Research and Management Sciences
• Journal: INFORMS Journal on Computing
• Publication date: 2026-04-16
• DOI: 10.1287/ijoc.2024.1073.cd
• EISSN: 1526-5528
• ISSN: 1091-9856
• Language: English
• Keywords: faster linear approximation; Wasserstein distributionally robust joint chance constraints; conditional value-at-risk; robustness maximization