Strengthened and Faster Linear Approximation to Joint Chance Constraints with Wasserstein Ambiguity (2412.12992v1)

Abstract: Many real-world decision-making problems in energy systems, transportation, and finance have uncertain parameters in their constraints. Wasserstein distributionally robust joint chance constraints (WDRJCC) offer a promising solution by explicitly guaranteeing the probability of the simultaneous satisfaction of multiple constraints. WDRJCC are computationally demanding, and although manageable for small problems, practical applications often demand more tractable approaches -- especially for large-scale and complex problems, such as power system unit commitment problems and multilevel problems with chance-constrained lower levels. To address this, this paper proposes a novel inner-approximation for a specific type of WDRJCC, namely WDRJCC with right-hand-side uncertainties (RHS-WDRJCC). We propose a Strengthened and Faster Linear Approximation (SFLA) by strengthening an existing convex inner-approximation that is equivalent to the worst-case conditional value-at-risk (W-CVaR) method under specific hyperparameters. This strengthening process reduces the number of constraints and tightens the feasible region for ancillary variables, leading to significant computational speedup. Despite the tightening, we prove that the proposed SFLA does not introduce additional conservativeness and can even lead to less conservativeness. The significance and superiority of the proposed SFLA are validated in two important real-world problems. In a power system unit commitment problem, the proposed SFLA achieves up to 10x and on average 3.8x computational speedup compared to the strengthened and exact mixed-integer reformulation in finding comparable high-quality feasible solutions. In a bilevel strategic bidding problem where the exact reformulation is not applicable due to non-convexity, we show that the proposed SFLA can lead to 90x speedup compared to existing convex approximation methods such as W-CVaR.