Data-Driven Conditional Flexibility Index

2026-01-22

AI Summary

This work proposes a Conditional Flexibility Index (CFI) to address the limitations of traditional flexibility metrics, which often neglect historical data and contextual information—such as forecasts—leading to overly conservative or distorted uncertainty sets. CFI introduces, for the first time, a data-driven and conditionally modeled approach to flexibility quantification: it employs normalizing flows to learn the distribution of historical data, establishing a bijective mapping from a Gaussian latent space to the actual data space. Within this latent space, an admissible set is defined as a hypersphere, which is then conditioned on contextual information to yield an adaptive uncertainty set that tightly covers only the plausible realizations of uncertainty. Validation on the security-constrained unit commitment problem demonstrates that CFI effectively incorporates temporal context, significantly enhancing both the robustness and accuracy of scheduling decisions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

With the increasing flexibilization of processes, determining robust scheduling decisions has become an important goal. Traditionally, the flexibility index has been used to identify safe operating schedules by approximating the admissible uncertainty region using simple admissible uncertainty sets, such as hypercubes. Presently, available contextual information, such as forecasts, has not been considered to define the admissible uncertainty set when determining the flexibility index. We propose the conditional flexibility index (CFI), which extends the traditional flexibility index in two ways: by learning the parametrized admissible uncertainty set from historical data and by using contextual information to make the admissible uncertainty set conditional. This is achieved using a normalizing flow that learns a bijective mapping from a Gaussian base distribution to the data distribution. The admissible latent uncertainty set is constructed as a hypersphere in the latent space and mapped to the data space. By incorporating contextual information, the CFI provides a more informative estimate of flexibility by defining admissible uncertainty sets in regions that are more likely to be relevant under given conditions. Using an illustrative example, we show that no general statement can be made about data-driven admissible uncertainty sets outperforming simple sets, or conditional sets outperforming unconditional ones. However, both data-driven and conditional admissible uncertainty sets ensure that only regions of the uncertain parameter space containing realizations are considered. We apply the CFI to a security-constrained unit commitment example and demonstrate that the CFI can improve scheduling quality by incorporating temporal information.

Problem

• flexibility index
• uncertainty set
• contextual information
• process scheduling
• data-driven

Innovation

• conditional flexibility index
• data-driven uncertainty set
• normalizing flow
• contextual information
• robust scheduling