Robust Optimization using a new Volume-Based Clustering approach

We propose a new data-driven technique for constructing uncertainty sets for robust optimization problems. The technique captures the underlying structure of sparse data through volume-based clustering, resulting in less conservative solutions than most commonly used robust optimization approaches. This can aid management in making informed decisions under uncertainty, allowing a better understanding of the potential outcomes and risks associated with possible decisions. The paper demonstrates how clustering can be performed using any desired geometry and provides a mathematical optimization formulation for generating clusters and constructing the uncertainty set. In order to find an efficient solution to the problem, we explore different approaches since the method may be computationally expensive. This contribution to the field provides a novel data-driven approach to uncertainty set construction for robust optimization that can be applied to real-world scenarios