Data-driven robust optimization based on position-regulated support vector clustering

The changes experienced in integrating machine learning and data science into mathematical programming over the past decade remain unprecedented. They have created a novel optimization component under deep uncertainty known as "Data-Driven Robust Optimization" (DDRO). It considers a dataset's complexity, hidden information, and inherent form when creating data-driven uncertainty sets. One of the more practical machine learning algorithms for creating data-driven uncertainty sets is support vector clustering (SVC). There are no prerequisites for preliminary information to generate uncertainty sets with arbitrary geometry. Moreover, it can regularize the conservatism level and adjust a balance between the magnitude of the uncertainty set and information loss by a control parameter. Despite being superior and effective, SVC needs help selecting the best value for the trade-off parameter. This parameter impacts the robustness of the solution and the ability of SVC to handle information loss; hence, it must be accurately determined. Irrational data elimination as outliers alters the degree of conservatism, resulting in information loss and suboptimal solutions. This paper seeks to remedy this problem by suggesting position-regulated support vector clustering (PRSVC) to involve the importance of each data point in estimating the trade-off parameter. Experiments on artificial and real-world data collections indicate that, in comparison to the current SVC-based model, the proposed approach offers a more accurate decision boundary.