سميه دانش عسگري

In recent years, integrating machine learning and data science with mathematical optimization under deep uncertainty has led to significant transformations, resulting in a new field called "Data-Driven Robust Optimization" (DDRO). In this branch of optimization, the complexity of data, hidden information, and their inherent structure are considered when constructing data-driven uncertainty sets. One of the practical algorithms for creating these uncertainty sets is Support Vector Clustering (SVC), which, without requiring simplifying assumptions about the range of potential scenarios or predefined shapes of the sets, can generate decision sets with arbitrary geometries. Despite the many advantages of this algorithm in constructing decision boundaries under deep uncertainty, its application comes with challenges, two of which are discussed in this dissertation, along with proposed solutions. The first challenge relates to managing the large volume of decision-making scenarios or the inability to access all scenarios at the start of the problem-solving process. This algorithm's lack of a systematic approach hinders its effective use of large datasets. The "Incremental Support Vector Clustering" approach is proposed to address this issue, which incrementally and efficiently manages many scenarios in constructing the uncertainty sets. This algorithm ensures that the previously learned knowledge is preserved when updating uncertainty sets, preventing information loss. Additionally, when dealing with large datasets, the algorithm forms uncertainty sets much faster than the support vector clustering algorithm while producing similar results. Importantly, there is no significant difference between the optimal solutions obtained from the incremental and non-incremental approaches. The second challenge pertains to selecting the control parameter of this algorithm to balance the size of the uncertainty set and the amount of information loss. To address this challenge, the "position-based support Vector Clustering" approach is proposed, which takes into account the importance of each data point in determining the control parameter. The results of the eva‎luations demonstrate that the proposed approach outperforms the traditional support vector clustering algorithm in terms of performance and efficiency.

بهينه‌سازي استوار داده محور , مجموعه عدم قطعيت داده محور , عدم قطعيت عميق , يادگيري ماشين , خوشه‌بندي بردار پشتيبان افزايشي , خوشه بندي بردار پشتيبان مبتني بر موقعيت

Data-driven robust optimization , Data-driven uncertainty set , Deep uncertainty , Machine learning , Incremental support vector clustering , Position-regulated support vector clustering

Somayeh danesh Asgari

Emran Mohammadi