Event Details

Data-driven robust optimization with cluster-based anomaly detection

Robust optimization is a decision-making paradigm in mathematical programming where models are built such that they remain feasible over a set of uncertainty realizations called the uncertainty set. Traditionally, the uncertainty set is constructed with minimal information from available data, usually its range and some bounds to prevent the consideration of extreme realizations. The idea is that the uncertainty set should contain realizations that enforce feasibility in planning, without exaggerated costs. In many situations, such as disasters, data is available in terms of events or scenarios. In such cases, constructing the uncertainty set without event-wise considerations is fundamentally flawed because it avoids the correlations that exist between data from the same event.

We propose a data-driven robust optimization approach where scenario data is used to form the geometry of the uncertainty set and cluster Voronois are used to identify and discard anomalous regions. With the recognition that not all anomalous data result in anomalous decisions, we also develop a method to maximizes the size of the non-anomalous regions, such that decisions remain non-anomalous. This allows protection over a larger subset of uncertainty realizations, without extreme impacts on costs. Our anomaly-based models show marked improvements in performances over the classical robust optimization with polyhedral uncertainty on a disaster response model that uses real data from the last 18 years of impacts of floods and landslides in Brazil.

Bio: Dr Aakil Caunhye is Senior Lecturer at The University of Edinburgh Business School. He obtained his PhD from Nanyang Technological University, Singapore. His main research interests are in robust optimization and stochastic programming, with application mainly in humanitarian logistics.